22 de agosto de 2026 · [[El Abismo de Máquina/Ecos|¿qué es un eco?]] # Eco: Vídeo - El verano en que las matemáticas cayeron ante las máquinas > [!entradilla] > Cinco minutos de Fireship repasando los problemas abiertos de matemáticas que han caído desde mayo. Va muy rápido, no enlaza nada, y aun así merece el rato. > [!tip]+ Qué tienes aquí > > Cinco minutos de The Code Report, el formato de Fireship, publicados el 19 de agosto. La idea de partida es que la IA ha tumbado más problemas abiertos de matemáticas en las últimas tres semanas que la humanidad entera en la década anterior, y a partir de ahí van desfilando los casos: la conjetura de las distancias unidad de Erdős, la Declaración de Leiden, la conjetura jacobiana, la de Dinitz-Garg-Goemans, los seis problemas de Erdős que resolvió un doctorando en cinco días, los diez resultados de OpenAI y el avance de Anthropic sobre la función zeta de Riemann. > > Traigo esto porque la lista está bastante bien elegida y porque es verdad, que a estas alturas no es poco. He ido caso por caso a las fuentes originales y están todos, con nombres, fechas y papers detrás. > > Ahora las pegas, que son las de siempre en este formato. Va rapidísimo y no enlaza ni una sola fuente, así que si queréis comprobar algo os toca buscarlo. Y se come los matices que más falta hacen: dice que Anthropic avanzó en la hipótesis de Riemann sin dejar claro que la hipótesis sigue sin demostrarse y que lo que ha subido es una cota lateral, y da por muerta la conjetura jacobiana aunque en dos dimensiones siga abierta. La transcripción automática, además, destroza los nombres propios. Fable sale como "Fabel", los grupos no sóficos como "non-Saugus groups" y a Dmitry Rybin le cambia el nombre por el camino. > > Aun así me parece que compensa, porque en cinco minutos os enteráis de que este verano ha pasado algo gordo. Lo que faltaba era comprobarlo y contarlo un poco más despacio, y eso lo he hecho aparte: [[Newsletter/2026/97-problemas-resueltos-verano-2026|los once casos, uno a uno, con sus fuentes y sus pegas]]. > > El original: [The summer Math fell to the machines](https://www.youtube.com/watch?v=iuZPTE5qsJY) > [!abstract]- Resumen esquemático > > #### Planteamiento > > - Afirmación de partida: en las tres semanas anteriores al 19 de agosto de 2026, los modelos de IA han resuelto más problemas abiertos de matemáticas que el conjunto de la comunidad matemática en la década previa. > - Contraste con el discurso habitual sobre programadores: el desplazamiento afecta antes a los matemáticos que a los desarrolladores. > - Punto de partida cronológico: hace un año varios modelos resolvieron cinco de los seis problemas de la Olimpiada Internacional de Matemáticas. Se interpretó como matemáticas de competición, no de investigación. > > #### Mayo de 2026 - Distancias unidad > > - Un modelo de OpenAI refuta una conjetura de Erdős de unos 80 años sobre distancias unidad en el plano. > - Primer caso que rompe la lectura tranquilizadora de "esto es solo competición". > > #### Junio de 2026 - Declaración de Leiden > > - Dieciséis investigadores de quince universidades publican un llamamiento a establecer límites al uso de IA en la investigación matemática. > - Recepción según el vídeo: ignorado. > > #### Julio de 2026 - Conjetura jacobiana > > - El matemático Levent Alpoge publica en X un contraejemplo que refuta la conjetura jacobiana, uno de los problemas más conocidos de la geometría algebraica. > - Enunciado en llano: si una función polinómica es reversible en cada punto al mirarla de cerca, la función entera debería ser reversible. > - Antigüedad: desde 1939. Figura en la lista de Smale de problemas difíciles del siglo XXI. > - Herramienta usada: Fable (Claude Fable 5). > > #### Julio de 2026 - Conjetura densa de Dinitz-Garg-Goemans > > - Problema de teoría de grafos abierto durante 30 años, formulable como problema de rutas de reparto: si los envíos pueden repartirse entre varias rutas, ¿pueden agruparse siempre en rutas únicas sin que suba el coste total? > - Dmitry Rybin dirige GPT-5.6 hacia el problema con una instrucción mínima. > - Resultado del modelo: red de siete nodos y nueve aristas en la que forzar ruta única siempre resulta más caro que permitir el reparto. Conjetura refutada. > > #### Julio de 2026 - Problemas de Erdős en serie > > - Un doctorando de Columbia resuelve seis problemas