The Man Who Loved Only Numbers -Part1

Two days back i and my wife Sneha started reading The Man Who Loved Only Numbers by Paul Hoffman.

Actually my manager Hugh Barney gave me this book and he was so kind to give it to me seeing my enthu of maths.

Great book written by Great Author about Great Person Paul Erdos.

Today i want to share few important quotations from the 1st chapter and also about great people mentioned in this book.

Later i will update with remaining imp people found from this book.

The Man Who Loved Only Numbers is a biography of the famous mathematician Paul Erdos written by Paul Hoffman. It was first published in 1998 as a hardcover edition. A paperback edition appeared in 1999. The book is, in the words of the author, "a work in oral history based on the recollections of Erdos, his collaborators and their spouses". The book was a bestseller in the United Kingdom and has been published in 15 different languages.

Contents

A large part of the book concerns Erdos, but a lot of it is about other mathematicians, past and present, including Ronald Graham, Carl Friedrich Gauss, Srinivasa Ramanujan and G.H. Hardy. In the book Erdos enjoys listening to Hardy when he speaks about Ramanujan. Hoffman also tries to give examples of what mathematics is and why he views it as important, and why many mathematicians such as Erdos devote their whole lives to mathematics. It also contains some history of Europe and the US of Erdos' time.


1) Ludwig Josef Johann Wittgenstein (April 26, 1889 – April 29, 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. His influence has been wide-ranging and he is generally regarded as one of the twentieth century's most important philosophers.

Before his death at the age of 62, the only book-length work Wittgenstein had published was the Tractatus Logico-Philosophicus. Philosophical Investigations, which Wittgenstein worked on in his later years, was published shortly after he died. Both of these works are regarded as highly influential in analytic philosophy.

Ludwig grew up in a household that provided an exceptionally intense environment for artistic and intellectual achievement. His parents were both very musical and all their children were artistically and intellectually educated. Karl Wittgenstein was a leading patron of the arts, and the Wittgenstein house hosted many figures of high culture — above all, musicians. The family was often visited by musicians such as Johannes Brahms and Gustav Mahler. Ludwig's older brother Paul Wittgenstein went on to become a world-famous concert pianist, even after losing his right arm in World War I. Ludwig himself had absolute pitch, and his devotion to music remained vitally important to him throughout his life: he made frequent use of musical examples and metaphors in his philosophical writings, and was said to be unusually adept at whistling lengthy and detailed musical passages. He also played the clarinet and is said to have remarked that he approved of this instrument because it took a proper role in the orchestra.

2) In 1906, Wittgenstein began studying mechanical engineering in Berlin, and in 1908 he went to the Victoria University of Manchester to study for his doctorate in engineering, full of plans for aeronautical projects. He registered as a research student in an engineering laboratory, where he conducted research on the behaviour of kites in the upper atmosphere, and worked on the design of a propeller with small jet engines on the end of its blades. During his research in Manchester, he became interested in the foundations of mathematics, particularly after reading Alfred N. Whitehead and Bertrand Russell's Principia Mathematica and Gottlob Frege's Grundgesetze der Arithmetik, vol. 1 (1893) and vol. 2 (1903). In the summer of 1911 Wittgenstein visited Frege and, after having corresponded with him for some time, was advised by Frege to attend the University of Cambridge to study under Russell.

3) Paul Erdos March 26, 1913 – September 20, 1996) was an immensely prolific (and famously eccentric) Hungarian mathematician. With hundreds of collaborators, he worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory.

Paul Erdos was born in Budapest, Hungary, as Erdos Pal. similar to Air-doesh.) After his siblings died before his birth at the ages of 3 and 5, he was the only child of Anna and Lajos Erdos. His parents were both Jewish mathematicians, from a vibrant intellectual community. At the age of three, he could calculate how many seconds his family's friends had lived (Hoffman 1998). Erdos showed early promise as a prodigy, and soon became regarded as a mathematical genius by his peers.

Both of Erdos's parents were high school mathematics teachers, and Erdos received much of his early education from them. Erdos always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdos became an ardent solver of the problems proposed each month in KoMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdos later published several articles in it about problems in elementary plane geometry.

In 1934, he was awarded a doctorate in mathematics. Because anti-Semitism was increasing, he moved that same year to Manchester, England, to be a guest lecturer. In 1938, he accepted his first American position as a scholarship holder at Princeton University. At this time, he began to develop the habit of traveling from campus to campus. He would not stay long in one place and traveled back and forth between mathematical institutions until his death.

4) Possessions meant little to Erdos; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were in general donated to people in need and various worthy causes. He spent most of his life as a vagabond, travelling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom he (Erdos) should visit next. His working style has been humorously compared to traversing a linked list.

5) His colleague Alfred Renyi said, "a mathematician is a machine for turning coffee into theorems", and Erdos drank copious quantities. (This quotation is often attributed incorrectly to Erdos.) After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month. Erdos won the bet, but complained during his abstinence that mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." After he won the bet, he promptly resumed his amphetamine habit.

6) He had his own idiosyncratic vocabulary: he spoke of "The Book", an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF). He accused the SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from The Book!". This later inspired a book entitled Proofs from THE BOOK.

7) During the last decades of his life, Paul Erdos received at least fifteen honorary doctorates. He became a member of the scientific academies of eight countries, including the U.S. National Academy of Sciences and the U.K. Royal Society. Shortly before his death, he renounced his honorary degree from the University of Waterloo over what he considered to be unfair treatment of a colleague. He died 'in action' of a heart attack on September 20, 1996, at the age of 83, while attending a conference in Warsaw, Poland. Erdos never married and had no children.

8) His life was documented in the film N Is a Number: A Portrait of Paul Erdos, made while he was still alive.

9) Of his contributions, the development of Ramsey theory and the application of the probabilistic method especially stand out. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory. Erdos found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original one. He also discovered an elementary proof for the Prime number theorem, along with Atle Selberg, which showed how combinatorics was an efficient method of counting collections. Erdos also contributed to fields in which he had little real interest, such as topology, where he is credited as the first person to give an example of totally disconnected topological space that is not zero-dimensional.

10) Erdos get maths at the age of three but for the last 25 years of his life he worked 19 hour days.

11) The Erdos number, honoring the late Hungarian mathematician Paul Erdos, one of the most prolific writers of mathematical papers, is a way of describing the "collaborative distance", in regard to mathematical papers, between an author and Erdos.

In order to be assigned an Erdos number, an author must co-write a mathematical paper with an author with a finite Erdos number. Paul Erdos is the one person having an Erdos number of zero. If the lowest Erdos number of a coauthor is k, then the author's Erdos number is k + 1.

The Erdos number was most likely first defined in print by Casper Goffman, an analyst whose own Erdos number is 1. Goffman published his observations about Erdos's prolific collaboration in a 1969 article entitled "And what is your Erdos number?"

12) S. B. Rao is an Indian born mathematician and a professor. He has published many papers, mainly in the area of graph theory. His Erdos number is 1.

13) Ronald Lewis Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society with being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He has done important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness.

He holds the posts of Chief Scientist at the California Institute for Telecommunication and Information Technology (also known as Cal-(IT)2), and Irwin and Joan Jacobs Professor at the Department of Computer Science and Engineering of the University of California, San Diego (UCSD).

He was born in Taft, California. In 1962, he got his Ph.D. in mathematics from the University of California, Berkeley.

A 1977 paper of his discussed a problem in Ramsey theory, and gave a large number as an upper bound for its solution. This number has since become famous as the largest number ever used in a serious mathematical proof (and is listed in the Guinness Book of Records as such), and is now known as Graham's number.

Graham popularized the concept of the Erdos number, named after the highly prolific Hungarian mathematician Paul Erdos (1913 - 1996). A mathematician's Erdos number is the minimum number of links away from Erdos they are, where mathematician A is linked to mathematician B if they have co-authored a paper. Graham's Erdos number is 1. He co-authored nearly 30 papers with Erdos, and was also a good friend. Erdos often stayed with him, and let him look after his mathematical papers and even his money for him.

He has published about 320 papers and five books, including Concrete Mathematics with Donald Knuth.

He is married to Fan Chung Graham (known professionally as Fan Chung), who is the Akamai Professor in Internet Mathematics at the University of California, San Diego. He has four children—three daughters, Che, Laura, Christy and a son, Marc—from an earlier marriage.

14) Fan Rong K Chung Graham known professionally as Fan Chung, is a mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdos-Renyi model for graphs with general degree distribution (including power-law graphs in the study of large information networks).

She is the Akamai Professor in Internet Mathematics at the University of California, San Diego (UCSD) in the United States since 1998. She received her doctorate from the University of Pennsylvania in 1974, under the direction of Herbert Wilf. After working at the Bell Laboratories and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first woman tenured professor in mathematics. She serves on the editorial boards of more than a dozen international journals. Since 2003 she is the editor-in-chief of Internet Mathematics. She has given invited lectures in many conferences, including International Congress of Mathematicians in 1994, and a plenary lecture on the mathematics of PageRank at the 2008 Annual meeting of American Mathematical Society.

Chung has two children, the first born during her graduate studies, from her first marriage. She has been married to the mathematician Ronald Graham since 1983. The couple were close friends of the mathematician Paul Erdos, and have both published papers with him; thus, both have Erdos numbers of 1.

15) Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent British-Indian-American mathematician, specializing in number theory.

He was born in London, since his father, Gopal Chowla, a professor of mathematics in Lahore, was then studying in Cambridge. His family returned to India, where he received his masters degree in 1928 from the Government College in Lahore. In 1931 he received his doctorate from the University of Cambridge, where he studied under J. E. Littlewood.

