Many of the first scientists would now be considered madly interdisciplinary. Aristotle’s fields of study ranged from mechanics and optics to medicine and the classification of animals, not to mention philosophy and other fields outside the natural sciences. Archimedes not only was fascinated by proving mathematical principles, he also applied them to physics, astronomy, and engineering. Newton invented principles which now are part of calculus while developing his theory of motion. Leonardo da Vinchi and other known Renaissance men were notoriously broad in their fields of knowledge and investigation. Gradually, mathematicians and scientists became more specialized. Darwin focused on biology, Cauchy on mathematics, Einstein on physics, and so on. Now, we recognize some academics as experts in such fields as number theory, particle physics, or Lie groups.

Henri Poincaré was one of the last of the generation of Renaissance men. While he was principally a mathematician, some of his work extended firmly into the world of physics. On the side he was a mining engineer and a philosopher. To see how varied and numerous his contributions were, see this list of things named after him, most of which are mathematical or physical topics.

Henri Poincaré Image: Connormah via Wikimedia Commons. Public domain. |

Classical physics works very well for large objects with low speeds. In the late 1800s, physicists simultaneously realized that their understanding of the universe utterly failed to explain the behavior of small objects or fast objects. Two theories forever revolutionized our understanding of the universe: relativity, which explains fast moving objects, and quantum mechanics, which explains the behavior of very small objects like electrons. Poincaré contributed mathematically to both of them. Hendrik Antoon Lorentz derived the famous Lorentz transforms which explain relativity on a simple level. Lorentz discovered the Lorentz transforms without collaborating with Poincaré. However, Poincaré did critique Lorentz’ papers and offer additional input, ideas, and encouragement. It was this relationship with Lorentz that would later lead Poincaré into quantum mechanics.

Out of quantum mechanics and relativity, quantum mechanics has by far influenced the world more. It contributed to several major developments, including the understanding of atoms, nuclear power, and semiconductors. Of course, to semiconductors we owe much of our modern society. The development of the transistor would not have been possible without quantum mechanics. Transistors enabled the building of modern computers, cell phones, and the Internet.

For these reasons, Poincaré’s contributions to quantum mechanics are among his most important contributions to math and science. Poincaré was invited to the first Solvay Conference in 1911 on quantum theory by Lorentz. This appears to be the first time Poincaré was exposed to this new theory. In spite of this, his energetic participation in the discussions at the conference were noted by the other participants. In that conference, Max Planck presented a new theory about black body radiation.

Participants in the First Solvay Conference, 1911. Image: Fastfission via Wikimedia Commons. Public domain. |

Black body radiation simply refers to the light given off by all objects as they cool. By 1911, enough experiments had been done that the wavelengths of light emitted from black bodies of different temperatures were known. However, classical physics failed to explain these results. Plank attempted to explain them by introducing the idea of “resonators” which could produce electromagnetic radiation. Although Planck didn’t consider matter to be made up of these resonators, this is a natural extension of his theory. Poincaré thought of this and questioned how Planck’s theory could explain the transfer of heat within an object. He quickly got to work rederiving Planck’s result and putting it on a more solid theoretical ground. In keeping with quantum theory, his reasoning used probability rather than absolute knowledge about particles. He did arrive at the same result as Planck, although he was more rigorous in doing so:

Unfortunately, just eight months after the First Solvay conference, Henri Poincaré passed away without living to see the impact his research would have on math and physics.

## References

McCormmach, Russell (Spring 1967), “Henri Poincaré and the Quantum Theory”, Isis 58 (1): 37-55, doi:10.1086/350182

Plank’s Law on Wikipedia

Henri Poincaré on Wikipedia

Poincaré’s original paper on Planck’s theory (in French) can be seen here.