The Man Who Loved Only Numbers - Part2

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 2nd chapter and also about great people mentioned in this book.

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

1) Ramsey theory, named for Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory typically ask a question of the form: how many elements of some structure must there be to guarantee that a particular property will hold?

Examples:

Suppose, for example, that we know that n pigeons have been housed in m pigeonholes. How big must n be before we can be sure that at least one pigeonhole houses at least two pigeons? The answer is the pigeonhole principle: if n > m, then at least one pigeonhole will have at least two pigeons in it. Ramsey's theory generalizes this principle as explained below.

A typical result in Ramsey theory starts with some mathematical structure, which is then cut into pieces. How big must the original structure be, in order to ensure that at least one of the pieces has a given interesting property?

For example, consider a complete graph of order n; that is, there are n vertices and each vertex is connected to every other vertex by an edge. A complete graph of order 3 is called a triangle. Now color every edge red or blue. How large must n be in order to ensure that there is either a blue triangle or a red triangle? It turns out that the answer is 6. See the article on Ramsey's theorem for a rigorous proof.

2) Frank Plumpton Ramsey (February 22, 1903 – January 19, 1930) was a British mathematician who, in addition to mathematics, made significant contributions in philosophy and economics.

He was born on 22 February 1903 in Cambridge where his father, also a mathematician, was President of Magdalene College. He was the eldest of one brother and two sisters, and his brother Michael Ramsey later became Archbishop of Canterbury. He entered Winchester College in 1915 and later returned to Cambridge to study mathematics at Trinity College. Easy-going, simple and modest, Ramsey had many interests besides his scientific work. Even as a teenager Ramsey showed both his profound abilities and the heterogeneity of the issues that concerned him. His brother Lord Ramsey was well aware of both these facts:

Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy’s Hospital in London at the age of 26.

3) László Babai (called Laci by friends and colleagues), born July 20, 1950 in Budapest, is a Hungarian professor of mathematics and computer science at the University of Chicago. His research focuses on computational complexity theory, algorithms, combinatorics, and finite groups, with an emphasis on the interactions between these fields. He is the author of over 150 academic papers.

His notable accomplishments include the introduction of interactive proof systems, the introduction of the term Las Vegas algorithm, and the introduction of group theoretic methods in graph isomorphism testing

He received his doctorate from the Hungarian Academy of Sciences in 1975.

He is editor-in-chief of the refereed online journal Theory of Computing.

Babai was also involved in the creation of the Budapest Semesters in Mathematics program and first coined the name.

His Erdos number is one.

Honors

Gödel Prize for outstanding papers in the area of theoretical computer science (1993)
Llewellyn John and Harriet Manchester Quantrell Award for Excellence in Undergraduate Teaching (June 2005).

4) John L. Selfridge is an American mathematician who has contributed to the field of analytic number theory. He co-authored 14 papers with Paul Erdos (giving him an Erdos number of 1).

Selfridge received his Ph.D. in 1958 from the University of California, Los Angeles under the supervision of Theodore Motzkin.

In 1962, he proved that 78,557 is a Sierpinski number; he showed that, when k=78,557, all numbers of the form k2n+1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. Five years after, he and Sierpinski proposed (but could not prove) the conjecture that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem. A distributed computing project called Seventeen or Bust is currently trying to proove this statement, at this moment 6 from the original 17 possibilities remain.

Selfridge served on the faculties of the University of Illinois at Urbana-Champaign and Northern Illinois University, chairing the Department of Mathematical Sciences for several years. He was executive editor of Mathematical Reviews from 1978 to 1986, overseeing the computerization of its operations. He was a founder of the Number Theory Foundation , which has named its Selfridge prize in his honour.

5) In number theory, a Sierpinski number is an odd natural number k such that integers of the form k2n + 1 are composite (i.e. not prime) for all natural numbers n.

In 1960 Waclaw Sierpinski proved that there are infinitely many odd integers that when used as k produce no primes.

In 1962, John Selfridge proved that 78,557 is a Sierpinski number; he showed that, when k=78,557, all numbers of the form k2n+1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}.

6) Arthur Harold Stone (September 30, 1916 – August 6, 2000) was a British mathematician born in London, who worked mostly in topology. His wife was American mathematician Dorothy Maharam. His first paper dealt with squaring the square. He proved the Erdos-Stone theorem with Paul Erdos. The Stone's metrization theorem has been named after him. Not to be confused with American mathematician Marshall Harvey Stone.

7) Dorothy Maharam Stone is an American mathematician who made important contributions to measure theory. Her husband was British mathematician Arthur Harold Stone.

She earned her B.S. degree at Carnegie Institute of Technology in 1937 and graduated from Bryn Mawr College with a dissertation entitled On measure in abstract sets. Part of her thesis was published in Transactions of AMS. Then she went on to a postdoc at Institute for Advanced Study in Princeton, where she first met Arthur Harold Stone. They married in April 1942.

She pioneered the research of finitely additive measures on integers.

They both lectured at various universities in the USA and Great Britain. Their two children, David and Ellen, have both become mathematicians as well.

