The Man Who Loved Only Numbers - Part3

Just now i finished reading The Man Who Loved Only Numbers by Paul Hoffman.

Actually as said previously 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 3rd chapter.

1) 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 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.

2) László Lovász (born March 9, 1948 in Budapest, Hungary) is a mathematician, best known for his work in combinatorics, for which he was awarded the Wolf Prize and the Knuth Prize in 1999.

In high school, Lovasz won gold medals at the International Mathematical Olympiad (in years 1964, 1965, 1966) and so did his son in 2008 [1].

Lovász received his Ph.D. in 1970 at Hungarian Academy of Sciences. His advisor was Tibor Gallai.

Lovász was a professor at Yale University during the 1990s and was a collaborative member of the Microsoft Research Center until 2006. Now he has returned to Eötvös Loránd University, Budapest, where he is the director of the Mathematical Institute.

He has served as president of the International Mathematical Union since January 1, 2007[3].

Lovász was awarded the Bolyai prize in 2007 and Hungary's Széchenyi Grand Prize (2008).

He has an Erdos number of 1.

3) Herbert Saul Wilf (born 1931) is a mathematician, specializing in combinatorics. He is the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He has written numerous books, research papers, and is a popular speaker.

H. S. Wilf is the author of numerous papers and books, and has been adviser and mentor to many students and colleagues. His collaborators include Doron Zeilberger and Donald Knuth. One of Wilf's former students is Richard Garfield, the creator of the collectible card game Magic: The Gathering. He also served as a thesis advisor for E. Roy Weintraub in the late 1960s.

Herbert Wilf is well known for writing generatingfunctionology.

4) Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages".

Fibonacci is best known to the modern world for:

The spreading of the Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.

A modern number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.

5) Al-Khwarizmi was a Persian mathematician, astronomer, astrologer and geographer. He was born around 780 in Khwarizm, then part of the Persian Empire and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra, a title he shares with Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the twelfth century. He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book.

6) Ernst Gabor Straus (February 25, 1922 – July 12, 1983) was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions. His extensive list of co-authors includes Albert Einstein and Paul Erdos as well as other notable researchers including Richard Bellman, Bela Bollobas, Sarvadaman Chowla, Ronald Graham, Laszlo Lovasz, Carl Pomerance, and George Szekeres. It is due to his collaboration with Straus that Einstein has Erdos number 2.

Straus was born in Munich, Germany, February 25, 1922, the youngest of five children of a prominent attorney, Eli Straus, and his wife Rahel Straus née Goitein, a medical doctor and feminist. Ernst Gabor Straus became known as a mathematical prodigy from a very young age. Following the death of his father, the family fled the Nazi regime for Palestine in 1933, and Straus was educated at the Hebrew University in Jerusalem. Despite never receiving an undergraduate degree, he began graduate studies at Columbia University in New York, earning a Ph.D. in 1948 under the advisement of F. J. Murray. Two years later, he then became the assistant of Albert Einstein. After a three-year stint at the Institute for Advanced Study, Straus took a position at the University of California, Los Angeles, which he kept for the rest of his life. Straus died July 12, 1983 of heart failure.

Straus's interests ranged widely over his career, beginning with his early work on relativity with Einstein and continuing with deep work in analytic number theory, extremal graph theory, and combinatorics. One of his best known contributions in popular mathematics is the Erdos–Straus conjecture on Egyptian fractions for numbers of the form 4/n.

7) 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.

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, 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).

8) 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. (In the end, the answer was "no", in general.)

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.

Hope you enjoy reading this book.