Chowla then returned to India, where he taught at several universities, becoming head of mathematics at Government College in 1936.During the difficulties arising from the partition of India in 1947, he left for the United States. There he visited the Institute for Advanced Study until the fall of 1949, then taught at the University of Kansas in Lawrence until moving to the University of Colorado in 1952. He moved to Penn State in 1963 as a research professor, where he remained until his retirement in 1976. He was a member of the Indian National Science Academy and received the Padma Bhushan award.

Among his contributions are a number of results which bear his name. These include the Bruck-Chowla-Ryser theorem, the Ankeny-Artin-Chowla congruence, the Chowla-Mordell theorem, and the Chowla-Selberg formula.

16) Navin M. Singhi (1949–) is an Indian born mathematician and a professor. He has published many papers in reputed journals. His Erdos number is 1.

17) Krishnaswami Alladi who made fundamental contributions to several fields of study since 1947 and founded the Institute of Mathematical Sciences (MATSCIENCE).

Dr. Ramakrishnan was the Director of MATSCIENCE in Chennai for 22 years, during which he built up an ethos of innovative thinking and an ambience that was ever responsive to new ideas. Now a Deemed University, this institution was inspired by the visit of scientist Neils Bohr to Dr. Ramakrishnan’s family home — the “Ekamra Nivas” (house with a tree).

Dr. Ramakrishnan’s has been a life devoted to the restless world of science; a ceaseless probing of the intrigues of mathematics and high energy physics.

Dr. Ramakrishnan graduated in Physics from Madras University in 1943. He took his Ph.D. from the University of Manchester in 1951 and later taught theoretical physics at the University of Madras until 1962 and became a Fellow of the Indian Academy of Sciences.

He has authored or co-authored over 150 influential scientific papers in leading journals on topics ranging over Stochastic Processes, Elementary Particle Physics, Matrix Algebra, and the Special Theory of Relativity, and was invited for guest lectures at leading scientific institutions in the United States, Europe and Japan.

In an interview to The Hindu in July 1989, Dr. Ramakrishnan bemoaned the decline in the quality of research in India when benchmarked against the standards set by Sir C.V. Raman and Srinivasa Ramanujam. “I trace it to one main source — there is not enough liaison between teaching and research unlike in the U.S., where these two go together.”

Dr. Ramakrishnan felt that the “brain drain” could be countered only by creating an environment in India that scientists would want to return to. Prestige and peer acceptance are key drivers of scientific ambition. He once remarked that “We will not be able to contribute effectively unless our scientists are stricken with a Nobel fever, which is a noble fever.”

A regular for years at the Music Academy in Chennai during the “Margazhi” festival season, Dr. Ramakrishnan could identify with the sheer mastery of Semmangudi and M.S. Subbulakshmi in attaining the proper balance between alapana, swara and kirtana.

18) Prasad Tetali is a Professor at School of Mathematics & College of Computing at the Georgia Institute of Technology.

19) This is the website for the Erdös Number Project, which studies research collaboration among mathematicians.

20) Andrew "Andy" Beal (born 1952) is a Dallas, Texas-based businessman. He made his fortune in banking and real estate, and is the founder and chairman of Beal Bank and Beal Aerospace Technologies. Beal is also known for his high-stakes poker and mathematics activities.

Beal wanted to be a businessman since he was a teenager in Lansing, Michigan. During his years in high school, he would earn money by fixing televisions and installing apartment alarms, and with his friends he began to relocate dislodged houses. Beal linked hydraulic jacks, and his friends would raise the homes at night, then move them.

Beal, who had excelled on his high school debate team, enrolled at Michigan State University and subsequently attended Baylor University in Texas. At age 19, Beal bought a house for $6,500 (USD) and started renting it for $119 per month, which eventually led to his first net gain as a businessman.

Beal's work in mathematical number theory includes his 1993 articulation of Beal's conjecture, and he has offered a $100,000 (USD) prize for its proof or disproof.

21) Joel Spencer (born April 20, 1946) is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervision of Andrew Gleason.He is currently (as of 2007) a professor at the Courant Institute of Mathematical Sciences of New York University.

22) Bertrand Arthur William Russell (18 May 1872–2 February 1970), was a British philosopher, historian, logician, mathematician, advocate for social reform, and pacifist. Although usually regarded as English, as he spent the majority of his life in England, he was born and raised in Wales.

A prolific writer, Russell was a populariser of philosophy and a commentator on a large variety of topics. Continuing a family tradition in political affairs, he was a prominent anti-war activist, championing free trade between nations and anti-imperialism. He wrote the essay On Denoting and was co-author (with Alfred North Whitehead) of Principia Mathematica, an attempt to ground mathematics on the laws of logic. Both works have had a considerable influence on logic, mathematics, set theory, linguistics and analytic philosophy.

