## Wednesday, January 23, 2008

### Paul Langevin, David Hilbert, Hideki Yukawa: birthdays

Paul Langevin was born on 1/23/1872 in Paris. Because he was a rather important representative of French science and a science official, great physicists have encountered him at many conferences. Langevin was also a leading figure who promoted relativity in France.

The modern interpretation of diamagnetism and paramagnetism in terms of electron clouds asymmetrically or anisotropically located within atoms is due to Langevin. In statistical physics, he wrote down the Langevin equation describing Langevin dynamics. The simplest example is Brownian motion in a potential: Langevin's equation is then Newton's equation of motion with the classical potential term, a friction term, and a noise term. He also designed some ultrasound-based technology based on the piezoelectric effect (previously demonstrated by the Curie brothers) to locate submarines during the war but when the gadget was ready, the war was over.

It is a matter of rumors whether Langevin was ever dating Marie Curie. However, there is no doubt that his granddaughter and her grandson are married to each other today. ;-) Langevin was an outspoken opponent of Nazism and was removed from his chair by the Vichy government and returned there in 1944. He died in 1946.

David Hilbert was born on 1/23/1862 in Königsberg, a Russian island in Prussia. He was one of the most important mathematicians of the late 19th and early 20th century.

There's a lot of things he has done - the Hilbert space, 23 Hilbert's problems, Einstein-Hilbert action, ... Let me omit his name in each entry of this list except for the first: Hilbert class field, cube, curve, function, inequality, matrix, polynomial, series, spectrum, symbol, transform, arithmetic of ends, axioms, basis theorem, constants, irreducibility problem, Nullstellensatz, hotel paradox (where you can always add one more guest), theorem (in differential geometry), theorem 90, syzygy theorem, -style deduction problem, -Pólya conjecture, -Schmidt operator, -Smith conjecture, -Speiser theorem, principles of theoretical logic, and others.

Hilbert believed Cantor's big program of formalizing mathematicis and proving every theorem and he was religiously saddened by Gödel's results. Camille Jordan has also said that the proof of the Hilbert Basis Theorem was theology, not mathematics.

His contributions to general relativity remain questionable but I tend to think that he arrived at the desirable result kind of independently. But I also think that Einstein couldn't really plagiarize Hilbert because it would be rather difficult for Einstein to understand Hilbert's formalism. Hilbert has said that "physics is becoming too difficult for the physicists". He proposed to measure the importance of a scientific work by the number of earlier publications rendered superfluous by it. ;-)

Hermann Minkowski was Hilbert's best friend but Hilbert was surrounded by a lot of great minds in Göttingen. Emmy Noether had problems to be hired because they didn't have restrooms for women. Hilbert famously said "Meine Herren, der Senat ist doch keine Badeanstalt" (the faculty is not a pool changing room).

Hilbert has never tried to solve Fermat's Last Theorem, claiming that one needs three years to study at the beginning and he didn't have enough time to waste for a probably failure. Nevertheless, he once gave a talk about "the proof of Fermat's Last Theorem". His talk had nothing to do with it and he explained that the title was only prepared for the case that the plane crashes.

At an engineering convention, engineers worried that Hilbert could insult someone because he didn't think much about the engineers. He replied: "Don't worry. How could I possibly offend anyone if engineering and mathematics have nothing in common!" :-)

Hideki Yukawa was born in Tokyo 101 years ago, on 1/23/1907.

In 1935, he published his theory of mesons as particles that inspire the strong nuclear force between protons and neutrons, via the Yukawa potential (A.exp(-kr)/r, the 3D Fourier transform of A'/(k²+m²)). In 1947, the pion was observed and two years later, Yukawa could grab the first Japanese Nobel prize. Yukawa also predicted K-capture, i.e. absorption of an electron by the Hydrogen nucleus.

He has been the member of all kinds of societies and editorial boards. Yukawa fought against nuclear weapons, too. He died in 1981.