Showing posts with label mathematical abilities. Show all posts
Showing posts with label mathematical abilities. Show all posts

Friday, 18 March 2016

Super Humans - Avicenna

"Avicenna" is the Latinate form of Ibn Sīnā. For the mountain peak known by this name, see Ibn Sīnā Peak. Avicenna (/ˌævᵻˈsɛnə/; Latinized form of Ibn-Sīnā, Arabic full name Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Al-Hasan ibn Ali ibn Sīnā[4] أبو علي الحسين ابن عبد الله ابن سينا; c. 980 – June 1037) was a Persian polymath who is regarded as one of the most significant thinkers and writers of the Islamic Golden Age. Of the 450 works he is known to have written, around 240 have survived, including 150 on philosophy and 40 on medicine. His most famous works are The Book of Healing. a philosophical and scientific encyclopedia, and The Canon of Medicine – a medical encyclopedia which became a standard medical text at many medieval universities and remained in use as late as 1650. In 1973, Avicenna's Canon Of Medicine was reprinted in New York. Besides philosophy and medicine, Avicenna's corpus includes writings on astronomy, alchemy, geography and geology, psychology, Islamic theology, logic, mathematics, physics and poetry.

Avicenna was born c. 980 in Afšana, a village near Bukhara (in present-day Uzbekistan), the capital of the Samanids, a Persian dynasty in Central Asia and Greater Khorasan. His mother, named Setareh, was from Bukhara; his father, Abdullah, was a respected Ismaili scholar from Balkh, an important town of the Samanid Empire, in what is today Balkh Province, Afghanistan, although this is not universally agreed upon. His father worked in the government of Samanid in the village Kharmasain, a Sunni regional power. After five years, his younger brother, Mahmoud, was born. Avicenna first began to learn the Quran and literature in such a way that when he was ten years old he had essentially learned all of them. A number of theories have been proposed regarding Avicenna's madhab (school of thought within Islamic jurisprudence). Medieval historian Ẓahīr al-dīn al-Bayhaqī (d. 1169) considered Avicenna to be a follower of the Brethren of Purity. On the other hand, Dimitri Gutas along with Aisha Khan and Jules J. Janssens demonstrated that Avicenna was a Sunni Hanafi.  However, the 14th cenutry Shia faqih Nurullah Shushtari according to Seyyed Hossein Nasr, maintained that he was most likely a Twelver Shia. Conversely, Sharaf Khorasani, citing a rejection of an invitation of the Sunni Governor Sultan Mahmoud Ghazanavi by Avicenna to his court, believes that Avicenna was an Ismaili. Similar disagreements exist on the background of Avicenna's family, whereas some writers considered them Sunni, some more recent writers contested that they were Shia. According to his autobiography, Avicenna had memorised the entire Quran by the age of 10. He learned Indian arithmetic from an Indian greengrocer, Mahmoud Massahi and he began to learn more from a wandering scholar who gained a livelihood by curing the sick and teaching the young. He also studied Fiqh (Islamic jurisprudence) under the Sunni Hanafi scholar Ismail al-Zahid. Avicenna taught some extent of philosophy books such as Introduction (Isagoge)'s Porphyry (philosopher), Euclid's Elements, Ptolemy's Almagest by an unpopular philosopher, Abu Abdullah Nateli, who claimed philosophizing. As a teenager, he was greatly troubled by the Metaphysics of Aristotle, which he could not understand until he read al-Farabi's commentary on the work. For the next year and a half, he studied philosophy, in which he encountered greater obstacles. In such moments of baffled inquiry, he would leave his books, perform the requisite ablutions, then go to the mosque, and continue in prayer till light broke on his difficulties. Deep into the night, he would continue his studies, and even in his dreams problems would pursue him and work out their solution. Forty times, it is said, he read through the Metaphysics of Aristotle, till the words were imprinted on his memory; but their meaning was hopelessly obscure, until one day they found illumination, from the little commentary by Farabi, which he bought at a bookstall for the small sum of three dirhams. So great was his joy at the discovery, made with the help of a work from which he had expected only mystery, that he hastened to return thanks to God, and bestowed alms upon the poor. He turned to medicine at 16, and not only learned medical theory, but also by gratuitous attendance of the sick had, according to his own account, discovered new methods of treatment. The teenager achieved full status as a qualified physician at age 18, and found that "Medicine is no hard and thorny science, like mathematics and metaphysics, so I soon made great progress; I became an excellent doctor and began to treat patients, using approved remedies." The youthful physician's fame spread quickly, and he treated many patients without asking for payment. He was a truly Renaissance man and polymath, the Leonardo da Vinci equivalent in the Arabic world.

Sunday, 13 March 2016

Super Humans - Mahmoud Wael

Mahmoud Wael (born 1999), an Egyptian boy, At 14 years old he became one of the youngest people qualified to teach university-level graduates in the programming language C++ after completing the Cisco Certified Network Associate, Cisco Certified Network Professional and Cisco Certified Internetwork Expert certificates in the American University in Cairo. He was sponsored by Microsoft to complete a series of certificates in computer programming. At the age of 4 Mahmoud could multiply 3 digit by 3 digit numbers in few seconds, he scored 155 on the IQ test he took at 6 years old. Multiple universities in Egypt and abroad have contacted him for scholarship offers since he was 7.

I found here an interview with him, age 14, one of the few in English, although you can find more in Arabic.

Friday, 19 February 2016

Super Humans - Gabriel See

   Gabriel See, born in 1998, achieved a 720 out of 800 score on the SAT math test at age 8, Performed T-cell receptor research at the Fred Hutchinson Cancer Research Center at age 10, and at age 11 won a silver medal at the international Genetically Engineered Machine (iGEM) competition on synthetic biology for undergraduate college students at the Massachusetts Institute of Technology. In 2011 he was named one of the US's top 10 high school inventors by Popular Science magazine. He has been taking upper division courses each semester at the University of Washington since 2010.

   I find very interesting the way his parents are trying to support him (as is described in an article from 2011, in Seattle Times):

   "His parents, Jason and Valerie, want him to have a normal teenage upbringing, so for half the day Gabriel attends a small, arts-oriented junior-high school in the Lake Washington School District called Renaissance School of Art and Reasoning, where he takes dance, drama and language arts.  He started taking upper-level math classes at the UW in 2009, and in 2010 began taking graduate math classes; this quarter, he’s taking applied linear algebra. He’s on the YMCA Sammamish Swim Team, takes music classes and plays Ultimate Frisbee on Fridays. Quiet and reserved, Gabriel is most comfortable discussing advanced mathematics or molecular biology. He’s not good with questions about typical teenage pursuits, but he will explain to you the concepts he is studying in applied linear algebra this fall, if you are smart enough to understand him. When he’s not in class, he’s working through a stack of books at home; he keeps a list of everything he has read. He’s absorbed 52 textbooks on science and math: read the physics lectures of Richard Feynman, and books on robot programming, systems biology, immunobiology, fractals, Latin (a new passion), music theory and the work of Fibonacci, René Descartes, Albert Einstein and Stephen Hawking, among others. He’s studied chaos theory, string theory, quantum mechanics and nuclear science. Along the way, he’s also devoured popular fiction and classic literature — Harry Potter, The Chronicles of Narnia and most of the works of William Shakespeare (“Not all of them,” he notes, modestly). He has a younger brother, Michael, 10, and the two boys are especially close, his mother said.

   Gabriel has a laser focus on math and science, but the UW’s Robinson Center program for early-entrance students — those younger than 15 — is not a good fit because he has already skipped over so much undergraduate work, his dad says. “Keeping him engaged is critical, and so far, reasonably successful,” said William Monahan, Gabriel’s Advanced Placement (AP) biology teacher at Eastlake High. In elementary school, Gabriel was placed in the district’s program for highly capable students, but it wasn’t until third grade that the adults around him started to realize the depths of his intellectual abilities. At age 8, he began teaching himself calculus and physics from sources he found on the Internet. Curious to know how much he was learning, his parents signed him up for the SAT; he scored a 720 out of 800 on the math portion, placing him in the 95th percentile for college-bound high-school students. That score plus Gabriel’s math notations — he had written out pages and pages of solutions to math and physics problems — sent the Sees to Elizabeth Sirjani, who was then the math chair at Eastlake. She confirmed that Gabriel had taught himself AP-level math and physics work on his own. “We started scrambling then,” said Phelan, of the Lake Washington district’s accelerated program. Gabriel began taking math and science at Eastlake, while remaining in elementary school for music, gym class, recess and library. When he was 9, he joined Monahan’s biology class, a college-level course usually taken by high-school juniors and seniors. Too small to see what was going on while sitting in a regular chair, Gabriel often ended up perched on a table, his short legs swinging in space, Monahan said. By November, he had finished reading the AP biology textbook on his own. He grasped the science quicker than students twice his age, and when it was time to do a biology lab, “he would get in there and tell the seniors, ‘Let me get it done,’ ” Monahan said. “It’s been, almost at every turn in the road, a unique experience,” he added. “It’s like a beautiful mind — we’re talking about something that’s pretty unique here.” His teachers say Gabriel is capable of digesting and storing information in great gulps, and then making connections with other things he had already learned. “Everything I threw at him, he just got,” said Melissa Nivala, who was a graduate student in the applied math department at the UW in 2007 when she began tutoring Gabriel in graduate-level math. “And he loved it. We would work until I was mentally exhausted. I would tell him, ‘OK, we need to stop, because I’m tired of thinking.’ “ Nivala would give Gabriel a textbook on a subject — say, chaos theory — and Gabriel would read the book in a few days. He could then answer specific questions and open-ended questions on the subject. He even remembered the exact page number in the book where certain formulas first appeared, Nivala said, hinting at a eidetic memory. For any parent whose child has unusual intellectual gifts, finding the right program is a challenge; for Gabriel’s parents, it’s been that process on steroids. In 2008, Jason See found a way for Gabriel to do research at Fred Hutchinson Cancer Research Center. And in 2009, he persuaded professors in the UW’s Department of Bioengineering to let Gabriel join a team that was assembling an entry for MIT’s International Genetically Engineered Machine (iGEM) competition for undergraduates. Jason See keeps a thick folder, filled with letters of recommendation from professors, test scores and transcripts, to help reinforce the somewhat hard-to-fathom story of his son’s accomplishments. “Gabriel’s dad is a pretty good advocate for him,” Phelan said. The iGEM competition has been Gabriel’s most public success, and it’s what caught the eye of Popular Science’s editors. “We originally had some other undergraduates interested in the project,” said postdoctoral student Sean Sleight. “He (Gabriel) pretty much intimidated them, because he was so brilliant. We kind of joke that he did more in one summer than a team of undergraduates.” With occasional help from bioengineering professor Herbert Sauro, Gabriel built a prototype model of a robot that could disperse small amounts of fluid into a plate of 96 wells. The greatest challenge was getting the robot to make tiny, precise movements in space — requiring Gabriel to puzzle out math formulas, and then write original computer programming that would allow the robot to move in three dimensions. Gabriel is quick to point out that he wasn’t successful right away: “The first one failed mostly because it was unstable.” The project required him to do three-dimensional trigonometry, which “is not elementary stuff — you do that in university,” Sauro said. “And he worked it out himself.” The project won a silver medal. “There was quite a bit of buzz that year at iGEM,” Sleight said. “Here’s this 11-year-old that turns everything on its head.” Gabriel’s machine could be built for about $750, much less than the $10,000 price tag for such machines, which would make it more affordable to startup companies and small universities. Because the interface is not user-friendly, though, it’s not a product that could be built for the mass market, Sauro said. Still, it hints at Gabriel’s potential — an intellect so powerful already that he can see unique solutions, or possibly find ways around problems that stump other researchers. “Maybe nobody will ever stamp his diploma, but he will be doing research that far exceeds what most people can comprehend,” Monahan said. "He’ll probably find a cure for cancer,” Sleight said. “Or something bigger.”


Sunday, 7 February 2016

Super Humans - Mohammad Abdus Salam

   Mohammad Abdus Salam (Punjabi, Urdu: محمد عبد السلام‎; pronounced [əbd̪ʊs səlɑm]; 29 January 1926 – 21 November 1996), was a Pakistani theoretical physicist. Salam, a major figure in 20th century theoretical physics, shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for his contribution to the landmark electroweak unification. He was the first (and until Malala Yousufzai the only) Pakistani to receive a Nobel Prize, the first Muslim to win a Nobel prize in science and the second Muslim Nobel Laureate (after Anwar Sadat of Egypt).

   Salam was a top level science advisor to the Government of Pakistan from 1960 to 1974, a position from which he played a major and influential role in the development of the country's science infrastructure. Salam was responsible not only for contributing to major developments in theoretical and particle physics, but also for promoting the broadening and deepening of high calibre scientific research in his country. He was the founding director of the Space and Upper Atmosphere Research Commission (SUPARCO), and responsible for the establishment of the Theoretical Physics Group (TPG) in the Pakistan Atomic Energy Commission (PAEC). As Science Advisor, Salam played an integral role in Pakistan's development of the peaceful use of nuclear energy, and may have contributed as well to development of atomic bomb project of Pakistan in 1972; for this, he is viewed as the "scientific father" of this programme. In 1974, Abdus Salam departed from his country, in protest, after the Pakistan Parliament passed a controversial parliamentary bill declaring the Ahmadiyya Community as not-Islamic. In 1998, following the country's nuclear tests, the Government of Pakistan issued a commemorative stamp, as a part of "Scientists of Pakistan", to honour the services of Salam. Salam's major and notable achievements include the Pati–Salam model, magnetic photon, vector meson, Grand Unified Theory, work on supersymmetry and, most importantly, electroweak theory, for which he was awarded the most prestigious award in physics – the Nobel Prize. Salam made a major contribution in quantum field theory and in the advancement of Mathematics at Imperial College London. With his student, Riazuddin, Salam made important contributions to the modern theory on neutrinos, neutron stars and black holes, as well as the work on modernising the quantum mechanics and quantum field theory. As a teacher and science promoter, Salam is remembered as a founder and scientific father of mathematical and theoretical physics in Pakistan during his term as the chief scientific advisor to the president. Salam heavily contributed to the rise of Pakistani physics to the physics community in the world. Even until shortly before his death, Salam continued to contribute to physics and tirelessly to advocate for the development of science in Third-World countries.

   Abdus Salam was born to Chaudhry Muhammad Hussain and Hajira Hussain, into an Ahmadi Muslim Punjabi family. Chaudhry Muhammad Hussain was Jat and Hajirah a Kakkezai. His own grandfather, Gul Muhammad, was a religious scholar apart from being a physician. Salam's father was an education officer in the Department of Education of Punjab State in a poor farming district. Salam  established very earlya reputation throughout the Punjab and later at the University of Cambridge for outstanding brilliance and academic achievement. At age 14, Salam scored the highest marks ever recorded for the matriculation (entrance) examination at the Punjab University. He won a full scholarship to the Government College University of Lahore, Punjab State. Salam was a versatile scholar, interested in Urdu and English literature in which he excelled. But he soon picked up Mathematics as his subject of concentration. Salam's mentor and tutors wanted him to become an English teacher, but Salam decided to stick with Mathematics As a fourth-year student there, he published his work on Srinivasa Ramanujan's problems in mathematics, and took his B.A. in Mathematics in 1944. His father wanted him to join Indian Civil Service. In those days, the Indian Civil Service was the highest aspiration for young university graduates and civil servants occupied a respected place in the civil society. Respecting his father's wish, Salam tried for the Indian Railways but did not qualify for the service as he failed the medical optical tests because he had worn spectacles since an early age. The results further concluded that Salam failed a mechanical test required by the railway engineers to gain a commission in Indian Railways, and moreover that Salam was too young to compete for the job. Therefore, Indian Railways rejected Abdus Salam's job application. While in Lahore, Abdus Salam went on to attend the graduate school of Government College University. He received his MA in Mathematics from the Government College University in 1946. That same year, he was awarded a scholarship to St John's College, Cambridge, where he completed a BA degree with Double First-Class Honours in Mathematics and Physics in 1949. In 1950, he received the Smith's Prize from Cambridge University for the most outstanding pre-doctoral contribution to Physics. After finishing his degrees, Fred Hoyle advised Salam to spend another year in the Cavendish Laboratory to do research in experimental physics, but Salam had no patience for carrying out long experiments in the laboratory. Salam returned to Jhang, Punjab (now part of Pakistan) and renewed his scholarship and returned to the United Kingdom to do his doctorate. He obtained a PhD degree in Theoretical Physics from the Cavendish Laboratory at Cambridge. His doctoral thesis contained comprehensive and fundamental work in quantum electrodynamics. By the time it was published in 1951, it had already gained him an international reputation and the Adams Prize. During his doctoral studies, his mentors challenged him to solve within one year an intractable problem which had defied such great minds as Dirac and Feynman. Within six months, Salam had found a solution for the renormalisation of meson theory. As he proposed the solution at the Cavendish Laboratory, Salam had attracted the attention of Bethe, Oppenheimer and Dirac.