Russell was born at the height of Britain's economic and political ascendancy. When he died almost a century later, the British Empire had all but vanished; its power had been dissipated by two world wars and its imperial system had been brought to an end. Among his post–Second World War political activities, Russell was a vigorous proponent of nuclear disarmament, antagonist to communist totalitarianism and an outspoken critic of the Vietnam War. Previously he had been imprisoned and deprived of his position at Trinity College, Cambridge because of his activity as a vigorous peace campaigner and opponent of conscription during the First World War. In 1920, Russell visited the emerging Soviet Union which subsequently met with his disapproval, but he also campaigned vigorously against Adolf Hitler in the 1930s.

In 1950, Russell was awarded the Nobel Prize in Literature, "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".

23) Godfrey Harold Hardy FRS (February 7, 1877 Cranleigh, Surrey, England – December 1, 1947 Cambridge, Cambridgeshire, England) was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.

Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for the layman.

His relationship as mentor, from 1914 onwards, of the Indian mathematician Srinivasa Ramanujan has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdos, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."

G.H. Hardy was born 7 February 1877, in Cranleigh, Surrey, England, into a teaching family. His father was Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College for teachers. Both parents were mathematically inclined.

Hardy's own natural affinity for mathematics was perceptible at a young age. When just two years old, he wrote numbers up to millions, and when taken to church he amused himself by factorizing the numbers of the hymns.

After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. In 1896 he entered Trinity College, Cambridge. After only two years of preparation he was fourth in the Mathematics Tripos examination. Years later, Hardy sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end. While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society.

As the most important influence Hardy cites the self-study of Cours d'analyse de l'Ecole Polytechnique by the French mathematician Camille Jordan, through which he became acquainted with the more precise mathematics tradition in continental Europe. In 1900 he passed part II of the tripos and was awarded a fellowship. In 1903 he earned his M.A., which was the highest academic degree at English universities at that time. From 1906 onward he held the position of a lecturer, who had to teach six hours per week leaving him plenty of time for research. In 1919 he left Cambridge to take the Savilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair during World War I. He returned to Cambridge in 1931, where he was Sadleirian Professor until 1942.

The Indian Clerk (2007) is a novel by David Leavitt based on Hardy's life at Cambridge, including his discovery of and relationship with Srinivasa Ramanujan.

24) Pythagoras of Samos born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy. Herodotus referred to him as "the most able philosopher among the Greeks". His name led him to be associated with Pythian Apollo; Aristippus explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian (Pyth-)," and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind.

He is best known for the Pythagorean theorem, which bears his name. Known as "the father of numbers", Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. According to Iamblichus, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons."

He was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato. Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.

25) Sir Isaac Newton, 4 January 1643 – 31 March 1727 [OS: 25 December 1642 – 20 March 1726]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist and theologian. His Philosophiæ Naturalis Principia Mathematica, published in 1687, is considered to be the most influential book in the history of science. In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated the scientific view of the physical universe for the next three centuries and is the basis for modern engineering. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.

In mechanics, Newton enunciated the principles of conservation of momentum and angular momentum. In optics, he invented the reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function, and contributed to the study of power series.

Newton was also highly religious (though unorthodox), producing more work on Biblical hermeneutics than the natural science he is remembered for today.

In a 2005 poll of the Royal Society asking who had the greater effect on the history of science, Newton was deemed much more influential than Albert Einstein.

26) Pierre de Fermat : (17 August 1601 or 1607/8[1] – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, as well as his research into the theory of numbers. He also made notable contributions to analytic geometry, probability, and optics.

Fermat was born at Beaumont-de-Lomagne, 58 kilometers (36 miles) north-west of Toulouse, France. The late 15th century mansion where Fermat was born in Beaumont-de-Lomagne is now a museum. Pierre Fermat's father was a wealthy leather merchant and second consul of Beaumont-de-Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. Although there is little evidence concerning his school education it must have been at the local Franciscan monastery.

He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a copy of his restoration of Apollonius's Plane loci to one of the mathematicians there. Certainly in Bordeaux he was in contact with Beaugrand and during this time he produced important work on maxima and minima which he gave to Étienne d'Espagnet who clearly shared mathematical interests with Fermat.

He died at Castres, age 63, 79 kilometers (49 miles) east of Toulouse. The oldest, and most prestigious, college in Toulouse is named after him - the Pierre de Fermat.

27) Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as the princeps mathematicorum (Latin, usually translated as "the Prince of Mathematicians", although Latin princeps also can simply mean "the foremost") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.

Gauss was a child prodigy. There are many anecdotes pertaining to 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 would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

Gauss was born in Braunschweig, in the Electorate of Brunswick-Lüneburg, now part of Lower Saxony, Germany, as the only son of poor working-class parents. There are several stories of his early genius. According to one, his gifts became very apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances.

