On the second memoir of Évariste Galois' last letter

Keywords: Essential elliptic function, depressing the degree of the modular equation, projective special linear group over a prime field, elliptic and coelliptic polynomials, solving the general quintic equation

Abstract

Évariste Galois' last letter, addressed to Auguste Chevalier, on the eve of the (so-called) duel on May 30, 1832 (which, perhaps, simpler and more accurately described by Alfred, who did not allow a priest to deprive him from the final moments on the following day with his elder brother Évariste, as murder), was written on seven pages and was divided into three memoirs. The first memoir consumes a little less than two pages. It gave rise to what has come to be known as Galois theory (as, in particular, told by Melvin Kiernan). Yet Galois went on with stunningly amazing constructions in the second memoir, which consumed a bit more than two pages. The third (and longest!) memoir begins on the fifth page and remains mysteriously unresolved, yet it undoubtedly inspired Alexander Grothendieck to formulate his period conjecture. The letter is concluded with a paragraph on the latest ``principal contemplations'', concerning ``the applications of the theory of ambiguity to transcendental analysis'', where Galois delivers his last puzzle to us, saying that ``one recognizes immediately lots of expressions to look for''. Unfortunately, the severity of the time pressure upon him permitted only succinct last instructions with no more last examples. Still and disgracefully, many ``historians'' keep on incessantly and mundanely telling us (and each other) that we ought not ``overestimate'' the significance of the letter, which was (contrary to their advice) eloquently and veraciously described by Hermann Weyl as ``the most substantial piece of writing in the whole literature of mankind''!

Author Biography

Semjon F. Adlaj, Federal Research Center “Informatics and Control”, Moscow, Russia

Semjon F. Adlaj, Scientific Researcher, Section of Stability Theory and Mechanics of Controlled Systems, Division of Complex Physical and Technical Systems Modeling, Computing Center of the Federal Research Center “Informatics and Control”, Russian Academy of Sciences; 119333, Russia, Moscow, Vavilov Street 40, semjonadlaj@gmail.com

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Published
2018-08-30
How to Cite
Adlaj, S. F. (2018). On the second memoir of Évariste Galois’ last letter. Computer Tools in Education, (4), 11-26. https://doi.org/10.32603/2071-2340-4-11-26
Section
Algorithmic mathematics and mathematical modelling