Thursday, 4 February 2016

Super Humans - Enrico Fermi

   Enrico Fermi (Italian: [enˈriko ˈfermi]; 29 September 1901 – 28 November 1954) was an Italian physicist, who created the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age", and the "architect of the atomic bomb". He was one of the few physicists to excel both theoretically and experimentally. Fermi held several patents related to the use of nuclear power, and was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and the discovery of transuranic elements. He made significant contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics. Fermi's first major contribution was to statistical mechanics. After Wolfgang Pauli announced his exclusion principle in 1925, Fermi followed with a paper in which he applied the principle to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are called "fermions". Later Pauli postulated the existence of an uncharged invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. Fermi took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino". His theory, later referred to as Fermi's interaction and still later as weak interaction, described one of the four fundamental forces of nature. Through experiments inducing radioactivity with recently discovered neutrons, Fermi discovered that slow neutrons were more easily captured than fast ones, and developed the Fermi age equation to describe this. After bombarding thorium and uranium with slow neutrons, he concluded that he had created new elements; although he was awarded the Nobel Prize for this discovery, the new elements were subsequently revealed to be fission products. Fermi left Italy in 1938 to escape new Italian Racial Laws that affected his Jewish wife Laura Capon. He emigrated to the United States where he worked on the Manhattan Project during World War II. Fermi led the team that designed and built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first artificial self-sustaining nuclear chain reaction. He was on hand when the X-10 Graphite Reactor at Oak Ridge, Tennessee, went critical in 1943, and when the B Reactor at the Hanford Site did so the next year. At Los Alamos he headed F Division, part of which worked on Edward Teller's thermonuclear "Super" bomb. He was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield. After the war, Fermi served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters and policy. Following the detonation of the first Soviet fission bomb in August 1949, he strongly opposed the development of a hydrogen bomb on both moral and technical grounds. He was among the scientists who testified on Oppenheimer's behalf at the 1954 hearing that resulted in the denial of the latter's security clearance. Fermi did important work in particle physics, especially related to pions and muons, and he speculated that cosmic rays arose through material being accelerated by magnetic fields in interstellar space. Many awards, concepts, and institutions are named after Fermi, including the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory, the Fermi Gamma-ray Space Telescope, the Enrico Fermi Nuclear Generating Station, and the synthetic element fermium (one of just over a dozen elements named after people). 
   Enrico Fermi was born in Rome on 29 September 1901. He was the third child of Alberto Fermi, a division head (Capo Divisione) in the Ministry of Railways, and Ida de Gattis, an elementary school teacher. His only sister, Maria, was two years older than him, and his brother Giulio was a year older. After the two boys were sent to a rural community to be wet nursed, Enrico rejoined his family in Rome when he was two and a half. Although he was baptised a Roman Catholic in accordance with his grandparents' wishes, his family, like most Italian families, was not particularly religious; Enrico was an agnostic throughout his adult life. As a young boy he shared the same interests as his brother Giulio, building electric motors and playing with electrical and mechanical toys. Giulio died during the administration of an anesthetic for an operation on a throat abscess in 1915. One of Fermi's first sources for his study of physics was a book he found at the local market at Campo de' Fiori in Rome. Published in 1840, the 900-page Elementorum physicae mathematicae, was written in Latin by Jesuit Father Andrea Caraffa, a professor at the Collegio Romano. It covered mathematics, classical mechanics, astronomy, optics, and acoustics, insofar as these disciplines were understood when the book was written. Fermi befriended another scientifically inclined student, Enrico Persico, and together the two worked on scientific projects such as building gyroscopes and trying to accurately measure the acceleration of Earth's gravity. Fermi's interest in physics was further encouraged by his father's colleague Adolfo Amidei, who gave him several books on physics and mathematics, which he read and assimilated quickly. Fermi graduated from high school in July 1918 and, at Amidei's urging, applied to the Scuola Normale Superiore in Pisa. Having lost one son, his parents were reluctant to let him move away from home for four years while attending the Sapienza University of Rome, but in the end they acquiesced. The school provided free lodging for students, but candidates had to take a difficult entrance exam that included an essay. The given theme was "Specific characteristics of Sounds". The 17-year-old Fermi chose to derive and solve the partial differential equation for a vibrating rod, applying Fourier analysis in the solution. The examiner, Professor Giuseppe Pittarelli from the Sapienza University of Rome, interviewed Fermi and praised that he would become an outstanding physicist in the future. Fermi achieved first place in the classification of the entrance exam. During his years at the Scuola Normale Superiore, Fermi teamed up with a fellow student named Franco Rasetti with whom he would indulge in light-hearted pranks and who would later become Fermi's close friend and collaborator. In Pisa, Fermi was advised by the director of the physics laboratory, Luigi Puccianti, who acknowledged that there was little that he could teach Fermi, and frequently asked Fermi to teach him something instead. Fermi's knowledge of quantum physics reached such a high level that Puccianti asked him to organize seminars on the topic. During this time Fermi learned tensor calculus, a mathematical technique invented by Gregorio Ricci and Tullio Levi-Civita that was needed to demonstrate the principles of general relativity. Fermi initially chose mathematics as his major, but soon switched to physics. He remained largely self-taught, studying general relativity, quantum mechanics, and atomic physics. In September 1920, Fermi was admitted to the Physics department. Since there were only three students in the department—Fermi, Rasetti, and Nello Carrara—Puccianti let them freely use the laboratory for whatever purposes they chose. Fermi decided that they should research X-ray crystallography, and the three worked to produce a Laue photograph—an X-ray photograph of a crystal. During 1921, his third year at the university, Fermi published his first scientific works in the Italian journal Nuovo Cimento. The first was entitled "On the dynamics of a rigid system of electrical charges in translational motion" (Sulla dinamica di un sistema rigido di cariche elettriche in moto traslatorio). A sign of things to come was that the mass was expressed as a tensor—a mathematical construct commonly used to describe something moving and changing in three-dimensional space. In classical mechanics, mass is a scalar quantity, but in relativity it changes with velocity. The second paper was "On the electrostatics of a uniform gravitational field of electromagnetic charges and on the weight of electromagnetic charges" (Sull'elettrostatica di un campo gravitazionale uniforme e sul peso delle masse elettromagnetiche). Using general relativity, Fermi showed that a charge has a weight equal to U/c2, where U was the electrostatic energy of the system, and c is the speed of light. The first paper seemed to point out a contradiction between the electrodynamic theory and the relativistic one concerning the calculation of the electromagnetic masses, as the former predicted a value of 4/3 U/c2. Fermi addressed this the next year in a paper "Concerning a contradiction between electrodynamic and the relativistic theory of electromagnetic mass" in which he showed that the apparent contradiction was a consequence of relativity. This paper was sufficiently well-regarded that it was translated into German and published in the German scientific journal Physikalische Zeitschrift in 1922. That year, Fermi submitted his article "On the phenomena occurring near a world line" (Sopra i fenomeni che avvengono in vicinanza di una linea oraria) to the Italian journal I Rendiconti dell'Accademia dei Lincei. In this article he examined the Principle of Equivalence, and introduced the so-called "Fermi coordinates". He proved that on a world line close to the time line, space behaves as if it were a Euclidean space. 
A light cone is a three-dimensional surface of all possible light rays arriving at and departing from a point in spacetime. Here, it is depicted with one spatial dimension suppressed. The time line is the vertical axis. Fermi submitted his thesis, "A theorem on probability and some of its applications" (Un teorema di calcolo delle probabilità ed alcune sue applicazioni), to the Scuola Normale Superiore in July 1922, and received his laurea at the unusually young age of 21. The thesis was on X-ray diffraction images. Theoretical physics was not yet considered a discipline in Italy, and the only thesis that would have been accepted was one on experimental physics. For this reason, Italian physicists were slow in embracing the new ideas like relativity coming from Germany. Since Fermi was quite at home in the lab doing experimental work, this did not pose insurmountable problems for him. While writing the appendix for the Italian edition of the book Fundamentals of Einstein Relativity by August Kopff in 1923, Fermi was the first to point out that hidden inside the famous Einstein equation (E = mc2) was an enormous amount of nuclear potential energy to be exploited. "It does not seem possible, at least in the near future", he wrote, "to find a way to release these dreadful amounts of energy—which is all to the good because the first effect of an explosion of such a dreadful amount of energy would be to smash into smithereens the physicist who had the misfortune to find a way to do it." In 1924 Fermi was initiated to the Freemasonry in the Masonic Lodge "Adriano Lemmi" of the Grand Orient of Italy. Fermi decided to travel abroad, and spent a semester studying under Max Born at the University of Göttingen, where he met Werner Heisenberg and Pascual Jordan. Fermi then studied in Leiden with Paul Ehrenfest from September to December 1924 on a fellowship from the Rockefeller Foundation obtained through the intercession of the mathematician Vito Volterra. Here Fermi met Hendrik Lorentz and Albert Einstein, and became good friends with Samuel Goudsmit and Jan Tinbergen. From January 1925 to late 1926, Fermi taught mathematical physics and theoretical mechanics at the University of Florence, where he teamed up with Rasetti to conduct a series of experiments on the effects of magnetic fields on mercury vapour. He also participated in seminars at the Sapienza University of Rome, giving lectures on quantum mechanics and solid state physics. While giving lectures of new quantum mechanics based on remarkable accuracy of predictions of Schrödinger equation, the Italian physicist would often say, "It has no business to fit so well!". After Wolfgang Pauli announced his exclusion principle in 1925, Fermi responded with a paper "On the quantisation of the perfect monoatomic gas" (Sulla quantizzazione del gas perfetto monoatomico), in which he applied the exclusion principle to an ideal gas. The paper was especially notable for Fermi's statistical formulation, which describes the distribution of particles in systems of many identical particles that obey the exclusion principle. This was independently developed soon after by the British physicist Paul Dirac, who also showed how it was related to the Bose–Einstein statistics. Accordingly, it is now known as Fermi–Dirac statistics. Following Dirac, particles that obey the exclusion principle are today called "fermions", while those that do not are called "bosons".

