Professional mathematicians have been stunned by the progress amateurs have made in solving long-standing problems with the ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

Aravind Srinivas, the chief executive of AI search startup Perplexity, has said that artificial intelligence systems are still fundamentally dependent on humans to define what problems are worth ...

GPT-5.2 Pro delivers a Lean-verified proof of Erdős Problem 397, marking a shift from pattern-matching AI to autonomous ...

The AI companies I see building real traction are the companies solving the routine burdens and everyday friction people ...

A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working ...

MIT’s Recursive Language Models rethink AI memory by treating documents like searchable environments, enabling models to ...

JP Morgan’s words encourage us to see a problem in terms of a specific idea and not just as a vague thought. Problems rarely defeat us because they are too big; they defeat us because they are ...

The reasons for hiding cables are now well established, ranging from professional riders seeking marginal gains to bike designers wanting to create cleaner, leaner-looking bikes. The downsides of ...

Robots at CES 2026 are smarter, more helpful and more fun. Here are our favorites so far.

Aravind Srinivas, CEO and co-founder of AI-powered search engine Perplexity, has reinforced the critical distinction between artificial intelligence (AI) as a powerful tool and human ingenuity as the ...

From reproductive rights to climate change to Big Tech, The Independent is on the ground when the story is developing. Whether it's investigating the financials of Elon Musk's pro-Trump PAC or ...