Is it true that the Spanish mathematician Valmes was burned by the Inquisition for solving fourth-degree equations?

According to published information, the scientist, having informed the Grand Inquisitor Torquemada about his discovery, went to prison and was then executed. We checked whether a similar story took place in reality.

This is what the Soviet magazine reported:Technology for youth" in 1971: “The clerics of the Middle Ages declared the equation of the fourth degree to be a mystery of God, which is inaccessible to the human mind. In 1486, in the city of Toledo (Spain), the mathematician Paolo Valmes met with his friends the Grand Inquisitor Torquemada, who was also a lover of mathematics. We were talking about solving a fourth degree equation. When Valmes stated that he had solved this equation in a very simple way, Torquemada did not object to him, but that same night Valmes was thrown into the dungeon of the Inquisition for “fighting the divine will,” and a week later he was burned at the stake, without having time to tell anyone the essence of his discovery. This is just one of many cases of the church’s brutal reprisals against leading scientists.”

This information has found wide distribution in a wide variety of literature, from popular science to methodological. In particular, you can read about the unenviable fate of the mathematician Valmes in the books of the prominent Soviet popularizer of science Ivan Depman "From the history of mathematics" (1950), "Stories about Mathematics" (1954), "Stories about old and new algebra" (1967), as well as in the works of other authors: "Cybernetics and life" (1968), "Religion in History and Culture" (1995) and "At the Crossroads of the Universe" (1997). They wrote about her in magazines "World of Adventure" (1926), "Science and Religion" (1973), "Public Education" (1980), "Math at school" (1981), "Mathematics. Everything for the teacher" (2010) and "Mathematics" (2015).

Nowadays, information is found in textbooks used in Russian universities "Philosophical questions of science and technology" And "History of Mathematics", on popular educational portals "Multilesson", "Info lesson", "Teachers Council", "Lesson.rf", "Extended", "Treasury of Lessons" (where assignments and manuals are usually posted by the teachers themselves), as well as on websites secondary schools and in scientific works.

They know about Valmes in the West, including thanks to such works as the book by Peter Beckman "The History of Pi" (1970), and various works on history of mathematics.

In mathematics, an equation of the fourth degree is an algebraic equation of the form:

Norwegian mathematician Niels Henrik Abel in the 19th century provedthat 4 is the maximum degree of the equation for which there is a solution in radicals in general form (that is, for any values ​​of the coefficients). As for the actual solution of this type of equations, ancient Indian scientists struggled to obtain the formula, then in the 16th century Lodovico Ferrari was able reduce problem to solve the cubic equation, and in 1545 his teacher Gerolamo Cardano, who owned the secret of this solution, published both conclusions in his work Ars Magna (“Great Art”). However, modern scientists bow down to the version that the solution to incomplete cubic equations was first found by Cardano’s senior contemporary, Scipio del Ferro, then the self-taught mathematician Niccolo Tartaglia independently came to a more general conclusion, and from the latter, Cardano learned the secret of the solution, in his own words.

So, judging by the year that appears in history, Paolo Valmes, if his solution had reached us, would have every reason to be considered the author of the first formula for finding the roots of a fourth-degree equation. However, first I would like to understand what we generally know about this mathematics. There is no page dedicated to him in any language version of Wikipedia, and there is not even a short biographical sketch about him on any mathematical website. Moreover, among almost two hundred holders of the name Paolo in the corresponding list In the English Wikipedia there is only one - his nationality is Spanish, since the name is originally Italian. And yet, after a long search, you can come across the following interesting document, posted for some reason on the website of the US National Library of Medicine. It represents the correspondence of the powerful Inquisitor Thomas Torquemada with Pope Innocent VIII. In one of the letters (judging by previous correspondence, it was written in 1489), Torquemada says: “As you remember, at the beginning of this year I burned the mathematician Valmes at the stake. He claimed to have solved a fourth degree equation. I told him that it was God’s will that this decision should be beyond human understanding.”

However, a careful reading of the entire correspondence convinces us that this is nothing more than a parody. So, the last letter is dated already 1984, and in it the pope asks the inquisitor: “In the name of the Lord, stop!” And the postscript says that this document is dedicated to QA (quality assurance) workers.

Judging by numerous attributions, the story of Paolo Valmes became known to a wide range of English-speaking readers thanks to the above-mentioned book by the Czechoslovak emigrant Petr Beckman "The History of Pi". As a source, Beckman points to Ivan Depman’s book “Stories about Mathematics,” which is well known to Soviet readers, and writes in the notes: “In fairness, I must add that I have not found any mention of this event anywhere else and that Soviet books are unreliable where the issue of religious competition is raised.”

This was in 1970, and two decades later, the editors of American Mathematical Monthly, the most widely read mathematical magazine in the world, came to letter from one California reader:

“I am a software engineer by profession and, alas, only an amateur in the history of mathematics. As you probably know, California has a significant Latino population. During the course, some high school students asked me if there had ever been a famous Spanish-speaking mathematician. This topic seemed vaguely familiar to me, and I managed to find a book that I had read several years ago. Peter Beckman, now professor emeritus of engineering at Colorado, wrote a history of pi and mentioned a 15th-century Spanish mathematician named Valmes. It seems like Valmes was burned at the stake by Tomás Torquemada in 1486 for claiming to have solved the general equation of the fourth degree.

Besides finding an example of a Spanish mathematician, the story piqued my interest. If Valmès indeed predated Lodovico Ferrari's published solution to the fourth degree equation by some 50 years, it would be fair for Valmès to receive credit for the feat that cost him his life. Even if Valmes's solution had been wrong, it seemed to me that mathematics owed him a debt. But I could not find any mention of Valmes in any work on the history of mathematics or the Spanish Inquisition.

I wrote to Professor Beckman. He was very kind and immediately replied that the source of his story about Valmes was a Russian textbook called “Stories about Mathematics” by a certain Ivan Y. Depman. Alas, there were no bibliographical references or footnotes about Valmes. The book was published in Leningrad by Gosdetizdat in 1954. The Soviet Consulate in San Francisco kindly provided me with the address of Gosdetizdat, and I sent there a letter professionally translated into Russian. I hoped that Depman, his editor, or the students were still alive. Unfortunately, there was no response. I also wrote to Henry Kamen through his publisher. I am told that he is the foremost modern historian of the Spanish Inquisition.

Is there a Russian mathematical journal whose editor and readers could shed light on Ivan Depman and his sources? Likewise - is there a Spanish mathematics journal I could contact? My last hope is that you will be able to print part or all of my letter and one of my fellow readers will be able to point out that there is a known solution to my problem.”

Unfortunately, the magazine's readers were unable to help their colleague. One of the mathematicians, Spanish by birth, confirmed, that the sources available to him do not write about any Paolo Valmes, and advanced algebra (Italian and German schools) reached Spain only in 1552 thanks to one German mathematician. This is where the story of the search for Valmes ended. However, she convinces us that the traces of the legend lead to the Soviet Union. But it would be unfair to give all the dubious laurels in this matter to the historian of mathematics Ivan Yakovlevich Depman. After all, almost a quarter of a century before his works, the legend was told in the aforementioned magazine “World of Adventures”, and it was integrated into a mathematical problem for readers:

The system of two quadratic equations mentioned in the problem has nothing to do with the known methods of solving a fourth-degree equation and, apparently, has become part of a fictitious legendary problem. It seems that the author killed two birds with one stone, simultaneously developing the theme of confrontation between religion and science, so popular in the USSR. Unfortunately, the result was that the legend ended up in fairly serious mathematical literature.

Cover image: Wikipedia.

Fake

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