Wednesday, 27 January 2016

Super Humans - Gerald David "Jerry" Newport

   Gerald David "Jerry" Newport (born August 19, 1948) is an author and public speaker with Asperger syndrome whose life was the basis for the 2005 feature-length movie Mozart and the Whale. He is known for his frank advice and humor when giving presentations. A graduate of the University of Michigan with a B.A. in mathematics, he is also a savant with the ability to perform difficult mathematical calculations in his head. He has two elder brothers, John (born c. 1941) and James (Jim) (born c. 1945). In June 2010, Jerry Newport competed in the Mental Calculation World Cup in Magdeburg, Germany. He won four of ten events, a second and a third and the World Cup Trophy for "Most Versatile Calculator." On his 46th birthday, Jerry married Star Trek actress Mary Louise Meinel (born March 6, 1955), also a savant with Asperger Syndrome. While Jerry has advanced math skills, Mary is an artist and former music teacher. From previous relationships, she has two sons, Stephen and Peter, and two grandchildren. The couple lives in Arizona. They separated in 1997 and divorced in June 1999, though later reconciled and remarried on Valentine's Day 2002. Together, he and Mary released Autism-Aspergers & Sexuality: Puberty and Beyond on July 1, 2002 and Mozart and the Whale: An Asperger's Love Story on New Year's Day 2007.

Tuesday, 26 January 2016

Super Humans - Zerah Colburn

   Zerah Colburn (September 1, 1804 – March 2, 1839) was a child prodigy of the 19th century who gained fame as a mental calculator. Colburn was born in Cabot, Vermont, in 1804. He was thought to be intellectually disabled until the age of seven. However, after six weeks of schooling his father overheard him repeating his multiplication tables. His father wasn't sure whether or not he learned the tables from his older brothers and sisters, but he decided to test him further on his mathematical abilities and discovered that there was something special about his son when Zerah correctly multiplied 13 and 97. Colburn's abilities developed rapidly and he was soon able to solve such problems as the number of seconds in 2,000 years, the product of 12,225 and 1,223, or the square root of 1,449. When he was seven years old he took six seconds to give the numbers of hours in thirty-eight years, two months, and seven days. Zerah is reported to have been able to solve fairly complex problems. For example, the sixth Fermat number is 225+1 (or 232+1). The question is whether this number, 4,294,967,297, is prime or not. Zerah calculated in his head that it was not and has divisor 641. The other divisor is 6,700,417 and can easily be found using a calculator. His father capitalized on his boy's talents by taking Zerah around the country and eventually abroad, demonstrating the boy's exceptional abilities. The two left Vermont in the winter of 1810-11. Passing through Hanover, New Hampshire, John Wheelock, then president of Dartmouth College, offered to take upon himself the whole care and expense of his education, but his father rejected the offer. At Boston, the boy's performances attracted much attention. He was visited by Harvard College professors and eminent people from all professions, and the newspapers ran numerous articles concerning his powers of computation. After leaving Boston, his father exhibited Zerah for money throughout the middle and part of the southern states and, in January 1812, sailed with him for England. In September 1813 Colburn was being exhibited in Dublin. Colburn was pitted against the 8-year-old William Rowan Hamilton in a mental arithmetic contest, with Colburn emerging the clear victor. In reaction to his defeat, Hamilton dedicated less time to studying languages and more time to studying mathematics. After traveling over England, Scotland, and Ireland, they spent 18 months in Paris. Here Zerah was placed in the Lycée Napoléon, but was soon removed by his father, who, at length, in 1816, returned to England in the deepest penury. The Earl of Bristol soon became interested in the boy, and placed him in Westminster School, where he remained until 1819. In consequence of his father's refusal to comply with certain arrangements proposed by the earl, Zerah was removed from Westminster, and his father now proposed to Zerah that he should study to become an actor. Accordingly, he studied for this profession, and was for a few months under the tuition of Charles Kemble. His first appearance, however, satisfied both his instructor and himself that he was not adapted for the stage, and accordingly he accepted a situation as assistant in a school, and soon afterward commenced a school of his own. To this he added the performing of some astronomical calculations for Thomas Young, then secretary of the Board of Longitude. In 1824, on the death of his father, he was enabled by the Earl of Bristol and other friends to return to the United States. Though Zerah's schooling was rather irregular, he showed talent in languages. He went to Fairfield, New York, as assistant teacher of an academy; but not being pleased with his situation, he moved in March following to Burlington, Vermont, where he taught French, pursuing his studies at the same time in the University of Vermont. Toward the end of 1825 he connected himself with the Methodist Church and, after nine years of service as an itinerant preacher, he settled in Norwich, Vermont, in 1835, where he was soon after appointed professor of languages in Norwich University. In 1833 he published his autobiography. From this it appears that his faculty of computation left him about the time he reached adulthood. He died of tuberculosis at the age of 34 and was buried in Northfield’s Old Meeting House Cemetery.