She retired in 2001. Her husband, Arthur Stone, died August 6, 2000.

8) 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-Rényi 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.

9) Mark Kac was a Ukrainian and American mathematician of Jewish ancestry.His main interest was probability theory. His question, "Can you hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry.

Kac completed his Ph.D. in mathematics at the University of Lwów in 1937 under the direction of Hugo Steinhaus. While there, he was a member of the Lviv School of Ukrainian mathematics. After receiving his degree he began to look for a position abroad, and in 1938 was granted a scholarship from the Parnas Foundation which enabled him to go work in the United States. He fled dictator-ruled militaristic and anti-Semitic Poland and arrived in New York City in November, 1938. From 1939 until 1961 he was at Cornell University, first as an instructor, then from 1943 as assistant professor and from 1947 as full professor. While there, he became a naturalized US citizen in 1943. In 1961 he left Cornell and went to Rockefeller University in New York City. After twenty years there, he moved to the University of Southern California where he spent the rest of his career.

10) Kurt Gödel (April 28, 1906, Brünn, Austria-Hungary (now Brno, Czech Republic) – 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.

In later life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he wouldn't eat unless his wife, Adele, tasted his food for him. Late in 1977, Adele was hospitalized for six months and could not taste Gödel's food anymore. In her absence, he refused to eat, eventually starving himself to death. He was 65 pounds when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.

11) 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.

12) Michael Golomb (May 3, 1909 in Munich – April 9, 2008) was an American mathematician and educator who was affiliated with Purdue University for over half a century. He was a student of Erhard Schmidt and Adolf Hammerstein, and received his doctorate from the University of Berlin in 1933. However, as a Jew, he had to leave Germany shortly afterwards to avoid Nazi persecution. After a short period in Zagreb in the former Yugoslavia, Michael Golomb arrived in the U.S. in 1939, when he turned to applied mathematics. He was one of the first mathematicians to apply normed vector spaces in numerical analysis. He taught mathematics at Purdue University from 1942 until his retirement in 1975, at times holding joint appointment with the Schools of Engineering. He continued to teach as Professor Emeritus.

In 1998 in Berlin, Michael Golomb was honored as part of a special exhibition entitled "Terror and Exile: Persecuted and expelled Berlin mathematicians in the time of the Nazi regime." The exhibition was organized by the city of Berlin to coincide with the International Congress of Mathematicians there. His Erdos number is 1.

13) John von Neumann (December 28, 1903 – February 8, 1957) was a Hungarian American mathematician who made major contributions to a vast range of fields[2] including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics (of explosions), and statistics, as well as many other mathematical fields. He is generally regarded as one of the foremost mathematicians of the 20th century. The mathematician Jean Dieudonne called von Neumann "the last of the great mathematicians." Most notably, von Neumann was a pioneer of the application of operator theory to quantum mechanics, 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 and the universal constructor. Along with Edward Teller and Stanislaw Ulam, von Neumann worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

The oldest of three brothers, von Neumann was born Neumann János Lajos (in Hungarian the family name comes first) in Budapest, Hungary, to a wealthy non-practicing Jewish family. His father was Neumann Miksa (Max Neumann), a lawyer who worked in a bank. His mother was Kann Margit (Margaret Kann). Von Neumann's ancestors had originally immigrated to Hungary from Russia.

Johnny, was a prodigy who showed aptitudes for languages, memorization, and mathematics.

The IEEE John von Neumann Medal is awarded annually by the IEEE "for outstanding achievements in computer-related science and technology."

Von Neumann, a crater on Earth's Moon, is named after John von Neumann.

The professional society of Hungarian computer scientists, John von Neumann Computer Society, is named after John von Neumann.

14) Shizuo Kakutani (August 28, 1911–August 17, 2004) was a Japanese mathematician, best known for his eponymous fixed-point theorem.

Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujiro Shimizu. Early in his career he spent two years at the Institute for Advanced Study in Princeton at the invitation of the German mathematician Hermann Weyl. While there, he also met John von Neumann.

Kakutani received his Ph.D. in 1941 from Osaka University and taught there through World War II. He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale in 1949.

His daughter, Michiko Kakutani, is a Pulitzer Prize-winning literary critic for the New York Times.

15) Richard Phillips Feynman was an American physicist known for the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, as well as work in particle physics (the parton model was proposed by him). For his contributions to the development of quantum electrodynamics, Feynman was a joint recipient of the Nobel Prize in Physics in 1965, together with Julian Schwinger and Sin-Itiro Tomonaga. Feynman developed a widely-used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams.

He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing, and introducing the concept of nanotechnology (creation of devices at the molecular scale). He held the Richard Chace Tolman professorship in theoretical physics at Caltech.

16) Martin Gardner (b. October 21, 1914, Tulsa, Oklahoma) is a popular American mathematics and science writer specializing in recreational mathematics, but with interests encompassing magic (conjuring), pseudoscience, literature (especially Lewis Carroll), philosophy, and religion. He wrote the "Mathematical Games" column in Scientific American from 1956 to 1981 and has published over 70 books.

