Super Humans - Évariste Galois

   Évariste Galois (French: [evaʁist ɡaˈlwa]; 25 October 1811 – 31 May 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He died at age 20 from wounds suffered in a duel.

   Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (born Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. His father became mayor of the village after Louis XVIII returned to the throne in 1814. His mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years. At the age of 10, Galois was offered a place at the college of Reims, but his mother preferred to keep him at home. In October 1823, he entered the Lycée Louis-le-Grand, and despite some turmoil in the school at the beginning of the term (when about a hundred students were expelled), Galois managed to perform well for the first two years, obtaining the first prize in Latin. He soon became bored with his studies and, at the age of 14, he began to take a serious interest in mathematics. He found a copy of Adrien Marie Legendre's "Éléments de Géométrie", which, it is said, he read "like a novel" and mastered at the first reading. At 15, he was reading the original papers of Joseph Louis Lagrange, such as the landmark ''Réflexions sur la résolution algébrique des équations'' which likely motivated his later work on equation theory, and "Leçons sur le calcul des fonctions", work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way. In 1828, he attempted the entrance examination for the École Polytechnique, the most prestigious institution for mathematics in France at the time, without the usual preparation in mathematics, and failed for lack of explanations on the oral examination. In that same year, he entered the École Normale (then known as l'École préparatoire), a far inferior institution for mathematical studies at that time, where he found some professors sympathetic to him. In the following year Galois's first paper, on continued fractions, was published. It was at around the same time that he began making fundamental discoveries in the theory of polynomial equations. He submitted two papers on this topic to the Academy of Sciences. Augustin Louis Cauchy refereed these papers, but refused to accept them for publication for reasons that still remain unclear. However, in spite of many claims to the contrary, it is widely held that Cauchy recognized the importance of Galois's work, and that he merely suggested combining the two papers into one in order to enter it in the competition for the Academy's Grand Prize in Mathematics. Cauchy, an eminent mathematician of the time though with political views that were at the opposite end from Galois', considered Galois's work to be a likely winner. On 28 July 1829 Galois's father committed suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt to enter the Polytechnique, and failed yet again. It is undisputed that Galois was more than qualified; however, accounts differ on why he failed. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, which enraged Galois. The recent death of his father may have also influenced his behavior. Having been denied admission to the Polytechnique, Galois took the Baccalaureate examinations in order to enter the École Normale. He passed, receiving his degree on 29 December 1829. His examiner in mathematics reported, "This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research." He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. As noted before, his first attempt was refused by Cauchy, but in February 1830 following Cauchy's suggestion he submitted it to the Academy's secretary Joseph Fourier, to be considered for the Grand Prix of the Academy. Unfortunately, Fourier died soon after, and the memoir was lost. The prize would be awarded that year to Niels Henrik Abel posthumously and also to Carl Gustav Jacob Jacobi. Despite the lost memoir, Galois published three papers that year, one of which laid the foundations for Galois theory. The second one was about the numerical resolution of equations (root finding in modern terminology). The third was an important one in number theory, in which the concept of a finite field was first articulated.

Super Humans - William Rowan Hamilton

Sir William Rowan Hamilton (midnight, 3–4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Hamilton is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarked of the 18-year-old Hamilton, 'This young man, I do not say will be, but is, the first mathematician of his age.' Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819), who lived in Dublin at 38 Dominick Street. Hamilton's father, who was from Dunboyne, worked as a solicitor. By the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim Co. Meath. His uncle soon discovered that Hamilton had a remarkable ability to learn languages, and from a young age, had displayed an uncanny ability to acquire them (although this is disputed by some historians, who claim he had only a very basic understanding of them). At the age of seven he had already made very considerable progress in Hebrew, and before he was thirteen he had acquired, under the care of his uncle (a linguist), almost as many languages as he had years of age. These included the classical and modern European languages, and Persian, Arabic, Hindustani, Sanskrit, and even Marathi and Malay. He retained much of his knowledge of languages to the end of his life, often reading Persian and Arabic in his spare time, although he had long stopped studying languages, and used them just for relaxation. In September 1813 the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other 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. Hamilton was part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, which he entered at age 18. He studied both classics and mathematics, and was appointed Professor of Astronomy in 1827, prior to his graduation taking up residence at Dunsink Observatory where he spent the rest of his life.