28) David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He invented or developed a broad range of fundamental ideas, in invariant theory, the axiomatization of geometry, and with the notion of Hilbert space, one of the foundations of functional analysis.

Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.

Hilbert and his students supplied significant portions of the mathematical infrastructure required for quantum mechanics and general relativity. He is also known as one of the founders of proof theory, mathematical logic and the distinction between mathematics and metamathematics.

29) Kurt Godel (April 28, 1906, Brünn, Austria-Hungary – January 14, 1978 Princeton, New Jersey) was an Austrian-American logician, mathematician and philosopher.

One of the most significant logicians of all time, Gödel's work has had immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

30) Stanislaw Marcin Ulam (April 13, 1909 – May 13, 1984) was a Polish mathematician who participated in the Manhattan Project and proposed the Teller–Ulam design of thermonuclear weapons. He also invented nuclear pulse propulsion and developed a number of mathematical tools in number theory, set theory, ergodic theory, and algebraic topology.

Stanislaw Ulam was born to a Polish Jewish family in Lwów, Galicia, then in Austria-Hungary; since 1918 in Poland and since 1939 in USSR. He was part of the city's large Jewish minority population; when he grew up in the city, it was in the Second Polish Republic. His mentor in mathematics was Stefan Banach, a great Polish mathematician and one of the moving spirits of the Lwów School of Mathematics and more broadly of the remarkable Interbellum Polish School of Mathematics.

Ulam went to the United States in 1938 as a Harvard Junior Fellow. He visited Poland in summer 1939 and together with his brother, Adam, escaped from Poland on the eve of the Second World War; the rest of their family died in The Holocaust. When his fellowship was not renewed, he served on the faculty of the University of Wisconsin-Madison. While in U.S., in the midst of the war, his friend John von Neumann invited him to a secret project in New Mexico. Ulam researched the invitation by checking out a book on New Mexico from the university library. He found on the book's check-out card the names of all those who had successively disappeared from the campus at the UW. Ulam then joined the Manhattan Project at Los Alamos.

31) Marin Mersenne, Marin Mersennus (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics".

Marin Mersenne (pronounced Mehr-SENN) was born of peasant parents near Oizé, Maine (present day Sarthe). He was educated at Le Mans and at the Jesuit College of La Flèche. On July 17, 1611, he joined the Minim Friars, and, after studying theology and Hebrew in Paris received his full holy orders in 1613. Anatomy]] at Nevers but returned to Rome in 1620 at the convent of L'Annonciade. There, with other kindred spirits such as Descartes, Étienne Pascal, Gilles de Roberval and Nicolas-Claude Fabri de Peiresc, he studied mathematics and music. He corresponded with Giovanni Doni, Constantijn Huygens and other scholars in Italy, England and Holland. For four years he devoted himself entirely to philosophic and theological writing, and published Quaestiones celeberrimae in Genesim (1623); L'Impieté des déistes (1624); La Vérité des sciences (Truth of the Sciences against the Sceptics, 1624). It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus. He taught theology and philosophy at Nevers and Berlin. In 1635 Mersenne met with Tommaso Campanella, but concluded that he could "teach nothing in the sciences (...) but still he has a good memory and a fertile imagination." Mersenne asked if René Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Germany fifteen times, in 1640, 1641 and 1645.

He died through complications arising from a lung abscess.

32) In mathematics, a Mersenne number is a number that is one less than a power of two,

A Mersenne prime is a Mersenne number that is a prime number. As of August 2008, only 44 Mersenne primes were known; the largest known prime number is a Mersenne prime and in modern times the largest known prime has nearly always been a Mersenne prime. Like several previous Mersenne primes, it was discovered by a distributed computing project on the Internet, known as the Great Internet Mersenne Prime Search (GIMPS). GIMPS reported the finding of a potential 45th Mersenne prime on 2008-08-23, ditto a potential 46th on 2008-09-06, and 'enough' independent verifications of each potential M(p) prime to confirm them as primes. An announcement about both primes will be made around 2008-09-17. Given the delay, chances are at least one of these has over 10 million decimal digits.

33) Frank Nelson Cole, Ph.D. (September 20, 1861 –May 26, 1926) was an American mathematician, born at Ashland, Massachusetts, and educated at Harvard, where he lectured on mathematics from 1885 to 1887.

Later, he was employed at the University of Michigan and Columbia University. Professor Cole became secretary of the American Mathematical Society in 1895 and an editor of its Bulletin in 1897.

Cole died in New York City, aged 64. The American Mathematical Society's Cole Prize was named in his honor.

34) Eric Temple Bell (February 7, 1883, Peterhead, Scotland - December 21, 1960, Watsonville, California) was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life. He published his non-fiction under his given name and his fiction as John Taine.

He was born in Peterhead, Scotland; but his father, a fish-factor, moved to San Jose, California in 1884, when he was fifteen months old; the family returned to Bedford, England after his father's death, on January 4, 1896. Bell returned to the United States, by way of Montreal in 1902.

