Mathematician James Maynard, an Oxford professor and Fields Medal winner, has been grappling with the future of his field after OpenAI revealed it solved 10 long-standing mathematics problems using an advanced unreleased model called Astra. Some of these problems had confounded academics for decades.
The breakthroughs span diverse areas including sphere packing in higher dimensions (relevant to data encoding), error-correcting codes (for recovering information from noisy signals), and questions about complexity thresholds in connected networks. Other results addressed quantum game theory and techniques for post-quantum cybersecurity.
Mathematicians The Verge spoke with describe a complex mix of emotions—from excitement about accelerating mathematical discovery to apprehension about what this means for those who have dedicated their lives to the field. Few doubt that a profound upheaval is already underway in the traditionally slow-moving discipline.