Super Humans - Johann Carl Friedrich Gauss

Johann Carl Friedrich Gauss (/ɡaʊs/; German: Gauß, pronounced [ɡaʊs] ( listen); Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.

Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), as the son of poor working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension, which itself occurs 39 days after Easter. Gauss later solved this puzzle about his birthdate in the context of finding the date of Easter, deriving methods to compute the date in both past and future years. He was christened and confirmed in a church near the school he attended as a child. Gauss was a child prodigy. When he was eight, he figured out how to add up all the numbers from 1 to 100. There are also many other anecdotes about his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it was not published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day. Gauss's intellectual abilities attracted the attention of the Duke of Brunswick, who sent him to the Collegium Carolinum (now Braunschweig University of Technology), which he attended from 1792 to 1795, and to the University of Göttingen from 1795 to 1798. While at university, Gauss independently rediscovered several important theorems. His breakthrough occurred in 1796 when he showed that a regular polygon can be constructed by compass and straightedge if and only if the number of sides is the product of distinct Fermat primes and a power of 2. This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone. The stonemason declined, stating that the difficult construction would essentially look like a circle. The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the heptadecagon on 30 March. He further advanced modular arithmetic, greatly simplifying manipulations in number theory. On 8 April he became the first to prove the quadratic reciprocity law. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers. Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the note: "ΕΥΡΗΚΑ! num = Δ + Δ + Δ". On October 1 he published a result on the number of solutions of polynomials with coefficients in finite fields, which 150 years later led to the Weil conjectures.

Super Humans - André-Marie Ampère

André-Marie Ampère (/ˈæmpɪər/; French: [ɑ̃pɛʁ]; 20 January 1775 – 10 June 1836)[2] was a French physicist and mathematician who was one of the founders of the science of classical electromagnetism, which he referred to as "electrodynamics". The SI unit of measurement of electric current, the ampere, is named after him. I admire the most his early work on probabilities ( see book “Considerations on the Mathematical Theory of Games”)

Andre-Marie Ampère was born on 20 January 1775 to Jean-Jacques Ampère, a prosperous businessman, and Jeanne Antoinette Desutières-Sarcey Ampère, during the height of the French Enlightenment. He spent his childhood and adolescence at the family property at Poleymieux-au-Mont-d'Or near Lyon. Jean-Jacques Ampère, a successful merchant, was an admirer of the philosophy of Jean-Jacques Rousseau, whose theories of education (as outlined in his treatise Émile) were the basis of Ampère’s education. Rousseau believed that young boys should avoid formal schooling and pursue instead an “education direct from nature.” Ampère’s father actualized this ideal by allowing his son to educate himself within the walls of his well-stocked library. French Enlightenment masterpieces such as Georges-Louis Leclerc, comte de Buffon’s Histoire naturelle, générale et particulière (begun in 1749) and Denis Diderot and Jean le Rond d'Alembert’s Encyclopédie (volumes added between 1751 and 1772) thus became Ampère’s schoolmasters. The young Ampère, however, soon resumed his Latin lessons, which enabled him to master the works of Leonhard Euler and Daniel Bernoulli. In addition, Ampère used his access to the latest mathematical books to begin teaching himself advanced mathematics at age 12. In later life Ampère claimed that he knew as much about mathematics and science when he was eighteen as ever he knew; but, a polymath, his reading embraced history, travels, poetry, philosophy, and the natural sciences. His mother was a devout woman, so Ampère was also initiated into the Catholic faith along with Enlightenment science. The French Revolution (1789–99) that began during his youth was also influential: Ampère’s father was called into public service by the new revolutionary government, becoming a justice of the peace in a small town near Lyon. When the Jacobin faction seized control of the Revolutionary government in 1792, his father Jean-Jacques Ampère resisted the new political tides, and he was guillotined on 24 November 1793, as part of the Jacobin purges of the period. In 1796 Ampère met Julie Carron, and in 1799 they were married. André-Marie Ampère took his first regular job in 1799 as a mathematics teacher, which gave him the financial security to marry Carron and father his first child, Jean-Jacques (named after his father), the next year. (Jean-Jacques Ampère eventually achieved his own fame as a scholar of languages). Ampère’s maturation corresponded with the transition to the Napoleonic regime in France, and the young father and teacher found new opportunities for success within the technocratic structures favoured by the new French First Counsel. In 1802 Ampère was appointed a professor of physics and chemistry at the École Centrale in Bourg-en-Bresse, leaving his ailing wife and infant son in Lyon. He used his time in Bourg to research mathematics, producing Considérations sur la théorie mathématique de jeu (1802; “Considerations on the Mathematical Theory of Games”), a treatise on mathematical probability that he sent to the Paris Academy of Sciences in 1803.