abiertos de Erdős en cinco días. > - Un aficionado de 23 años resuelve otro. > - Lectura del vídeo: la actividad no se limita a investigadores profesionales, y todo esto ocurre antes de que los grandes laboratorios publiquen sus propios resultados. > > #### Agosto de 2026 - Los diez de OpenAI > > - OpenAI anuncia que su próximo modelo, sin publicar, ha resuelto diez problemas abiertos de matemáticas y de informática teórica. > - Publica los diez en GitHub con certificado en Lean, es decir, demostraciones que un compilador puede verificar mecánicamente. > - Resultado destacado: mejora de la cota general del empaquetamiento de esferas, sin movimiento desde 1978. > - Otros: primera construcción explícita de un grupo no sófico y refutación de la conjetura de rigidez de Connes. Varios llevaban abiertos desde los años noventa. > > #### Agosto de 2026 - Función zeta de Riemann > > - Anthropic anuncia que un modelo suyo sin publicar avanza en un problema ligado a la hipótesis de Riemann (1859, uno de los siete problemas del milenio, con un premio de un millón de dólares). > - Origen del intento: Jarred Sumner, creador de Bun, pide al modelo durante una carrera que le meta mano al problema. > - Primer intento: 650 ideas, ninguna válida. > - Segundo intento: día y medio coordinando 60 subagentes dentro de Claude Code, 2.400 comandos de shell, cientos de scripts de Python, 31 millones de tokens de salida. > - Resultado: la fracción de ceros que se sabe que satisfacen la hipótesis pasa del 41% al 67%. La hipótesis sigue sin demostrarse. > - Validación: dos matemáticos de Anthropic, dos expertos externos en teoría de números y formalización en Lean. > > #### Reacción de la comunidad > > - Terence Tao, en el Congreso Internacional de Matemáticos, advierte de una crisis en los fundamentos de los valores y las prácticas de las matemáticas. # Contenido original: The summer Math fell to the machines... Fuente: [The summer Math fell to the machines...](https://www.youtube.com/watch?v=iuZPTE5qsJY)  Railway is the smoothest way to deploy software. Get $20 in free credits - https://railway.com/?referralCode=fireship AI has killed more open math problems in the last few weeks than the entire human race managed in the previous decade. Let's dive in. > [!example]- Transcripción completa (automática, en inglés, sin corregir) > > **0:00** · For years now, every developer has had to put up with hearing about how AI is going to make them obsolete and steal the food they've been putting on their family. But, besides the occasional identity crisis, I feel like most of us are actually doing pretty well. Sadly, our mathematician friends may not be so lucky because over the last 3 weeks, AI has killed more open math problems than the entire human race managed in the previous decade. One 87-year-old conjecture from a list of the hardest problems of the 21st century got disproven during the World Cup final. > > **0:29** · Another 30-year-old graph theory conjecture fell to four prompts in 58 words. The things have gotten so bad that Terence Tao, a man who won an International Math Olympiad medal at age 10 while the rest of us were making cinnamon sugar sandwiches and watching Rocket Power, stood up at the International Congress of Mathematicians and warned of a crisis in the foundations of mathematical values and practices. In today's video, we'll look back at the summer mathematics fell to machines and find out what that may mean for the rest of us. > > **0:57** · It is August 19th, 2026 and you're watching The Code Report. This whole AI doing math thing started about a year ago when some models solved five of the six problems at the International Math Olympiad. But, at the time, it felt mostly harmless because competition math is the lead code of math problems. Then back in May, an OpenAI model disproved an 80-year-old Erdos Erdős conjecture about unit distances and suddenly it didn't feel so harmless anymore. > > **1:24** · Couldn't believe it. I I had trouble sleeping for the first couple of nights I went out. > > **1:28** · In June, 16 researchers from 15 universities published what they called the Leiden Declaration, which politely asked the world to establish some guardrails around AI and mathematics research, which the world then politely ignored. And last month, while Americans were pretending to like soccer and Europeans were pretending