Hacker News with Generative AI: Conjectures

What if they are all wrong? (2020) (wordpress.com)
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some of them are famous, classical, general, important, inspirational, far-reaching, audacious, exiting or popular, while others are speculative, narrow, technical, imprecise, far-fetched, misleading or recreational. That’s a lot of beliefs about unproven claims, yet we persist in dispensing them, inadvertently revealing our experience, intuition and biases.
The Secret of Ramsey Numbers (cacm.acm.org)
Mathematicians recently gathered for a workshop in Canadaa to thrash out ideas inspired by a breakthrough a pair of researchers made in 2023 on a conjecture by Paul Erdős.
Math's 'Bunkbed Conjecture' Has Been Debunked (quantamagazine.org)
It was intuitive, even obvious. It was also wrong.
Big advance on simple-sounding math problem was a century in the making (quantamagazine.org)
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
Monumental proof settles geometric Langlands conjecture (quantamagazine.org)