Gift - Albert Einstein - A biographical memoir

For all the friends of this little blog - a free book that i like it. For one unique inside of the mind of...

Albert Einstein - a biographical memoir

by John Archibald Wheeler

Super Humans - Blaise Pascal

Blaise Pascal (1623–1662) was a French mathematician, physicist, and religious philosopher who wrote a treatise on vibrating bodies at the age of nine; his first proof, on a wall with a piece of coal, at 11 years old, and a theorem by 16 years old. He is famous for Pascal's theorem and many other contributions in mathematics, philosophy, and physics.

He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method. In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and fifty prototypes, he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following ten years, establishing him as one of the first two inventors of the mechanical calculator. Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646, he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted. In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. His father died in 1651. Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids. Pascal had poor health, especially after his 18th year, and his death came just two months after his 39th birthday. Pascal was born in Clermont-Ferrand, which is in France's Auvergne region. He lost his mother, Antoinette Begon, at the age of three. His father, Étienne Pascal (1588–1651), who also had an interest in science and mathematics, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte. In 1631, five years after the death of his wife, Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science. Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", Essai pour les coniques ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line). Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child." In France at that time offices and positions could be—and were—bought and sold. In 1631 Étienne sold his position as second president of the Cour des Aides for 65,665 livres. The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300. Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbor Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos. In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.[12] Though these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of computer engineering, the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol, for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.

Super Humans - Juan Caramuel y Lobkowitz

Juan Caramuel y Lobkowitz (Juan Caramuel de Lobkowitz, May 23, 1606 in Madrid — September 7 or 8, 1682 in Vigevano) was a Spanish Catholic scholastic philosopher, ecclesiastic, mathematician and writer. 

He was a precocious child, early delving into serious problems in mathematics and even publishing astronomical tables in his tenth year. After receiving a superficial education at college, where his unusual ability brought rapid advancement, this prodigy turned his attention to the Asiatic languages, especially Chinese. He was received into the Cistercian Order at the monastery of La Espina, in the diocese of Palencia, and after ordination entered upon a varied and brilliant career. His sermons attracted the favorable attention of the Infante Ferdinand, Governor of the Low Countries, while he was attached to the monastery of Dunes in Flanders, and in 1638 he was honored with the degree of Doctor of Theology by the University of Leuven. When he was obliged to leave the Electorate of the Palatinate, Philip IV of Spain made him his envoy to the court of Emperor Ferdinand III. He was in turn Abbot of Melrose, Scotland (Scotland), Abbot-Superior of the Benedictines of Vienna, and Grand-Vicar to the Archbishop of Prague. In 1648, when the Swedes attacked Prague, he armed and led a band of ecclesiastics who did yeoman service in the defence of the city. His bravery on this occasion merited for him a collar of gold from the emperor. Soon after he became Bishop of Satrianum, then Campagna, and at his death was Bishop of Vigevano. His books are even more numerous than his titles and his varied achievements; for, according to Jean-Noël Paquot, he published no less than 262 works on grammar, poetry, oratory, mathematics, astronomy, architecture, physics, politics, canon law, logic, metaphysics, theology and asceticism. He loved to defend novel theories, and in Theologia moralis ad prima atque clarissima principia reducta (Leuven, 1643) tried to solve theological problems by mathematical rules. He was a leading exponent of probabilism and his permissive moral opinions were criticized in Pascal's Provincial Letters and gained for him from Alphonsus Liguori the title of "Prince of the Laxists". His mathematical work centred on combinatorics and he was one of the early writers on probability, republishing Huygens's work on dice with helpful explanations. The Cardinal was also responsible for the design of the facade of the Vigevano Cathedral.