Human mathematics owes a lot to coffee – 09/06/2022 – Marcelo Viana

Hungarian mathematician Alfréd Rényi (1921–1970) is the author of many important discoveries in discrete mathematics topics, such as graph theory, combinations, and number theory. He once wrote, “When I’m unhappy, I do math to be happy. And when I’m happy, I do math to stay happy.” I think many of my colleagues sympathize with these principles.

Rainey is also indebted to the important discovery that “a mathematician is a device for turning coffee into theories” – although it is often credited to his colleague and compatriot Paul Erdos (1913-1996), another large coffee consumer and prolific coffee producer. theories. Moreover, the validity of Rényi’s law is validated by the dramatic testimony given by one other Henri Poincare (1854-1912).

In his book Science and Method, published in 1908, Poincaré describes his process of mathematical discovery. “I struggled for 15 days to prove that there could never be a job like what I have since called Fuchsian jobs. I was so clueless. Every day, I would sit at my desk and stay there for an hour or two. I would try different combinations., and didn’t get any consequences “.

But one night everything changed. “In the evening, contrary to my habit, I drank black coffee and could not sleep. Thoughts flowed incessantly. I felt them in conflict with each other, until pairs intertwine, so to speak, to form stable groups. The next morning I demonstrated the existence of a class of functions Fuchsia. All that remained was to write down the results, which only took a few hours.”

It was the starting point for one of Poincaré’s greatest contributions, the theory of functions with machine form. This name was suggested by German mathematician Felix Klein (1849-1925). Poincaré named the Fuchsia functions Lazarus Fuchs (1833–1902), when the domain is the disk, and the Kleinian functions, after Klein, in all other cases. But Klein felt that this did not do justice to the importance of his work on the subject. Ironically, Poincaré rejected his colleague’s objection, citing the great poem “Faust” by Goethe: “Name ist Schall und Rauch” (“Names are nothing but noise and smoke”, in German).

Reflecting on these and other stages of his work, he led Poincaré to distinguish the three stages of mathematical discovery: preparation, incubation and illumination.

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