Monday, 25 January 2016

Super Humans - Tristan Pang

   Tristan Pang (born 18 October 2001, East Grinstead, West Sussex, England), is a child prodigy who excelled academically from an early age. According to TVNZ, he is the top mathematician and scientist, a clever problem solver and a great communicator.[2] He started reading independently and doing high school maths at the age of two. He self-learned[11] and sat the Cambridge International Examinations IGCSE maths (Year 11 / O Level) and earned the top grade A* scoring 97% at only nine. By age eleven he top scored with A* at the Cambridge A level exams (Year 13), delivered a TED talk  and became one of the youngest speakers in the world. He started his university studies at the University of Auckland by the age of twelve. In the same year, Tristan created a free online learning platform, Tristan's Learning Hub. By age thirteen, he created his own weekly radio show, Youth Voices with Tristan Pang. He also co-created Change Agents NZ, a Twitter chat group. Tristan is the youngest student at the University of Auckland studying maths and physics. He is also a former head boy at Ficino School. Since he was young, he has been teaching himself in multi-levels on all subjects at home. He has always been fascinated by the relationships between light and energy, and is also interested in quantum physics and time travel, as well as how the human body and mind works. He is planning to be a science researcher in these fields. His role models are, Professor Eamonn O'Brien, Professor Cather Simpson, Professor Roger Penrose and Professor Steven Hawking. His mentor, Andrew Patterson, mentioned on TVNZ that he isn't a typical gifted child who justs operates in the back corner and doesn't talk to anybody, instead, he's willing to share his knowledge and passions at schools, education institutes, on-stage and on-screen. He has been delivering numerous speeches with an aim to inspire and help young people. He has been named as one of the 25 most influential Kiwis. and one of the ten child prodigies who may change the world. He is set to make his mark internationally.

   Tristan Pang hosts a radio show called Youth Voices on PlanetFM 104.6FM. He shares inspirational talks, interviews, stories and quotes from a youth perspective. It was aired every Saturday at 5:20 pm NZT from 7 March until 2 September 2015. Due to his heavy workload, Tristan now airs every first Wednesday of the month at 2:10 pm NZT. Tristan has created websites including Tristan's Learning Hub[25] and Quest-is-fun. Tristan's learning hub consists of educational videos while Quest-is-fun has inspirational material, including his radio shows. One notable video Tristan has recently created was featured on the Khan Academy website. In this video, Tristan talks about the Theory of Everything, also known as the string theory. He has also created a website for the 40th-anniversary conference of the New Zealand Association for Gifted Children. Tristan co-hosts a Twitter chat group with a teacher, Change Agents. This chat is ongoing using the hashtag #changeagentsnz on Twitter, involving educators, students and parents from around the world. Tristan has done numerous speeches and interviews. These include some overseas, some to educators and some to students. Tristan has received rewards from different organisations including one from Shiva Ayyadurai, USA. He has also spoken at different institutes including the Auckland Primary Principals Association, the New Zealand Association for Gifted Children's conference, in the Sharjah Children’s Reading Festival 2015, UAE and at the Festival of Education

Super Humans - Raúl Arturo Chávez Sarmiento

Raúl Arturo Chávez Sarmiento (born 24 October 1997) is a Peruvian child prodigy in mathematics. At the age of 11 years, 271 days, he won a bronze medal at the 2009 International Mathematical Olympiad, making him the second youngest medalist in IMO history, behind Terence Tao who won bronze in 1986 at the age of 10. He won a silver medal at the 2010 IMO, a gold medal (6th ranked overall) at the 2011 IMO, and again a silver medal at the 2012 IMO.

This is impressive:

Sunday, 24 January 2016

Super Humans - Promethea Olympia Kyrene Pythaitha

   Promethea Olympia Kyrene Pythaitha (born March 13, 1991) is an American child genius with an IQ of 173. She started reading at age 1, began learning college-level calculus and was profiled by a CBS News 48 Hours special on "Whiz Kids!" at age 7, and at age 13 became the youngest student to complete work for a bachelor's degree from Montana State University in Mathematics. Promethea was born to Georgia Smith, a Greek-born artist, and has two older siblings, Vanessa and Apollo. For several months when Promethea was 4, she and her family were homeless and lived in their car in San Francisco. This was when her mother began to teach her advanced mathematics. At age 5, she was enrolled in Stanford University's Education Program for Gifted Youth. After being featured on a national CBS News special "Whiz Kids!", she was allowed to enroll as a regular student earning credit toward graduation at Montana State University. She audited her first M.S.U. course, calculus, at age 7. At age 13, she completed the course work necessary for a bachelor's degree in Mathematics, and at age 14 she officially graduated with that degree. Paying for college had always been a difficulty for the young student. Due to her young age, she was automatically disqualified for most university scholarships, and couldn't hold a job. A local family had paid for her tuition through the completion of her first degree. After her graduation, she spoke of her desire to continue her education, but due to her family's low income could not afford to continue with her studies. She wrote to Montana politicians, arguing that the state of Montana pledges a taxpayer funded education to other teenagers (throughout what is generally their high school years), but that she was being abandoned. Her alma mater offered to waive her tuition until she turned 16. In 2004, she changed her name, selecting names reflecting her aspirations and the ideals that she admired in ancient Greek history. In 2006, Promethea was awarded a $10,000 scholarship by the PanHellenic Scholarship Foundation. In January 2007, she was invited to speak in Chicago at a banquet to honor the Festival of the Three Hierarchs, a commemoration of the three founders of the Greek Orthodox Church. Her topic was to be the role of the church in education. During her research on the church founders, Promethea became convinced that the Church had committed genocide. In her speech, she demanded a separation of church and state, as well as the end of church control on education. The event was posted to YouTube and seen by Greeks around the world. Promethea received messages from passionate Greeks in America and Greece. Some sent her hate mail, but others commended her courage and sent books and offers of tuition. After her speech, she was invited to visit Greece for five days and was interviewed by Alpha TV. In 2011, she was involved in a shooting incident. In 2013, a settlement was reached in the subsequent court case.

Friday, 22 January 2016

Super Humans - Anne-Marie Imafidon

   Anne-Marie Imafidon (born 1990) is a British computing, mathematics and language child prodigy. She is one of the youngest to pass two GCSEs in two different subjects while in primary school. She passed two GCSE Examinations (in Mathematics and Information technology) at the age of 11. Imafidon's father is of Nigerian descent. Imafidon studied at the Lyceum Institute of Technology in East Ham, London, where she became the youngest person ever to obtain a qualification in Information Technology. At age 10 she won a scholarship to the private School St Joseph's Convent School in Reading, a year younger than usual. At 13, in 2003, she received a British scholarship to study mathematics at Johns Hopkins University. At 15, in 2005, she was admitted a degree program by the University of Oxford. At 17, she started a Masters degree at Oxford University and, at 19 in June 2010, she became the youngest ever graduate with a masters degree. Since leaving Oxford Imafidon has started work at Deutsche Bank. She is notable for championing the work of women in STEM and for setting up the organisation Stemettes, who run panel sessions and hackathons supporting girls and young women who are considering a STEM career. In April 2014, Imafidon was the keynote speaker at the BCS Women Lovelace Colloquium.

