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Encyclopedia > George Pólya

George Pólya (December 13, 1887 - September 7, 1985, in Hungarian Pólya György) was a mathematician, who was born in Budapest, Hungary and died in Palo Alto, USA. December 13 is the 347th day of the year (348th in leap years) in the Gregorian calendar. ... 1887 is a common year starting on Saturday (click on link for calendar). ... September 7 is the 250th day of the year (251st in leap years). ... 1985 is a common year starting on Tuesday of the Gregorian calendar. ... A mathematician is a person whose area of study and research is mathematics. ... Budapest (pronounced or ), the capital city of Hungary and the countrys principal political, industrial, commercial and transportation centre, has more than 1. ... Downtown Palo Alto Palo Alto is a city in Santa Clara County, in the San Francisco Bay Area of California, USA. Palo Alto is located at the northern end of the Silicon Valley, and is home to Stanford University (which is technically located in an adjacent area — Stanford, California), and...

He worked on a great variety of mathematical topics, including series, number theory, combinatorics, and probability. In mathematics, a series is a sum of a sequence of terms. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... The word probability derives from the Latin probare (to prove, or to test). ...

In his later days, he spent considerable effort on trying to characterize the general methods that we use to solve problems, and to describe how problem-solving should be taught and learned. He wrote three books on the subject: How to Solve It, Mathematics of Plausible Reasoning Volume I: Induction and Analogy in Mathematics, and Mathematics of Plausible Reasoning Volume II: Patterns of Plausible Reasoning. George Polyas 1945 book How to Solve It (ISBN 0691080976) is a small volume describing methods of problem-solving. ...

In How to Solve It, Pólya provides general heuristics for solving problems of all kinds, not simply mathematical ones. The book includes advice for teaching students mathematics and a mini-encyclopedia of heuristic terms. It was translated into several languages and has sold over a million copies. Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book. For heuristics in computer science, see heuristic (computer science) Heuristic is the art and science of discovery and invention. ... The word physicist should not be confused with physician, which means medical doctor. ... Zhores Ivanovich Alferov (also Alfyorov) (Russian: Жоре́с Ива́нович Алфёров) (born March 15, 1930) is a Soviet/Russian physicist with a Belarusian origin. ... List of Nobel Prize laureates in Physics from 1901 to the present day. ... 2000 is a leap year starting on Saturday of the Gregorian calendar. ...

In Mathematics of Plausible Reasoning Volume I, Pólya discusses inductive reasoning in mathematics, by which he means reasoning from particular cases to the general rule. (He also includes a chapter on the technique called mathematical induction, but that technique is not his main theme.) In Mathematics of Plausible Reasoning Volume II, he discusses more general forms of inductive logic that can be used to roughly determine to what degree a conjecture (in particular, a mathematical conjecture) is plausible. This article is about induction in philosophy and logic. ... Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers, or otherwise is true of all members of an infinite sequence. ... This article is about induction in philosophy and logic. ...

Some quotes:

  • How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics. (This is a mnemonic for the first fourteen digits of π, the lengths of the words are the digits)
  • If you can't solve a problem, then there is an easier problem you can solve: find it.

Fig. ... The minuscule, or lower-case, pi The mathematical constant π represents the ratio of a circles circumference to its diameter and is commonly used in mathematics, physics, and engineering. ...

See also

Burnsides lemma, sometimes also called Burnsides counting theorem, Pólyas formula or Cauchy-Frobenius lemma, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects. ... In mathematics, the Hilbert-Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory. ...

External links

  • http://www.cis.usouthal.edu/misc/polya.html
  • Biography (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Polya.html) at the MacTutor archive



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