Learning more about Claude's mathematical capabilities \ Anthropic
An unreleased version of Claude has made strides on a problem related to the Riemann hypothesis. It improved the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis, increasing it from 41.6% to 67.2%.
Recently, a member of staff at Anthropic gave Claude an unreasonable challenge. It was about one of the most famous unsolved problems in mathematics: Take a real stab at the Riemann hypothesis. Claude did take a real stab, but as you might have expected if you’re familiar with the difficulty of the task (the Riemann hypothesis dates back to 1859 and has a million-dollar bounty), it didn’t succeed. Nevertheless, during its attempt, it unexpectedly made strides on a related problem. An unreleased research version of Claude has improved on a longstanding lower bound for the fraction of zeros…
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related reading
- The Riemann Hypothesis: Past, Present and a Letter Through Timearxiv.org
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- cs.stanford.edu/~knuth/papers/claude-cycles.pdfcs.stanford.edu
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- Riemann–von Mangoldt formula - Wikipediaen.wikipedia.org