Bell attended Stanford University and Columbia University (where he was a student of Cassius Jackson Keyser) and was on the faculty first at the University of Washington and later at the California Institute of Technology.

He did research in number theory; see in particular Bell series. He attempted—not altogether successfully—to make the traditional umbral calculus (understood at that time to be the same thing as the "symbolic method" of Blissard) logically rigorous. He also did much work using generating functions, treated as formal power series, without concern for convergence. He is the eponym of the Bell polynomials and the Bell numbers of combinatorics. In 1924 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.

35) Eratosthenes of Cyrene 276 BC - 194 BC) was a Greek mathematician, poet, athlete, geographer and astronomer. He made several remarkable discoveries and inventions: he devised a system of latitude and longitude. He was the first person to calculate the circumference of the Earth (with remarkable accuracy), and the tilt of the earth's axis (again with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the Great Library of Alexandria and died in the capital of Ptolemaic Egypt. He never married.

Eratosthenes studied in Alexandria and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Apollonius of Rhodes, in that post [2]. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere, which was widely used until the invention of the orrery in the 18th century.

In 194 BC Eratosthenes became blind and, according to legends, a year later, he starved himself to death.

He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).

36) Christian Goldbach (March 18, 1690 – November 20, 1764) was a Prussian mathematician who also studied law. He is remembered today for Goldbach's conjecture.

Born in the Duchy of Prussia's capital Königsberg, part of Brandenburg-Prussia, Goldbach was the son of a pastor. He studied at the University of Königsberg and went on to work at the newly opened St Petersburg Academy of Sciences in 1725. Later on, he was a tutor to the later Tsar Peter II in 1728. In 1742 he entered the Russian Ministry of Foreign Affairs.

Goldbach traveled widely throughout Europe and met with many famous mathematicians, such as Gottfried Leibniz, Leonhard Euler, and Nicholas I Bernoulli. He is most noted for his correspondence with these mathematicians, especially in his 1742 letter to Euler stating his Goldbach's Conjecture. He also studied and proved some theorems on perfect powers, such as the Goldbach-Euler theorem, and made several notable contributions to analysis.

37) Pafnuty Lvovich Chebyshev was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebyshov, Tchebycheff or Tschebyscheff (French and German transcriptions).

One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk, province of Kaluga. His father, Lev Pavlovich, was a wealthy landowner. Pafnuty Lvovich was first educated at home by his mother Agrafena Ivanovna (in reading and writing) and by his cousin Avdotya Kvintillianovna Sukhareva (in French and arithmetic). Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis".

A physical handicap (of unknown cause) affected Chebyshev's adolescence and development. From childhood, he limped and walked with a stick and so his parents abandoned the idea of his becoming an officer in the family tradition. His disability prevented his playing many children's games and he devoted himself instead to the passion of his life, building machines.

38) Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics.

Bellman was born in 1920 and studied mathematics at Brooklyn College (B.A. 1941) and the University of Wisconsin-Madison (M.A.). He then went to work for a Theoretical Physics Division group in Los Alamos. In 1946 he received his Ph.D. at Princeton under the supervision of Solomon Lefschetz.

He was a professor at the University of Southern California, a Fellow in the American Academy of Arts and Sciences (1975), and a member of the National Academy of Engineering (1977).

He was awarded the IEEE Medal of Honor in 1979, "For contributions to decision processes and control system theory, particularly the creation and application of dynamic programming". His key work is the Bellman-Equation.

39) Baron Jurij Bartolomej Vega (March 23, 1754 – September 26, 1802) was a Slovene mathematician, physicist and artillery officer.

Born in the small village of Zagorica, near Dolsko, east of Ljubljana in Slovenia, Jurij was 6 years old when his father Jernej Veha died. Jurij (or George in English) was educated first in Moravce and later in 1767 attended high school for six years in Ljubljana, studying Latin, Greek, religion, German, history, geography, science, and mathematics. At that time there were about 500 students there. He was a schoolfellow of Anton Tomaz Linhart, a Slovenian writer and historian. Jurij completed high school when he was 19, in 1773. After completing Lyceum in Ljubljana he became a navigational engineer. Tentamen philosophicum, a list of questions for his comprehensive examination, was preserved and is available in the Mathematical Library in Ljubljana. The problems cover logic, algebra, metaphysics, geometry, trigonometry, geodesy, stereometry, geometry of curves, ballistics, and general and special physics.

40) Johann Heinrich Lambert (August 26, 1728 – September 25, 1777), was a Swiss mathematician, physicist and astronomer.

