In pure arithmetic, very often, breakthroughs arrive like bolts from the blue – the results of such impressed feats of reasoning and creativity that they appear to push the very bounds of intelligence. In 2016, as an illustration, mathematician Timothy Gowers marvelled at an answer to the cap set downside, which has to do with discovering the biggest sample of factors in area the place no three factors type a straight line. The proof “has a magic high quality that leaves one questioning how on Earth anyone considered it”, he wrote.
You would possibly assume that such feats are distinctive to people. However you could be mistaken. As a result of final 12 months, synthetic intelligence firm Google DeepMind introduced that its AI had found a greater resolution to the cap set downside than any human had. And that was simply the newest demonstration of AI’s rising mathematical prowess. Having lengthy struggled with this type of refined reasoning, at this time’s AIs are proving themselves remarkably succesful – fixing advanced geometry issues, aiding with proofs and producing recent avenues of assault for long-standing issues.

All of which has prompted mathematicians to ask if their subject is coming into a brand new period. Nevertheless it has additionally emboldened some pc scientists to recommend we’re pushing the bounds of machine intelligence, edging ever nearer to AI able to genuinely human-like reasoning – and possibly even synthetic basic intelligence, AI that may carry out in addition to or higher than people on a variety of duties. “Arithmetic is the language of reasoning,” says Alex Davies at DeepMind. “If fashions can…