Person: Pólya, George
Pólya worked in probability, analysis, number theory, geometry, combinatorics and mathematical physics.
Mathematical Profile (Excerpt):
- Perhaps we should say a little about George Pólya's names, for the situation is not quite as it appears.
- Before that his name had been Jakab Pollák but, in order to understand why Jakab Pollák changed his name to Pólya, we need to look at both his career and at a little Hungarian history.
- He did just that in 1882 and whether it contributed to his success in getting an appointment as a Privatdozent at the University of Budapest, one cannot say but he received such a post shortly before he died in his early fifties when George was ten years old.
- Although George's parents were Jewish, he was baptized into the Roman Catholic Church shortly after his birth.
- It is worth pointing out that Jenö, who loved mathematics and always regretted not having pursued that subject, is perhaps as well known to medical people as George is to mathematicians.
- At school Pólya's favourite subjects were biology and literature and in this latter subject he received "outstanding" grades as he did in geography and other subjects.
- It is rather unusual that someone who went on to spend their life being so fascinated by so many different branches of mathematics should not have fallen in love with the subject at school but in Pólya's case this is exactly what happened.
- At the University of Budapest Pólya was taught physics by Eötvös and mathematics by Fejér.
- Pólya left Göttingen in rather unfortunate circumstances.
- From the wide range of mathematical stars that Pólya had met the mathematician who was the greatest influence on him was Hurwitz.
- In Zürich, in addition to Hurwitz, Pólya had Geiser, Bernays, Zermelo and Weyl as colleagues.
- Life became more difficult as the war progressed, however, since the Hungarian army, becoming more desperate for soldiers as the war progressed, required Pólya to return to Hungary, to join the army, and to fight for his country; he refused.
- This did have the consequence that it would be many years after the war ended before Pólya was able to return to Hungary without fear of arrest for failing to undertake war service.
- Although it is difficult to see why he waited so long, Pólya did not return to Hungary until 1967, 54 years after his last visit to his native land.
- Pólya first met Szegő on Budapest in around 1913 when he returned there between his various studies abroad.
- Szegő at this time was a student at Budapest and Pólya discussed a conjecture he had made on Fourier coefficients with Szegő.
- Szegő went on to prove Pólya's conjecture and this became his first publication.
- When several years later Pólya decided to write a problem book on analysis he knew that it was not a task he could accomplish without help, so he turned to Szegő and over a number of years the two assembled a wonderful collection of problems.
- What was the great novelty which made Pólya and Szegő's book of analysis problems so different?
- It was Pólya's idea to classify the problems not by their subject, but rather by their method of solution.
- Pólya and Szegő approached the publisher Springer in 1923 with their idea for a two volume work and in 1925 Aufgaben und Lehrsätze aus der Analysis Ⓣ(Problems and theorems from calculus) appeared.
- Pólya had been promoted to extraordinary professor at ETH in Zürich in 1920.
- While the book was being worked on, Pólya continued a remarkable series of publications, with a total of 31 papers appearing during the three years 1926-28.
- In 1933 Pólya was awarded a second Rockefeller Fellowship, this time to allow him to visit Princeton.
- Before going to the United States Pólya had a draft of a book How to solve it written in German.
- Pólya published further books on the art of solving mathematical problems.
- While we are looking at Pólya's contributions to teaching, and many people consider this to be his greatest contribution to mathematics, let us give some further quotes from Pólya on this topic.
- Let us briefly discuss some of the research which Pólya carried out in many different areas of mathematics.
- In probability Pólya looked at the Fourier transform of a probability measure, showing in 1923 that it was a characteristic function.
- Geometric symmetry and the enumeration of symmetry classes of objects was a major area of interest for Pólya over many years.
- Pólya's work using generating functions and permutation groups to enumerate isomers in organic chemistry was of fundamental importance.
- A whole new area of graph theory called enumerative graph theory grew up based on Pólya's ideas.
- Pólya's interest in complex analysis led him to investigate singularities of power series, gap theorems, power series with integral coefficients and those taking integral values at the positive integers, the Pólya representation for entire functions of exponential type, and the location of zeros.
- In 1953 Pólya retired from Stanford, but continued with an exceedingly active mathematical life particularly concerning himself with mathematical education.
Born 13 December 1887, Budapest, Hungary. Died 7 September 1985, Palo Alto, California, USA.
View full biography at MacTutor
Tags relevant for this person:
Astronomy, Origin Hungary
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive