Meet A Great Mathematician, Little Known To The General Public, That I Admire : Mr. Paul ErdősSubmitted by Cyril on Wed, 04/17/2013 - 08:40
(I had first heard about his name through his theorems, but, as often, didn't look until late into who he was, or what was his life, etc. I wasn't disappointed by who I found after looking him up eventually...)
From Wikipedia, which has good introductory content about him and references to his works - enjoy learning about his posterity:
"Paul Erdős (26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős worked with hundreds of collaborators, pursuing problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He was also known for his eccentric personality.
His parents were both Jewish mathematicians from a vibrant intellectual community. His fascination with mathematics developed early—at the age of four, he could calculate in his head how many seconds a person had lived, given their age. Both of Erdős's parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős 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, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry. In 1934, at the age of 21, he was awarded a doctorate in mathematics.
Second Most Prolific Mathematician, after Euler
Erdős was one of the most prolific publishers of papers in mathematical history, comparable only with Leonhard Euler; Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself. He wrote around 1,525 mathematical articles in his lifetime, mostly with co-authors. He strongly believed in and practiced mathematics as a social activity, having 511 different collaborators in his lifetime.
An Outstanding Problem Solver
In terms of mathematical style, Erdős was much more of a "problem solver" than a "theory developer". (See "The Two Cultures of Mathematics" by Timothy Gowers for an in-depth discussion of the two styles, and why problem solvers are perhaps less appreciated.) Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career." Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did, a pattern that extends to other prizes.
Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life as a vagabond, traveling 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 (Erdős) should visit next.
His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems", and Erdős drank copious quantities. (This quotation is often attributed incorrectly to Erdős, but Erdős himself ascribed it to Rényi.) 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. Erdős won the bet, but complained that during his abstinence 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 use.
All countries which he thought failed to provide freedom to individuals as long as they did no harm to anyone else were classified as imperialist and given a name that began with a lowercase letter. For example, the U.S. was "samland" (after Uncle Sam), the Soviet Union was "joedom" (after Joseph Stalin), and Israel was "isreal". For his epitaph he suggested, "I've finally stopped getting dumber.""
Paul Erdős :
Finally, one of the coolest theorems from him among my all time favorites:
The Erdős–Kac theorem
"[...]Stated somewhat heuristically, what Erdős and Kac proved was that if n is a randomly chosen large integer, then the number of distinct prime factors of n has approximately the normal distribution with mean and variance log log n.
This means that the construction of a number around one billion requires on average three primes. For example 1,000,000,003 = 23 × 307 × 141623.
Around 12.6% of 10,000 digit numbers are constructed from 10 distinct prime numbers and around 68% (±σ) are constructed from between 7 and 13 primes.
A hollow sphere the size of the planet Earth filled with fine sand would have around 10^33 grains. A volume the size of the observable universe would have around 10^93 grains of sand. There might be room for 10^185 quantum strings in such a universe.
Numbers of this magnitude—with 186 digits—would require on average only 6 primes for construction.[...]"