Descartes' visual revolution

Amateur mathematics, for the pleasure of research

Y Is there a place for amateurs in mathematical research? We quote many famous amateurs, but often it is in distant history. Pierre de Fermat (1607–1665)For example, one of the greatest arithmeticians of all time was a judge in Toulouse and practiced mathematics as a hobby. But it was on the 17the century.

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There is also the case of Srinivasa Ramanujan, this genius, born in India in 1887, who discovered an incredible number of mathematical wonders in total scientific isolation. In 1914 he sent a letter to Professor Hardy of Cambridge, who wrote it later“A single glance at these formulas was enough to realize that they could only have been devised by a mathematician of the first rank”. But all this happened a century ago. Is Ramanujan still possible today?

Mathematics has become so complex and specialized that it is inaccessible to the general public. Mathematicians who risk being popularized know very well that they can only recall certain results, the easiest ones, usually very old ones, which do not really represent the core of their field. This creates a certain frustration among the research community, which tends to lock itself in its ivory tower and behave as if it were ‘misunderstood’. However, there is an undeniable demand from the public that we must try to respond to.

The duty to respond

I receive many letters from amateurs presenting their mathematical discoveries. The themes discussed are almost always the same. First, there are “solutions” to squaring the circle or “proofs” of Euclid’s fifth postulate, which we have known for more than a century to be impossible. But there is also evidence for the Riemann hypothesis or even solutions to the Syracuse conjecture, which seem to arouse the curiosity of amateurs. The situation is then different, because it is not impossible, although very unlikely, that these letters contain correct evidence. It should be added that these manuscripts are often very long and consist of incomprehensible sequences of formulas.

Finding an error in such a mess takes a lot of time. Worse still, the simple act of pointing out an error almost always results in a new “corrected” version by return post. Should we ignore these types of letters, as most of my colleagues do, at the risk of further separating the research community from the general population? Don’t we have a duty to respond? Can I pretend not to be interested in the result, when a proof of the Riemann hypothesis would delight me? I often recommend, in a somewhat hypocritical way, that the manuscript be sent to a scientific journal, but it is not uncommon for these amateurs to refuse to submit their discoveries to journals for fear that they will not be published.

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