🏆 Claude Smashed a 167 Year-Old Million Dollar Math Problem's Record in 36 Hours

For 167 years the Riemann hypothesis has beaten everyone who went at it, and last week an unreleased Claude went at it too and came up short. What it produced instead has number theorists paying attention, because a figure that human mathematicians nudged along for decades moved further in a day and a half than it had in forty-six years. Let's dive in!

In today’s insights:

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Evolving AI: An unreleased Claude cracked a Riemann barrier no mathematician passed in 167 years.

Key Points:

Anthropic set a staff member with no mathematics training on the hypothesis, and he mostly sent encouragement while sixty subagents refereed each other. The hypothesis survived and the record turned up as a side result, so the million Clay Mathematics Institute has offered since 2000 stays unclaimed. Two of the company's mathematicians checked it before Brian Conrey and Dan Goldston reviewed it from outside, and Conrey proved the 40% bound himself in 1989. Claude also wrote the argument out in Lean so a standard tool could check every step mechanically.

Claude produced mathematics nobody had written down before, which is a different job from summarising what already sat in its training. Anyone who uses these tools daily has been told to check the output, and on questions this hard no ordinary user could. A proof a machine can verify is the first honest answer to that, and it sets the standard to demand from any AI answer you cannot test.

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Evolving AI: Claude Haiku read out Opus 4.8's frontier reasoning word for word.

Kimi K3 answered like Opus after researchers seeded its reasoning with the first 1% of a recovered trace. The team came out of MATS and ELLIS Tübingen, and they built the attack on a loose end Johns Hopkins cryptographer Matthew Green left in May when Anthropic and OpenAI both told him replays carried no security risk. Providers patched several issues after disclosure, and no AI company has been shown to have used the method.

GitHub still holds logs developers published while nobody knew this was readable, and each of them checked a transcript showing none of the reasoning underneath. Anyone who has pushed a Claude Code or Codex session to a public repository is carrying the same gap. That reasoning layer is where these models do most of their work, and the people who produced it were the last ones able to read it.

Evolving AI: Grok Bot logs into your apps with a password like any new hire would.

Elon Musk's company ran Grok Bot as an internal tool first, and staff there now keep several bots working at once on separate jobs. One bot can sit above the rest as a chief of staff, and the bots message each other directly to pass work along without a person copying notes between chats. The beta covers desktop and iOS with Android still coming, and enterprise buyers go on a waitlist.

Gmail and the other accounts a person opens every morning sit behind ordinary logins, and connectors have never covered most of them. A bot that signs in the same way gets at that work with nothing to wire up first, and what it takes over is the repetitive middle of a day. The person still decides which accounts a bot gets and reads what comes back before any of it goes out.

QUICK HITS

🚪 Brad Lightcap, OpenAI's longest-serving exec, is leaving to "start something new" as the IPO nears.

🌊 xAI co-founder Igor Babuschkin's River AI raised $1.1B two months out of stealth, backed by Nvidia, AMD, and Temasek.

📈 Google's Gemini app crossed 1 billion monthly users, its fastest-growing product ever, with 63% now using voice.

🐧 OpenAI shipped a ChatGPT desktop app for Linux, completing its desktop lineup.

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