Ricardo Riaza

"Mathematical methods and human thought in the age of AI" (by Tanya Klowden, Terence Tao): arxiv.org/abs/2603.26524

In the late 1830s, Karl Weierstrass dropped out of university. He is said to have spent his school years drinking and fencing. Decades later, he published a function that threatened everything mathematicians thought they understood about calculus. quantamagazine.org/the-jagged-mon…

My favourite anecdote from the history of mathematics: tells you not only about mathematicians but about mathematics too

A happy heavenly birthday to Paul Erdős. youtu.be/EGc6rE24YSw?si… mathshistory.st-andrews.ac.uk/Biographies/Er…

We congratulate Gerd Faltings as the 2026 Abel Prize laureate! 🎉 He recives the Abel Prize "for introducing powerful tools in arithmetic geometry and resolving long-standing diophantine conjectures of Mordell and Lang".

Fabricio Macià nos responde a la famosa pregunta de Marc Kac de si podemos escuchar la forma de un tambor. Es decir, si podemos distinguir un tambor cuadrado de uno circular (u otra forma) solo por su sonido. blogs.upm.es/retazos-matema…

Un poquito de Retazos de matemáticas y realidad: Criptografía: blogs.upm.es/retazos-matema… La forma de un tambor: blogs.upm.es/retazos-matema… Nudos: blogs.upm.es/retazos-matema… Números imaginarios: blogs.upm.es/retazos-matema… Simetría eres tú: blogs.upm.es/retazos-matema…

Oh wait a second! Alain Connes just wrote (3 February 2026) a 42 page piece on the Riemann hypothesis and it's publicly available on arXiv! This is great!

Logician Kurt Gödel (1906–1978) was an eccentric and unworldly man who frequently needed to be protected from the vicissitudes of life by his friends. After Gödel had lived in this country for many years, he was persuaded to become an American citizen. He therefore began studying for the citizenship exam. Unfortunately, as soon as Gödel began reading the U. S. Constitution, he discovered troubling logical loopholes. This insight cast him into deep distress. John von Neumann (1903–1957)—Gödel’s colleague at the Institute for Advanced Study—was finally called in to convince Gödel that if you looked at things the right way then there would be no logical inconsistency. Albert Einstein (1879–1955) and the economist Oskar Morgenstern (1902–1976) were the ones who chaperoned Gödel to the hearing for his citizenship application. The judge was overwhelmed by this opportunity to talk to Einstein, and they conversed at length about events in Nazi Germany. Finally, as an afterthought, the judge turned to Gödel and said, “But of course from your reading of the Constitution you now know that nothing like that could happen here.” “As a matter of fact,” Gödel began—but then, under the table, Morgenstern kicked Gödel. So Gödel got his citizenship after all. [By some accounts, Morgenstern had to do a heck of a lot more than just kick Gödel. Fortunately, he was equal to the task.] Source: Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical by Steven G. Krantz

This gets me every time

I crossed an interesting threshold yesterday, which I think many other mathematicians have been crossing recently as well. In the middle of trying to prove a result, I identified a statement that looked true and that would, if true, be useful to me. 1/3

"Probability does not exist." This provocative quote is by the Italian statistician and probabilist Bruno de Finetti. It encapsulates the core idea of Subjectivism or Bayesianism, a major school of thought in probability. De Finetti argued that probability is not an objective property of the world (like mass or temperature). Instead, it's a measure of an individual's degree of belief about an uncertain event, based on their knowledge and evidence. Essentially, he meant that a "50% chance of rain" doesn't exist in the clouds themselves; it exists in the mind of the meteorologist who assigns that value based on the data they have. It's a powerful statement that reframes probability as a tool for reasoning under uncertainty, rather than a feature of physical reality.

¡Nos vemos este fin de semana en el Pabellón 3 de @Japan_Weekend ! #JapanWeekendMadrid Venid a aprender a jugar al go⚫️⚪️

Todavía quedan plazas para el máster en Matemáticas Avanzadas de la UPM. ¡Apúntate! El próximo 1 de julio a las 12:00 habrá un jornada informativa. También la podéis seguir por zoom: upm.zoom.us/j/89681828259

Libro ajedrez, ...Alfonso X el Sabio: "Cualquiera que firiere tablero con punta cuchiello por cada ferida que diere que peche medio maravedí. Otrosí si lo quebrantare de piedra... pero si lo quebrantare en su cabeça mesma que sea quito de lo non pechar” @leontxogarcia . Ver ALT

youtu.be/fVF8fFFLFyc The 45th WAGC was held in Vancouver, Canada this year, and I was the chief referee. I chose a beautiful game to comment on for this video.

This week’s guest on “The Joy of Why” is my friend L. Mahadevan. The Maha that I knew a long time ago was thinking about paper folds. These days, he’s moved on to brain folds. Tune in to our conversation, from @prx and @quantamagazine: quantamagazine.org/does-form-real…

Muere Peter Lax, el matemático que ayudó a predecir el clima, entender las ondas y salvó un superordenador elpais.com/ciencia/cafe-y… via @el_pais