**Paul Ehrenfest** was an Austrian mathematician who made important contributions to statistical mechanics and quantum mechanics.

- Johanna Ehrenfest worked long hours in their shop and Paul was looked after at home by a nursemaid.
- By the time he was six years old Paul could read, write and count.
- In 1890 Paul began his secondary education at the Akademisches Gymnasium.
- Ehrenfest became a student at the Technische Hochschule in Vienna in October 1899.
- Ehrenfest attended Boltzmann's lectures on the mechanical theory of heat during 1899-1900.
- In 1901 Ehrenfest moved to Göttingen where he studied under Klein and Hilbert.
- While attending courses by Klein and Hilbert, Ehrenfest saw a young Russian student of mathematics Tatyana Alexeyevna Afnassjewa.
- Ehrenfest challenged this rule and, after quite a battle, was able to get the rule changed.
- Ehrenfest returned to Vienna after spending eighteen months in Göttingen.
- It was considered a good piece of work but Ehrenfest himself never rated it very highly and chose not to publish it after receiving his doctorate on 23 June 1904.
- In 1905 Ehrenfest published a paper on Planck's theory of black-body radiation.
- shows Ehrenfest's real interests and particular talents and the beginning of his personal style.
- Ehrenfest took on the task of writing his obituary.
- Klein, Hilbert, Minkowski and Carathéodory were all working in Göttingen at this time and it was an important period for Ehrenfest's research.
- The two Ehrenfests began working on the article which would not appear in print until 1911.
- In 1907 Ehrenfest went to St Petersburg.
- Certainly Ehrenfest had mixed feelings about his own country given the anti-Semitic attitudes he had encountered.
- The Ehrenfests spent five years in St Petersburg.
- It was a time when Ehrenfest was deeply engrossed in research problems.
- He corresponded with Klein who told him that what was required was a survey, not a complete solution of all the problems of the subject by Ehrenfest himself.
- In the hope that this might lead to an academic post Ehrenfest, despite holding a doctorate, took the degree of Master of Physics at St Petersburg.
- An important paper was published by Ehrenfest in 1911 in Annalen der Physik on the essential features of quantum theory.
- In January 1912 Ehrenfest set out on a tour of universities in the German speaking world in the hope of a position.
- Poincaré had not known of Ehrenfest's contribution and therefore had not referred to his work.
- Ehrenfest returned to St Petersburg saddened that Poincaré's paper had been published before he could point out his own contribution to him -- he was paying the price for being isolated from mainstream research in St Petersburg.
- On 29 September 1912 Ehrenfest received a telegram saying that he had been named professor at Leiden.
- In 1917 and 1920 Ehrenfest published papers investigating the problem of the extent to which the three-dimensional nature of physical space is determined by the structure of basic physical equations or is reflected in these basic equations.
- Ehrenfest's arguments were based both on Newton's celestial mechanics and also on Einstein's relativity theory.
- Among Ehrenfest's contributions to quantum statistics was an understanding of the nature of photons, and their properties which were implied by Planck's radiation law.
- The modern theory of nonequilibrium thermodynamics brings together the molecular, collisional ideas of Boltzmann with the statistical ideas of Ehrenfest's to give a nonlinear, statistical theory.
- In 1933 Ehrenfest presented a classification of phase transitions based on the discontinuity in derivatives of the free energy function.
- Uhlenbeck was a student of Ehrenfest who began research for his Master's degree in 1920.
- Niels Bohr and Ehrenfest began to correspond in 1918.
- Their exchanges ranged over heaven and earth as Ehrenfest showed his new friend the treasures of the Dutch museums and the brilliant colours of the bulb fields.
- Ehrenfest presented Bohr's results to the third Solvay conference in 1921.
- Later in 1921 Bohr invited Ehrenfest to Copenhagen.
- Ehrenfest was unhappy at the disagreement between Bohr and Einstein over quantum theory.
- They did not and Ehrenfest was very unhappy that he was forced to take sides with one of his two close friends.
- All through his life Ehrenfest had suffered from low self esteem, which was in marked contrast to the high esteem in which he was held by his fellow scientists.
- Ehrenfest shot Wassik in the waiting room of the Professor Watering Institute in Amsterdam where Wassik was being treated.

Born 18 January 1880, Vienna, Austria. Died 25 September 1933, Leiden, Netherlands.

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Origin Austria, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive