Welcome back! A mathematician at Anthropic used Claude to break a math rule from 1939, and the proof fits in a tweet. Greptile tested 1,000 pieces of AI-written code and found every agent goes blind to the bugs it wrote itself. Elon Musk promised a full-length AI movie of The Odyssey before December 31 and Nvidia unveiled a chip aimed at the half of AI work nobody talks about.
In today's Generative AI Newsletter:
Claude: How did 216 characters end an 87-year rule?
Code review: Why should another model review your code?
Grok: What did Musk promise anyway?
Nvidia: Which chip decides how fast your AI answers?
A rule that beat professional mathematicians for 87 years fell on Sunday night, in a chat session.
Levent Alpöge, a mathematician at Anthropic, posted it on X on Sunday July 20. His opening line ran "hello there the jacobian conjecture is false." He credited Claude Fable 5 for the work.
Since 1939, mathematicians believed a certain family of formulas could always be run backwards, so every answer traced back to exactly one starting point. Nobody could prove it. Claude found a formula where three different starting points land on the same answer. One exception is all it takes to kill a rule.
The whole answer is 216 characters. Strangers checked it the same day. Kevin Buzzard of Imperial College London wrote it up within hours.
Alpöge picked a question with an instant right-or-wrong check, so a bad guess cost him 30 seconds and a good one could be verified by people who had never met him. Most of us are still asking these tools to summarize a document.
The list of unsolved problems is public and machine-readable. Anyone with an afternoon can point a model at the next one on it.
Special highlight from the network
How to get your Excel hours back without learning to code
Count the hours you burned last month cleaning exports, rebuilding the same pivot and retyping variance commentary. All of that has been automatable inside Excel for a while now.
Two courses at GenAI Academy, depending on how deep you need to go.
Claude Excel for Finance (early bird still open, cohort starts August 3)
Prompt Claude inside Excel in plain English, with no VBA and no code
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Run every AI output through a 4-checkpoint QA framework before it reaches the CFO
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Modern Excel with AI: From Manual to Automated
Know when to reach for Copilot, Python in Excel or Power Query on any given task
Turn a messy export into a clean table that refreshes with one click
Write and debug formulas with AI, then catch the places where it gets them wrong
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The finance cohort closes on August 3. The other one you can start tonight.
Ask an AI to check its own work and it misses the exact mistakes it just made.
Greptile ran the test on July 21. It took 1,000 pieces of code, half written by Claude and half by Codex, then asked each AI to hunt for serious bugs in both piles.
When Claude wrote the code, GPT found 60% of the bugs and Claude found 54% of its own. When Codex wrote it, the scores flipped: Claude found 62% and GPT found 51%.
The reason is the useful part. Each AI has habits, and the mistakes it makes most often are the ones it stops noticing, the same way you cannot proofread your own writing.
Their manners differ too. Codex leaves one or two notes per review. Claude leaves seven or eight.
So whichever one wrote it, hand it to the other one. It is free, it takes a minute and it catches roughly 8 more bugs out of every 100 that would have shipped.
Greptile turned this into a product feature. You can run the same rule by hand starting this afternoon.
A public deadline just landed on something no AI video tool has ever done.
On Wednesday July 22 he wrote on X that Grok Imagine will make a full-length movie of The Odyssey that is "historically accurate and true to the art of Homer." He attached a three-minute clip a user had generated with the tool.
The post caps months of attacks on Christopher Nolan's adaptation, most of them aimed at its casting. The AI short he shared has an all-white cast.
Set that aside and a real question is left. Grok Imagine makes clips a few seconds long. A movie runs close to two hours. No tool has kept a face, a voice and a story straight across that gap.
Nolan shot his version on real film with almost no computer graphics, and it took more than $264 million in its opening weekend.
If Grok delivers, every studio rewrites its plans in January. If it slips, it becomes the most visible broken promise in AI video.
Nvidia is moving on Intel and AMD, and what is at stake is the delay between your question and your answer.
On July 21 Nvidia published the full specs and first test scores for Vera, its first processor of this type built from scratch, CNBC reported. OpenAI, Anthropic and SpaceX each got units in June to try out.
Most of what an AI does is not thinking. It is opening files, running searches and waiting for one step to finish before the next can start. Vera is built for that half of the job, and Nvidia says the work finishes 1.8 times faster than on the standard chips everyone runs today.
ServeTheHome, a site that reviews data center hardware, went through the same document and says the scores are uneven.
You will never buy one of these. It sits underneath the AI service you already pay for, so what you would notice is answers arriving quicker and prices drifting down.
AMD opens its big event in San Francisco today and Intel reports earnings this week. Nvidia published a day ahead of both.
ccusage reads the logs Claude Code already saves on your machine and turns them into a bill you can actually look at. It runs through npx, so there is nothing to install and no account to create.
Try this yourself:
Open the terminal where you run Claude Code and type npx ccusage@latest.
Read the table it prints and find the day that cost the most.
Check which model and which project are behind that day.
Change one thing in your setup, run the command again and compare the two numbers.
Who it's for: anyone on Claude Code who wants to know what they burned this week instead of finding out on the invoice.
OpenAI's agent products hit 10 million users: Bloomberg reported on July 21 that Codex, its coding agent, and ChatGPT Work, its newer office agent launched July 9, together reach 10 million people, roughly double the count two weeks earlier.
Google starts pre-training Gemini 4: Buried at the end of the July 21 Flash announcement, Google says it has begun its most ambitious pre-training run yet while Gemini 3.5 Pro is still in partner testing.
Big Tech spent $41 million lobbying in the first half: Issue One's review of federal disclosures found 11 tech and AI companies spent $41 million from January to June, up 8% from 2025, with Meta the largest at $5.99 million.
The White House frontier framework is due before August 1: Executive Order 14409, signed June 2, gives federal agencies a voluntary 30-day window to review covered frontier models, and Meta is not part of the deal.
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