Every planar map can be coloured with just four colours so that neighbouring regions differ.
The theorem was proved in 1976 only after a computer checked 1,482 configurations.
Decades later, the proof itself was formally verified in Coq.
Four colours. Thousands of cases.
Terence Tao w/ @tylercowen says the Collatz conjecture is true, but nobody has any idea how to prove it, not even with today's AI, and he does not expect to see a proof in his lifetime.
The rule: if a number is odd, multiply by 3 and add 1; if it is even, halve it; repeat. The numbers bounce like hailstones, and Tao notes the first trillion tested all fall to 1. In the animation, 27 climbs to 9232 before landing after 111 steps.
What cannot be ruled out is one exceptional hailstone that floats up forever or falls into a loop. "None of the ideas we have in mathematics come close to ruling out this very extra special conspiracy," he says.
🤖 ¿Cómo integrar la IA en un centro educativo de forma responsable?
📘 Ya disponible la guía «Orientaciones para la integración de la inteligencia artificial en los centros educativos», con pautas para planificar su uso de forma segura y coherente
🔗 https://t.co/F4lLhocFiR
Fermat's Last Theorem took 358 years to prove.
Making that proof computer checkable was expected to take years. In September Anthropic reported doing it in 11 days.
This week it reported a second run: 30 hours with a team of 1,000 AI agents.
Amigas bonitas
tengo en la red,
Miradas sinceras
que tocan la piel.
Así tan bellos gestos
tienen ese poder,
Pintan una sonrisa,
llegan a socorrer,
Olvidas problemas
y piensas en querer
La vida y a la gente
que hace tanto bien,
Aquí os doy las gracias,
sin Mates esta vez 💙
¡¡Gracias, Fátima!! Leer tu hilo sobre el librito me alegra el día. Pd. Pequeño adelanto, parte de lo que se queda en el tintero será el foco de Taeko II.