to like medieval infrastructure without air conditioning, mathematician Levent Alpoge posted a counterexample to X that disproved the Jacobian conjecture, which is one of the most famous problems in algebraic geometry. > > **1:57** · The idea is that if you have a polynomial function whose derivative checks out at every single point, meaning it's perfectly reversible anywhere you zoom in, then the entire function should be reversible, too. Now, I know that probably doesn't mean much to you, but since 1939, that felt so obviously true to mathematicians that it made Smale's list of the hardest problems of the 21st century because nobody could actually prove or disprove it. That is until Levent did last month with some help from Fabel. > > **2:23** · And just 2 days later, it happened again with a 30-year-old graph theory problem called the dense Garg-Gommans conjecture, which you can think of like a delivery routing problem. If shipments are allowed to split across multiple routes, the question is whether you can always bundle them into single unsplit routes without the total delivery cost going up. And for 30 years, everyone assumed that you could, they just couldn't prove it. Then a researcher named Dimitri Rybin pointed GPT-5.6 at it and basically told it to make a breakthrough. > > **2:53** · The model responded with a tiny network of just seven nodes and nine edges where forcing every shipment into a single route was always more expensive than letting them split, disproving the conjecture. And it's not just the pros doing this. That same week, a Columbia PhD student knocked out six open Edges problems in 5 days, and a 23-year-old amateur banged out another. > > **3:14** · And this is mostly before any of the big tech labs took their own shots. But then just 2 weeks ago, OpenAI got in on the bullying when they revealed that internally their next major model solved 10 open problems across math and theoretical computer science, and they even shipped all of them to GitHub with a lean certificate, which is a formal proof the compiler can check mechanically. The most famous one on the list is one I know some of you have thought about a lot, which is how tightly you can cram identical-sized balls into a space. The general bound on this problem hasn't moved since 1978, but OpenAI just improved it. > > **3:45** · The other nine problems include things like the first explicit construction of a non-Saugus group and a disproof of Connes' rigidity conjecture, which I won't pretend to understand, but mathematicians have been chasing some of them since the '90s. But, of course, Dario couldn't just sit by and get big derivative by Sam. And so, just last week, Anthropic fired back by announcing that one of its own unreleased models made progress on the Riemann hypothesis, which is one of the most famous unsolved problems in all of mathematics. > > **4:12** · It's a 167-year-old question about the distribution of prime numbers, and it's one of the seven Millennium Prize Problems with a literal million-dollar bounty on its head. The best part is that it wasn't an Anthropic mathematician who discovered it. It was Jared Sumner, the creator of Bun JS, as he was on his jog for his I'm filthy rich now and need to get fit, too, era. > > **4:34** · During his run, Jared asked Claude to take a real stab at proving it, and so it did and generated 650 wrong ideas for solving the problem. Jared then told it to try again, and this time the model spent a day and a half coordinating 60 sub-agents inside Claude code, running 2,400 shell commands, writing hundreds of Python scripts, and burning 31 million output tokens. Now, that still didn't lead to it proving the hypothesis, but it did bump the fraction of solutions that probably satisfy the hypothesis from 41% to 67%, which I'm told is pretty groundbreaking. > > **5:05** · The result was validated by two mathematicians at Anthropic, and checked by two outside number theory experts, and formalized in Lean. We live in crazy times, but stuff like this wouldn't be possible without amazing cloud providers like Railway, the sponsor of today's video. They once again refused to waste your time with a full ad, and you can say thank you by checking them out for your next project at the link below. > > **5:27** · This has been the Code Report. Thanks for watching, and I will see you in the next one.