He was born in Mülhausen (now Mulhouse, Alsace, France). His father was a poor tailor, so Johann had to struggle to gain an education. He first worked as a clerk in an ironworks, then gained a position in a newspaper office. The editor recommended him as a private tutor to a family, which gave him access to a good library and provided enough leisure time in which to explore it. In 1759 he moved to Augsburg, then in 1763 he dwelled in Berlin. In the final decade of his life he gained the sponsorship of Frederick II of Prussia, and passed the rest of his life in reasonable comfort. He died in Berlin, Prussia (today Germany).

41) Johann Franz Encke (23 September 1791 – 26 August 1865) was a German astronomer, born in Hamburg. He is sometimes confused with Karl Ludwig Hencke, another German astronomer.

Encke studied mathematics and astronomy from 1811 at the University of Göttingen under Carl Friedrich Gauss; but he enlisted in the Hanseatic Legion for the campaign of 1813–1814, and became lieutenant of artillery in the Prussian army in 1815. Having returned to Göttingen in 1816, he was at once appointed by Bernhardt von Lindenau as his assistant in the observatory of Seeberg near Gotha.

42) Jacques Salomon Hadamard (December 8, 1865 – October 17, 1963) was a French mathematician best known for his proof of the prime number theorem in 1896.

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a rough description of how the primes are distributed.

Roughly speaking, the prime number theorem states that if you randomly select a number nearby some large number N, the chance of it being prime is about 1 / ln(N), where ln(N) denotes the natural logarithm of N. For example, near N = 10,000, about one in nine numbers is prime, whereas near N = 1,000,000,000, only one in every 21 numbers is prime.

Hadamard studied at the École Normale Supérieure under the direction of Charles Émile Picard. After the Dreyfus affair, which involved him personally (Dreyfus was his brother-in-law), Hadamard, Jewish himself in his historical identity, became politically active and became a staunch supporter of Jewish causes though he professed to be an atheist in his religion.

He introduced the idea of well-posed problem in the theory of partial differential equations. He also gave his name to the Hadamard inequality on volumes, and the Hadamard matrix, on which the Hadamard transform is based. The Hadamard gate in quantum computing uses this matrix.

His students included Maurice Fréchet, Paul Lévy, Szolem Mandelbrojt and André Weil.

43) Charles-Jean Étienne Gustave Nicolas, Baron de la Vallée Poussin (August 14, 1866 - March 2, 1962) was a Belgian mathematician. He is most well-known for proving the Prime number theorem.

He was born in Leuven, Belgium and spent most of his life there. He was taught mathematics at the Catholic University of Leuven by Louis-Philippe Gilbert (who was his uncle), after he obtained his diploma in engineering he was encouraged to obtain a doctorate in the sciences of physics and mathematics, and from 1891 when he was 25 he was assistant professor in Mathematical Analysis. He became a teacher at the same university (just like his father, Charles-Louis-Joseph-Xavier de la Vallée-Poussin, who taught mineralogy and geology) in 1892, obtaining Gilbert's chair at his death. While teaching he carried out research in mathematical analysis and the theory of numbers and in 1905 was awarded the Decennial Prize for Pure Mathematics 1894-1903. He was to be awarded this prize a second time in 1924 for his work in the period 1914 to 1923. In 1898 he was nominated correspondent to the Royal Academy (at the age of 32) and a Member of the Academy in 1908. In 1923 he was President of the Division of Sciences.In 1914 he escaped from Leuven on its destruction by the invading Germans and was invited to teach at Harvard in the United States, this was followed by professorships in Paris at the Collège de France and at the Sorbonne in 1918. After the war he returned to Belgium, The International Union of Mathematicians was created and he was invited to become its President; he was to remain Honorary President. Between 1918 and 1925 he traveled extensively, teaching in Geneva, Strasbourg and Madrid and then in the United States where he gave lectures at the Universities of Chicago, Berkeley, Brown, Yale, Princeton, Columbia, Philadelphia and the Rice Institute. He was Doctor Honoris Causa of the Universities of Paris, Toronto, Strasbourg and Oslo, Associate of the Institute of France and Member of the Pontifical Academy of Nuovi Lincei, Nazionale dei Lincei, Madrid, Naples, Boston. He was awarded the title of Baron by King Albert 1 of the Belgians in 1928 In 1961, he fractured his shoulder and this incident led him to death in Boitsfort (Watermaal-Bosvoorde), Brussels a couple of months later.

44) Atle Selberg (June 14, 1917 – August 6, 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.

Selberg was born in Langesund, Norway. While he was still at school he was influenced by the work of Srinivasa Ramanujan and he discovered the exact analytical formula for the partition function as suggested by the works of Ramanujan, however, this result was first published by Hans Rademacher. Selberg makes some observations about himself and Ramanujan in his Reflections Around the Ramanujan Centenary.

He studied at the University of Oslo and completed his Ph.D. in 1943.

45) Joel Spencer (born April 20, 1946) is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervision of Andrew Gleason. He is currently (as of 2007) a professor at the Courant Institute of Mathematical Sciences of New York University.