Thursday, 21 January 2016

Super Humans - John von Neumann

   John von Neumann (/vɒn ˈnɔɪmən/; Hungarian: Neumann János (Hungarian pronunciation: [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, fluid dynamics and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer. He published 150 papers in his life; 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. His last work, an unfinished manuscript written while in the hospital, was later published in book form as The Computer and the Brain. Von Neumann's mathematical analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932." During World War II he worked on the Manhattan Project with J. Robert Oppenheimer and Edward Teller, developing the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. After the war, served on the General Advisory Committee of the United States Atomic Energy Commission, and later as one of its commissioners. He was a consultant to a number of organizations, including the United States Air Force, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. Along with theoretical physicist Edward Teller, mathematician Stanislaw Ulam, and others, he worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

   Von Neumann was born Neumann János Lajos (in Hungarian the family name comes first), Hebrew name Yonah, in Budapest, Kingdom of Hungary, which was then part of the Austro-Hungarian Empire, to wealthy Jewish parents of the Haskalah. He was the eldest of three children. He had two younger brothers: Michael, born in 1907, and Nicholas, who was born in 1911. His father, Neumann Miksa (Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. Miksa's father and grandfather were both born in Ond (now part of the town of Szerencs), Zemplén County, northern Hungary. John's mother was Kann Margit (Margaret Kann); her parents were Jakab Kann and Katalin Meisels. Three generations of the Kann family lived in spacious apartments above the Kann-Heller offices in Budapest; von Neumann's family occupied an 18-room apartment on the top floor. In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning of Marghita. The family had no connection with the town; the appellation was chosen in reference to Margaret, as was those chosen coat of arms depicting three marguerites. Neumann János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann. Formal schooling did not start in Hungary until the age of ten. Instead, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken's Allgemeine Geschichte in Einzeldarstellungen. A copy was contained in a private library Max purchased. One of the rooms in the apartment was converted into a library and reading room, with bookshelves from ceiling to floor. Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a brilliant education system designed for the elite. Under the Hungarian system, children received all their education at the one gymnasium. Despite being run by the Lutheran Church, the majority of its pupils were Jewish. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius. Although Max insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are still on display at the von Neumann archive in Budapest. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition. At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics. Since there were few posts in Hungary for mathematicians, and those were not well-paid, his father wanted von Neumann to follow him into industry and therefore invest his time in a more financially useful endeavor than mathematics. So it was decided that the best career path was to become a chemical engineer. This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year non-degree course in chemistry at the University of Berlin, after which he sat the entrance exam to the prestigious ETH Zurich, which he passed in September 1923. At the same time, von Neumann also entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics. For his thesis, he chose to produce an axiomatization of Cantor's set theory. He passed his final examinations for his Ph.D. soon after graduating from ETH Zurich in 1926. He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert.

Super Humans - Gabriel Drew Carroll

   Gabriel Drew Carroll (born December 24, 1982) is an Assistant Professor of Economics at Stanford University. He graduated from Harvard with B.A. in mathematics and linguistics in 2005 and received his doctorate in economics from MIT in 2012. He was recognized as a child prodigy and received numerous awards in mathematics while a student. Carroll won two gold medals (1998, 2001) and a silver medal (1999) at the International Mathematical Olympiad, earning a perfect score at the 2001 International Mathematical Olympiad held in Washington, D.C., shared only with American teammate Reid W. Barton and Chinese teammates Liang Xiao and Zhiqiang Zhang. Gabriel earned a place among the top five ranked competitors (who are themselves not ranked against each other) in the William Lowell Putnam Competition all four years that he was eligible (2000–2003), a feat matched by only seven others (Don Coppersmith (1968–1971), Arthur Rubin (1970–1973), Bjorn Poonen (1985–1988), Ravi Vakil (1988–1991), Reid W. Barton (2001–2004), Daniel Kane (2003–2006), and Brian R. Lawrence (2007–08, 2010–11). His top-5 performance in 2000 was particularly notable, as he was officially taking the exam in spite of only being a high school senior, thus forfeiting one of his years of eligibility in college. He was on the first place Putnam team twice (2001–02) and the second place team once (2003). He has earned awards in science and math, including the Intel Science Talent Search, has taught mathematics classes and tutorials, and plays the piano. He was a Research Science Institute scholar in 2000. Carroll proposed Problem 3 of IMO 2009 and Problem 3 of IMO 2010. He also proposes problems to the USAMO such as problem 3 in 2007, 2008, 2010 and problem 6 in 2009. During the 2005-06 academic year, he taught English in Chaling, Hunan, China. He worked at the National Bureau of Economic Research from 2006 to 2007. Gabriel Carroll is an alumnus of Oakland Technical High School and graduated from Harvard University in 2005 with degrees in Mathematics and Linguistics. He graduated from the Economics Department at MIT in 2012, and spent one year at Microsoft Research as a postdoctoral researcher during 2012-2013.

Monday, 18 January 2016

Super Humans - Akshay Venkatesh

   Akshay Venkatesh (born 21 November 1981) is an Indian Australian mathematician. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. He is the only Australian to have won medals at both the International Physics Olympiad and International Mathematics Olympiad, which he did at the age of 12. Raised in Perth, Western Australia, where he attended Scotch College, Venkatesh attended extracurricular training classes for gifted students in the state mathematical olympiad program. In 1993, whilst aged only 11, he competed at the 24th International Physics Olympiad in Williamsburg, Virginia, winning a bronze medal. The following year in 1994, he switched his attention to mathematics, and after placing second in the Australian Mathematical Olympiad, he won a silver medal in the 6th Asian Pacific Mathematics Olympiad, before winning a bronze medal in the International Mathematics Olympiad held in Hong Kong that year. He completed his secondary education that year, turning 13 at the end of the year. He entered the University of Western Australia the following year as the youngest ever student at the institution and was awarded First Class Honours in Pure mathematics in 1997, the youngest ever to achieve this feat, as well as being awarded the J. A. Woods Memorial Prize for being the leading graduating student of the year. Venkatesh commenced his PhD at Princeton University in 1998 under Peter Sarnak, which he completed in 2002, producing the thesis Limiting forms of the trace formula. He was supported by the Hackett Fellowship for postgraduate study. He was then awarded a postdoctoral position at the Massachusetts Institute of Technology, where he served as a C.L.E. Moore instructor. Venkatesh then held a Clay Research Fellowship from the Clay Mathematics Institute from 2004 to 2006, and was an associate professor at the Courant Institute of Mathematical Sciences at New York University. Since 1 September 2008, he has been a professor at Stanford University. Venkatesh was awarded the Salem Prize and the Packard Fellowship in 2007 and the 2008 SASTRA Ramanujan Prize. The $10,000 prize was given at the International Conference on Number Theory and Modular Forms, held at SASTRA University, Kumbakonam, Ramanujan's hometown. In 2010, he was an invited speaker at the International Congress of Mathematicians (Hyderabad). Akshay Venkatesh has made contributions to a wide variety of areas in mathematics, including number theory, automorphic forms, representation theory, locally symmetric spaces and ergodic theory, by himself, and in collaboration with several mathematicians. Some samples:
– Using Ergodic methods, Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasse principle for integral representations of quadratic forms by quadratic forms.
– In a series of join works with Manfred Einsiedler, Elon Lindenstrauss and Philippe Michel, Venkatesh revisited the Linnik ergodic method and solved a longstanding conjecture of Yuri Linnik on the distribution of torus orbits attached to cubic number fields.
– Venkatesh also provided a very novel and more direct way of establishing sub-convexity estimates for L-functions in numerous cases, going beyond the foundational work of Hardy-Littlewood-Weyl, Burgess, and Duke-Friedlander-Iwaniec that dealt with important special cases. This approach eventually resulted in the complete resolution by Venkatesh and Philippe Michel of the sub-convexity problem for GL(1) and GL(2) L-functions over general number fields.

Saturday, 16 January 2016

Super Humans - Terence Tao

Terence Tao,  (born July 17, 1975, Adelaide, Australia), Australian mathematician awarded a Fields Medal in 2006 “for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.” Tao received a bachelor’s and a master’s degree from Flinders University of South Australia and a doctorate from Princeton University (1996), after which he joined the faculty at the University of California, Los Angeles. Tao’s work is characterized by a high degree of originality and a diversity that crosses research boundaries, together with an ability to work in collaboration with other specialists. His main field is the theory of partial differential equations. Those are the principal equations used in mathematical physics. For example, the nonlinear Schrödinger equation models light transmission in fibre optics. Despite the ubiquity of partial differential equations in physics, it is usually difficult to obtain or rigorously prove that such equations have solutions or that the solutions have the required properties. Along with that of several collaborators, Tao’s work on the nonlinear Schrödinger equation established crucial existence theorems. He also did important work on waves that can be applied to the gravitational waves predicted by Albert Einstein’s theory of general relativity. In work with the British mathematician Ben Green, Tao showed that the set of prime numbers contains arithmetic progressions of any length. For example, 5, 11, 17, 23, 29 is an arithmetic progression of five prime numbers, where successive numbers differ by 6. Standard arguments had indicated that arithmetic progressions in the set of primes might not be very long, so the discovery that they can be arbitrarily long was a profound discovery about the building blocks of arithmetic. Tao’s other awards include a Salem Prize (2000) and an American Mathematical Society Bocher Memorial Prize (2002).

Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of 9. He and Lenhard Ng are the only two children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just nine years old. Tao scored a 760. In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. He remains the youngest winner of each of the three medals in the Olympiad's history, winning the gold medal shortly after his thirteenth birthday. At age 14, Tao attended the Research Science Institute. When he was 15 he published his first assistant paper. He received his bachelor's and master's degrees at the age of 16 from Flinders University under Garth Gaudry. In 1992 he won a Fulbright Scholarship to undertake postgraduate study in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21. He joined the faculty of the University of California, Los Angeles in 1996. When he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution. Tao has two brothers living in Australia, both of whom represented Australia at the International Mathematical Olympiad. Nigel Tao was part of the team at Google Australia that created Google Wave. He now works on the Go programming language. Trevor Tao has a double degree in mathematics and music and is an autistic savant. If you are a mathematician,after you will read his maths blog, Tao will become almost a God in your eyes.

Monday, 11 January 2016

Super Humans - Jay Luo

Jay Luo (born 1970), received his B.Sc. from Boise State University with honors in mathematics at the age of 12 to become the youngest university graduate in United States history. I managed to find an 1982 article from NY Times about him. Seems that his family considered his privacy very important for his development.

BOISE, Idaho, May 1, 1982— A professor of a senior-level college mathematics course says he has had bright young students before, but none like 12-year-old Jay Luo, who is about to become the youngest university graduate in United States history. In June, Jay will receive his degree in mathematics from Boise State University. He is already planning to do post-graduate work at Stanford University. ''He's the brightest 12-year-old I've ever been associated with,'' says Robert Hughes, who taught Jay a linear programming math course. According to the Guinness Book of World Records, the youngest person to graduate from a United States college was Merrill Kenneth Wolf, who received his bachelor's degree in music from Yale in 1945, when he was 14. Jay enrolled at Boise State at the age of 9. In three years he has exceeded the requirements for a bachelor of science degree, maintaining a B-plus average, according to a Boise State spokesman, Larry Burke. The boy's father, Zong Luo, a computer engineer for Hewlett-Packard in Boise, enrolled his son at the university after reading an article in 1978 about exceptionally gifted students. The father, an American citizen of Taiwanese ancestry, sought out Boise State's Dr. William Mech, a former president of the National Collegiate Honors Council, Guiding Educational Force. Dr. Mech has been the boy's adviser and a guiding educational force in his life for the last three years. He has also been thrust into the role of the boy's spokesman because Jay's father has refused to allow his son to be interviewed. ''It's scary, it really is,'' Dr. Mech said of the boy's rapid progress. ''But somewhere, somebody has to take a stand and I believe this makes sense.'' Jay scored in the 98th percentile in mathematics and in the top 80 percent in verbal skills in the Scholastic Aptitude Test. He began his college career by taking two part-time courses in May 1979. By the end of the year, he had skipped junior and senior high school and was carrying more than a full load of college courses. Jay's rapid educational development has raised some unanswered questions about his future emotional and social well-being, according to Dr. Mech, who said he had agonized over the effects of moving Jay so far beyond his age group in academics. But Dr. Mech said he feels better about the decision each day. He also said he would not be surprised to see a Nobel Prize in the youngster's future if he changed from the field of mathematics. ''There is no Nobel Prize for mathematics, he understands that,'' Dr. Mech said.

Sunday, 10 January 2016

Super Humans - Ruth Elke Lawrence-Naimark

   Ruth Elke Lawrence-Naimark (Hebrew: רות אלקה לורנס-נאימרק‎, born 2 August 1971) is British mathematician and an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. Outside academia, she is best known for having been a child prodigy in mathematics. 

   Ruth Lawrence was born in Brighton, England. Her parents, Harry Lawrence and Sylvia Greybourne, were both computer consultants. When Lawrence was five, her father gave up his job so that he could educate her at home. At the age of nine, Lawrence gained an O-level in mathematics, setting a new age record (later surpassed in 2001 when Arran Fernandez successfully sat GCSE mathematics aged five). Also at the age of nine she achieved a Grade A at A-level Pure Mathematics. In 1981 Lawrence passed the Oxford University entrance examination in mathematics, coming first out of all 530 candidates sitting the examination, and joining St Hugh's College in 1983 at the age of just twelve. At Oxford, her father continued to be actively involved in her education, accompanying her to all lectures and some tutorials. Lawrence completed her bachelor's degree in two years, instead of the normal three, and graduated in 1985 at the age of 13 with a starred first and special commendation. Attracting considerable press interest, she became the youngest British person to gain a first-class degree, and the youngest to graduate from the University of Oxford in modern times. Lawrence followed her first degree with a second bachelor's degree in physics in 1986 and a Doctor of Philosophy (DPhil) degree in mathematics at Oxford in June 1989, at the age of 17. Her doctoral thesis title was Homology representations of braid groups and her thesis adviser was Sir Michael Atiyah. Lawrence's first academic post was at Harvard University, where she became a Junior Fellow in 1990 at the age of 19. In 1993, she moved to the University of Michigan, where she became an Associate Professor with tenure in 1997. In 1999, she took up the post of Associate Professor at the Hebrew University of Jerusalem.

Thursday, 7 January 2016

Super Humans - Charles Louis Fefferman

Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University. His primary field of research is mathematical analysis. A child prodigy, Fefferman entered college by the age of eleven and had written his first scientific paper by the age of 15 in German. After receiving his bachelor's degrees in physics and mathematics at the age of 17 from the University of Maryland and a PhD in mathematics at 20 from Princeton University under Elias Stein, Fefferman achieved a full professorship at the University of Chicago at the age of 22. This made him the youngest full professor ever appointed in the United States. At 24, he returned to Princeton to assume a full professorship there — a position he still holds. He won the Alan T. Waterman Award in 1976 (the first person to get the award) and the Fields Medal in 1978 for his work in mathematical analysis. He was elected to the National Academy of Sciences in 1979. He was appointed the Herbert Jones Professor at Princeton in 1984. In addition to the above, his honors include the Salem Prize, the Bôcher Memorial Prize, and the Bergman Prize, as well as election to the American Academy of Arts and Sciences. Fefferman contributed several innovations that revised the study of multidimensional complex analysis by finding fruitful generalisations of classical low-dimensional results. Fefferman's work on partial differential equations, Fourier analysis, in particular convergence, multipliers, divergence, singular integrals and Hardy spaces earned him a Fields Medal at the International Congress of Mathematicians at Helsinki in 1978. His early work included a study of the asymptotics of the Bergman kernel off the boundaries of pseudoconvex domains in \mathbb C^n. He has studied mathematical physics, harmonic analysis, fluid dynamics, neural networks, geometry, mathematical finance and spectral analysis, amongst others.

Charles Fefferman and his wife Julie have two daughters, Nina and Lainie. Lainie Fefferman is a composer, taught math at Saint Ann's School (New York City) and holds a degree in music from Yale University as well as a Ph.D. in music composition from Princeton. She has an interest in Middle Eastern music.[ Nina is a computational biologist whose research is concerned with the application of mathematical models to complex biological systems. Charles Fefferman's brother, Robert Fefferman, is also an accomplished mathematician and former Dean of the Physical Sciences Division at the University of Chicago. Fefferman has published several articles. His most cited papers include, in the order of citations:
-(with E. Stein) "Hp spaces of several variables", Acta Mathematica (1972).
-(with R. Coifman) "Weighted norm inequalities for maximal functions and singular integrals", Studia Mathematica (1974).
-(with E. Stein) "Some maximal inequalities", American Journal of Mathematics (1971).
-"The Bergman kernel and biholomorphic mappings of pseudoconvex domains", Inventiones mathematicae (1974).
-"The uncertainty principle", Bulletin of the American Mathematical Society (1983). ("online article". MR 707957.)
"Inequalities for strongly singular convolution operators", Acta Mathematica (1970).
(with P. Constantin and A. Majda) "Geometric constraints on potentially singular solutions for the 3-D Euler equations", Communications in Partial Differential Equations (1996).
"The multiplier problem for the ball", Annals of Mathematics (1971).