Gardner coined the term mathemagician.

17) Edward Teller (January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he claimed that he did not care for the title.

Teller is best known for his work on the American nuclear program, specifically as a member of the Manhattan Project during World War II, his role in the development of the hydrogen bomb, and his long association with Lawrence Livermore National Laboratory (which he co-founded and served as a director). He invited contention in the 1950s by his controversial testimony in the security clearance hearing of his former Los Alamos colleague Robert Oppenheimer, and thus became ostracized by much of the scientific community. He continued to find support from the U.S. government and military research establishment, particularly for his advocacy for nuclear energy development, a strong nuclear arsenal, and a vigorous nuclear testing program.

18) Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin – 26 July 1925, Bad Kleinen, Germany) was a German mathematician who became a logician and philosopher. He helped found both modern mathematical logic and analytic philosophy. His work had a far-reaching and foundational influence on 20th-century philosophy.

Frege was born in 1848 in Wismar, in the state of Mecklenburg-Schwerin (the modern German federal state Mecklenburg-Vorpommern). His father, Karl Alexander Frege, was the founder of a girls' high school, of which he was the headmaster until his death in 1866. Afterwards, the school was led by Frege's mother, Auguste Wilhelmine Sophie Frege (née Bialloblotzky, apparently of Polish extraction).

19) Jean le Rond d'Alembert – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. He was also co-editor with Denis Diderot of the Encyclopédie. D'Alembert's method for the wave equation is named after him.

D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an annuity of 1200 livres on his death in 1726. Under the influence of the Destouches family, at the age of twelve D'Alembert entered the jansenist Collège des Quatre-Nations (the institution was also known under the name "Collège Mazarin"). Here he studied philosophy, law, and the arts, graduating as bachelier in 1735. In his later life, D'Alembert scorned the Cartesian principles he had been taught by the Jansenists: "physical premotion, innate ideas and the vortices".

20) Nikolai Ivanovich Lobachevsky (December 1, 1792–February 24, 1856 November 20, 1792–February 12, 1856 (O.S.)) was a Russian mathematician.

Lobachevsky was born in Nizhny Novgorod, Russia. His parents were Ivan Maksimovich Lobachevsky, a clerk in a landsurveying office, and Praskovia Alexandrovna Lobachevskaya. In 1800, his father died and his mother moved to Kazan. In Kazan, Lobachevsky attended Kazan Gymnasium, graduating in 1807 and then Kazan University which was founded just three years earlier, in 1804.

At Kazan University, Lobachevsky was influenced by professor Johann Christian Martin Bartels (1769–1833), a former teacher and friend of German mathematician Carl Friedrich Gauss. Lobachevsky received a Master's degree in physics and mathematics in 1811. In 1814, he became a lecturer at Kazan University, and in 1822 he became a full professor. He served in many administrative positions and was the rector of Kazan University from 1827 to 1846. He retired (or was dismissed) in 1846, after which his health rapidly deteriorated. In addition to teaching mathematics and physics at Kazan University Lobachevsky also taught astronomy.

In 1832, he married Varvara Alexivna Moisieva. They had seven children.

21) Georg Friedrich Bernhard Riemann September 17, 1826 – July 20, 1866) was a German mathematician who made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity.

Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is today Germany. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother died before her children were grown. Riemann was the second of six children, shy, and suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age, but suffered from timidity and a fear of speaking in public.

In high school, Riemann studied the Bible intensively, but his mind often drifted back to mathematics. He even tried to prove mathematically the correctness of the Book of Genesis. His teachers were amazed by his genius and his ability to solve extremely complicated mathematical operations. He often outstripped his instructor's knowledge. In 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school). After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg. In 1846, at the age of 19, he started studying philology and theology in order to become a priest and help with his family's finances.

Bernhard Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein's general relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following Dirichlet's death, he was promoted to head the mathematics department at Göttingen. He was also the first to propose the theory of higher dimensions[citation needed], which greatly simplified the laws of physics. In 1862 he married Elise Koch and had a daughter. He died of tuberculosis on his third journey to Italy in Selasca (now a hamlet of Ghiffa on Lake Maggiore).

22) Alfred North Whitehead, OM (February 15, 1861, Ramsgate, Kent, England – December 30, 1947, Cambridge, Massachusetts, U.S.) was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education. He co-authored the epochal Principia Mathematica with Bertrand Russell.

Between 1880 and 1910, Whitehead studied, taught, and wrote mathematics at Trinity College, Cambridge, spending the 1890s writing his Treatise on Universal Algebra (1898) and the 1900s collaborating with his former pupil, Russell, on the first edition of Principia Mathematica.

23) Hermann Minkowski (June 22, 1864 – January 12, 1909) was a Russian-born German mathematician, of Jewish and Polish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.

Hermann Minkowski was born in Aleksotas (at the time a suburb of Kaunas, Lithuania, Russian Empire) to a family of Jewish and Polish descent. He was educated in Germany at the Albertina University of Königsberg, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences for his manuscript on the theory of quadratic forms.