46) Robert Lee Moore (14 November 1882, Dallas, Texas – 4 October 1974 Austin, Texas) was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.

Although Moore's father was reared in New England and was of New England ancestry, he fought in the American Civil War on the side of the Confederacy. After the war, he ran a hardware store in Dallas, then little more than a railway stop, and raised six children, Robert being the fifth.

Moore entered the University of Texas at the unusually low age of 16, in 1898, already knowing calculus thanks to self-study. He completed the B.Sc. in three years instead of the usual four; his teachers included G. B. Halsted and L. E. Dickson. After a year as a teaching fellow at Texas, he taught high school for a year in Marshall, Texas.

An assignment of Halsted's led Moore to prove that one of Hilbert's axioms for geometry was redundant. When E. H. Moore (no relation), who headed the Department of Mathematics at the University of Chicago, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. Oswald Veblen supervised Moore's 1905 thesis, titled Sets of Metrical Hypotheses for Geometry.

47) Alexander Soifer is a Russian-born American mathematician and mathematics author. His works include some 200 articles, and a number of books, listed below.

Soifer received his Ph.D. in 1973.

Every spring, Soifer, along with other mathematics colleagues, sponsor the Colorado Mathematical Olympiad (CMO) at the University of Colorado at Colorado Springs. Soifer compiles (and writes some of) the problems for the contest. On April 18, 2008 CMO will turn 25.

In 1991 Soifer founded the research quarterly "Geombinatorics," and publishes it with the Editorial Board, which includes Ronald L. Graham, Branko Grunbaum, Heiko Harborth, Peter D. Johnson Jr., and Janos Pach. Paul Erdos was also an editor.

Soifer has been a professor of mathematics at the University of Colorado since 1979. He was visiting fellow at Princeton University 2002–2004, and again 2006–2007. Soifer also teaches courses on European cinema.

Soifer's Erdos number is 1.

In July 2006 at the University of Cambridge, Alexander Soifer was presented with "The Paul Erdos" Award" by the World Federation of National Mathematics Competitions.

48) Richard Kenneth Guy (born 1916, Nuneaton, Warwickshire) is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary.

He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory (ISBN 0-387-94289-0), but he has also published over 100 papers and books covering combinatorial game theory, number theory and graph theory.

He is said to have developed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them — thus explaining many coincidences and patterns found among numerous cultures.

Guy is one of the few mathematicians with an Erdos number of 1.

49) Leonhard Paul Euler April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany.

Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, optics, and astronomy.

Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master [i.e., teacher] of us all."

Euler was featured on the sixth series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian postage stamps. The asteroid 2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on May 24th - he was a devout Christian (and believer in biblical inerrancy) who wrote apologetics and argued forcefully against the prominent atheists of his time.

50) Kenneth Appel (born 1932) is a mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Appel's children, including Laurel Appel, Peter Appel, and Andrew Appel, now a professor at Princeton, helped in the checking of over 1000 topological cases that constitute this proof.

The proof has been one of the most controversial of modern mathematics because of its heavy dependence on computer "number-crunching" to sort through possibilities. Even Appel has agreed, in numerous interviews, that it lacks elegance and provided no new insight that has guided future mathematical research.

Others, however, have pointed to this work as the start of a sea-change in mathematicians' attitudes toward computers - which they had largely disdained as a tool for engineers rather than for theoreticians - leading to the creation of what is sometimes called "experimental mathematics."

From 1993 through 2002, Appel was head of the mathematics department at the University of New Hampshire in Durham, New Hampshire. Although retired now, he still works and occasionally teaches there and has an office on campus (in the new Kingsbury Hall.)

51) Wolfgang Haken (born June 21, 1928) is a mathematician who specializes in topology, in particular 3-manifolds.

In 1976 together with colleague Kenneth Appel at the University of Illinois at Urbana-Champaign, Haken solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color.

Haken has introduced several important ideas, including Haken manifolds, Kneser-Haken finiteness, and an expansion of the work of Kneser into a theory of normal surfaces. Much of his work has an algorithmic aspect, and he is one of the influential figures in algorithmic topology. One of his key contributions to this field is an algorithm to detect if a knot is unknotted.

52) Carl Pomerance (born in 1944 in Joplin, Missouri) is a well known number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number N has at least 7 distinct prime factors. He immediately joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a Distinguished Professor at Dartmouth College.

He has won many teaching and research awards, including the Chauvenet Prize in 1985, MAA's distinguished university teaching award in 1997, and the Conant Prize in 2001. He has over 120 publications to his credit, including co-authorship with Richard Crandall of Prime numbers: a computational perspective, Springer-Verlag, 2001, 2005. He is the inventor of one of the most important factorisation methods, the quadratic sieve algorithm, which was used in 1994 for the factorisation of RSA-129. He is also one of the discoverers of the Adleman-Pomerance-Rumely primality test.

His Erdos number is 1.


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