Super Humans - Per H. Enflo

Per H. Enflo (Swedish: [ˌpæːɹ ˈeːnfluː]; born 1944) is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years.

The basis problem and the approximation problem and later the invariant subspace problem for Banach spaces. In solving these problems, Enflo developed new techniques which were then used by other researchers in functional analysis and operator theory for years. Some of Enflo's research has been important also in other mathematical fields, such as number theory, and in computer science, especially computer algebra and approximation algorithms. Enflo works at Kent State University, where he holds the title of University Professor. Enflo has earlier held positions at the University of California, Berkeley, Stanford University, École Polytechnique, (Paris) and The Royal Institute of Technology, Stockholm. Enflo is also a concert pianist.

Super Humans - Ted Kaczynski

Theodore John "Ted" Kaczynski (/kəˈzɪnski/; born May 22, 1942), also known as the "Unabomber", is an American anarchist and serial murderer. Between 1978 and 1995, Kaczynski engaged in a nationwide bombing campaign against people involved with modern technology, planting or mailing numerous homemade bombs, ultimately killing a total of three people and injuring 23 others. He is also known for his wide-ranging social critiques, which opposed industrialization and modern technology while advancing a nature-centered form of anarchism. Kaczynski was born and raised in Evergreen Park, Illinois. While growing up in Evergreen Park he was a child prodigy, excelling academically from an early age. Kaczynski was accepted into Harvard University at the age of 16, where he earned an undergraduate degree. He subsequently earned a PhD in mathematics from the University of Michigan. He became an assistant professor at the University of California, Berkeley in 1967 at age 25. He resigned two years later. As a Harvard undergraduate, Kaczynski was among twenty-two students who were research subjects in ethically questionable experiments (possibly part of Project MKUltra) conducted by psychology professor Henry Murray from late 1959 to early 1962. In 1971, he moved to a remote cabin without electricity or running water, in Lincoln, Montana, where he lived as a recluse while learning survival skills in an attempt to become self-sufficient. 17 years after beginning his mail bomb campaign, Kaczynski sent a letter to The New York Times on April 24, 1995 and promised "to desist from terrorism" if the Times or the Washington Post published his manifesto, Industrial Society and Its Future (also called the "Unabomber Manifesto"), in which he argued that his bombings were extreme but necessary to attract attention to the erosion of human freedom necessitated by modern technologies requiring large-scale organization. The Unabomber was the target of one of the Federal Bureau of Investigation's costliest investigations. Before Kaczynski's identity was known, the FBI used the title "UNABOM" (UNiversity & Airline BOMber) to refer to his case, which resulted in the media calling him the Unabomber. The FBI (as well as Attorney General Janet Reno) pushed for the publication of Kaczynski's "Manifesto", which led to his sister-in-law, and then his brother, recognizing Kaczynski's style of writing and beliefs from the manifesto, and tipping off the FBI. Kaczynski tried unsuccessfully to dismiss his court appointed lawyers because they wanted to plead insanity in order to avoid the death penalty, as Kaczynski did not believe he was insane. When it became clear that his pending trial would entail national television exposure for Kaczynski, the court entered a plea agreement, under which he pleaded guilty and was sentenced to life in prison with no possibility of parole. He has been designated a "domestic terrorist" by the FBI.[10] Some anarcho-primitivist authors, such as John Zerzan and John Moore, have come to his defense, while also holding some reservations about his actions and ideas.

Kaczynski was born on May 22, 1942, in Evergreen Park, Illinois, to second-generation Polish Americans Wanda (née Dombek) and Theodore Richard Kaczynski. At nine months of age, Kaczynski's body was covered in hives. He was placed in isolation in a hospital where visitors were not allowed, as physicians were unsure of the cause of the hives. He was treated several times at the hospital over an eight-month period. His mother wrote in March 1943, "Baby home from hospital and is healthy but quite unresponsive after his experience." Kaczynski attended grades one through eight in Evergreen Park District 124 Schools. As a result of testing conducted in the fifth grade, which determined he had an IQ of 167, he was allowed to skip the sixth grade and enroll in the seventh grade. Kaczynski described this as a pivotal event in his life. He recalled not fitting in with the older children and being subjected to their bullying. As a child, Kaczynski had a fear of people and buildings, and played beside other children rather than interacting with them. His mother was so worried by his poor social development that she considered entering him in a study for autistic children led by Bruno Bettelheim. He attended high school at Evergreen Park Community High School. Kaczynski excelled academically, but found the mathematics too simple during his second year. Sometimes he would cut classes and write in his journal in his room. During this period of his life, Kaczynski became obsessed with mathematics, spending prolonged hours locked in his room practicing differential equations. Throughout secondary schooling, Kaczynski had far surpassed his classmates, able to solve advanced Laplace transforms before his senior year. He was subsequently placed in a more advanced mathematics class, yet still felt intellectually restricted. Kaczynski soon mastered the material and skipped the eleventh grade. With the help of a summer school course for English, he completed his high school education when he was 15 years old. He was encouraged to apply to Harvard University, and was subsequently accepted as a student beginning in 1958 at the age of 16. While at Harvard, Kaczynski was taught by famed logician Willard Van Orman Quine, scoring at the top of Quine's class with a 98.9% final grade.

He also participated in a personality assessment study conducted by Henry Murray, an expert on stress interviews. These experiments may have been part of the controversial, top-secret CIA program that was later revealed as Project MKUltra. Students in Murray's study were told they would be debating personal philosophy with a fellow student. Instead, they were subjected to a "purposely brutalizing psychological experiment". During the test, students were taken into a room and connected to electrodes that monitored their physiological reactions, while facing bright lights and a one-way mirror. Each student had previously written an essay detailing their personal beliefs and aspirations: the essays were turned over to an anonymous attorney, who would enter the room and individually belittle each student based in part on the disclosures they had made. This was filmed, and students' expressions of impotent rage were played back to them several times later in the study. According to author Alston Chase, Kaczynski's records from that period suggest he was emotionally stable when the study began. Kaczynski's lawyers attributed some of his emotional instability and dislike of mind control techniques to his participation in this study. Indeed, some have suggested that this experience may have been instrumental in Kaczynski's future actions. Kaczynski graduated from Harvard University in 1962, at age 20, and subsequently enrolled at the University of Michigan, where he earned a PhD in mathematics. Kaczynski's specialty was a branch of complex analysis known as geometric function theory. His professors at Michigan were impressed with his intellect and drive. "He was an unusual person. He was not like the other graduate students," said Peter Duren, one of Kaczynski's math professors at Michigan. "He was much more focused about his work. He had a drive to discover mathematical truth." "It is not enough to say he was smart," said George Piranian, another of his Michigan math professors. Kaczynski earned his PhD with his thesis entitled "Boundary Functions" by solving a problem so difficult that Piranian could not figure it out. Maxwell Reade, a retired math professor who served on Kaczynski's dissertation committee, also commented on his thesis by noting, "I would guess that maybe 10 or 12 men in the country understood or appreciated it." In 1967, Kaczynski won the University of Michigan's Sumner B. Myers Prize, which recognized his dissertation as the school's best in mathematics that year. While a graduate student at Michigan, he held a National Science Foundation fellowship and taught undergraduates for three years. He also published two articles related to his dissertation in mathematical journals, and four more after leaving Michigan. In late 1967, Kaczynski became an assistant professor of mathematics at the University of California, Berkeley, where he taught undergraduate courses in geometry and calculus. He was also noted as the youngest professor ever hired by the university, but this position proved short-lived. Kaczynski received numerous complaints and low ratings from the undergraduates he taught. Many students noted that he seemed quite uncomfortable in a teaching environment, often stuttering and mumbling during lectures, becoming excessively nervous in front of a class, and ignoring students during designated office hours. Without explanation, he resigned from his position in 1969, at age 26. The chairman of the mathematics department, J. W. Addison, called this a "sudden and unexpected" resignation, while vice chairman Calvin Moore said that given Kaczynski's "impressive" thesis and record of publications, "He could have advanced up the ranks and been a senior member of the faculty today."