Extras

As everyone knows, every mathematical adventure must start with a set of axioms. It is often difficult to agree on the precise content and formulation of these axioms. Here is a set of axioms that I include in my standard toolbox, which has been laid out for the notices of the AMS by Federico Ardila-Mantilla.

• Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries. 

• Everyone can have joyful, meaningful, and empowering mathematical experiences. 

• Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs. 

• Every student deserves to be treated with dignity and respect.

Science is about truth. Which is missing from the unjust treatment of Azat Miftakhov, Giulio Regeni and many other academics in the world, who were jailed or murdered for their views, their identity or their acts of resistence.

Knowledge costs too much, as explained here and here. Therefore, I support diamond open access journals, like the ones listed on this page, as well as initiatives such as arXiv, Gallica, Sci-Hub, Library Genesis or Anna's Archive. I also believe that, as scientists, we should all thank those who fought for open knowledge, such as Alexandra Elbakyan and Aaron Swartz.

These websites are crucial for the development of science in the global south. Other ways to foster mathematical exchanges with developing countries are provided by associations such as SAMI, CIMPA and GANDA.

Nowadays, one can find many mathematical talks online. I put together a playlist containing some of them, strongly influenced by my personal mathematical interests. Moreover, you can find interesting list of documentaries about math and mathematicians on Abakcus and ZalaFilms. I also find the Abel Prize, CIRM and Math-Life Balance interviews particularly well made.

• Shigeru Amano, "Eisenstein equations of degree p in a p-adic field"

• Spencer Bloch, "Applications of the dilogarithm function in algebraic K-theory and algebraic geometry";

• Spencer Bloch, "The moving lemma for higher Chow groups";

• Christopher Deninger, "Higher regulators of elliptic curves with complex multiplication"

• Max Deuring, "Die Zetafunktion einer algebraischen Kurve vom Geschlechte eins" (part I, II, III and IV);

• Noam D. Elkies, "Distribution of supersingular primes";

• Jean-Marc Fontaine, Bernadette Perrin-Riou, "Autour des conjectures de Bloch et Kato" (announcement version, part I, II, III);

• Annette Huber, "Realization of Voevosky's motives" (see also the corrigendum);

• Mathias Lerch, "Sur quelques formules relatives au nombre des classes";

• Andrey Levin, "An explicit formula for the motivic elliptic polylogarithm"

• Patrice Philippon, "Sur des hauteurs alternatives, III"

• Wayne Raskind, "« Le théorème de Mordell-Weil faible » pour H^0(X,K_2)/K_2(k)"

• David E. Rohrlich, "Elliptic curves and values of L-functions"

• Jean-Pierre Serre, "Une 'formule de masse' pour les extensions totalement ramifiées de degré donné d''un corps local"

• Jacques Vélu, "Isogénies entre courbes elliptiques" (see also the English translation by Alexandru Ghitza);

• Jean-Loup Waldspurger, "Sur les coefficients de Fourier des formes modulaires de poids demi-entier" (see also the digital version by John Voight)

Some of these are extracted from the works digitalized by the Bibliothèque nationale de France. A similar list of scanned papers can be found on Dino Lorenzini's webpage.