+ Anthropic's AI Cracked An 87-Year-Old Math Problem The Best Minds Could Not
On July 20, a mathematician at Anthropic used the company's most advanced model, Claude Fable 5, to settle a famous math question that had stood open since 1939. The problem, known as the Jacobian conjecture, is one professional mathematicians had chipped away at for 87 years without an answer. Claude produced a short counterexample, essentially one specific case that proves the long-standing assumption wrong, and it did it in a few lines. Within hours, mathematicians around the world checked the work by hand and agreed it held up.
The same week, a group led by a Nobel Prize winning physicist reported that Claude helped them solve a physics puzzle that had been open for years, with one saying it shifted his view of what these tools can do. The catch: the AI found the answer but could not explain why it works. It delivered the result the way a calculator does, without the human story of how it got there.
What it all means: For two years people argued about whether AI could do real, original work at the frontier of hard science or only remix what humans already knew. This week it did the former, in public, on a problem with an 87-year losing streak. What is left unsolved is understanding, because a correct answer that nobody can explain is powerful and unsettling at the same time.
+ Google Released Cheaper, Faster AI, And One Built To Hunt Security Holes
On July 21, Google released three new versions of its Gemini AI aimed at speed and cost rather than raw power. The main one, Gemini 3.6 Flash, does the same everyday work while using up to 17 percent fewer of the units companies pay for, which lowers the bill. A second is tuned for very high volume, and a third is a specialized model built to find, confirm, and patch security weaknesses in software.
That security model will be available only to governments and trusted partners at first. Google still has not shipped its long-delayed flagship, Gemini 3.5 Pro, which has slipped several times over reliability problems. So the company led with cheaper and faster while the top-tier model stays in the shop.
What it all means: The race at the top of AI is now matched by a race to the bottom on price, and this is Google's move in it. Making the same work cost less is how these companies compete for the businesses that run them at scale. The security model is the one to watch, because the same tools that find holes to fix are the tools that find holes to exploit.
+ ChatGPT Can Now Read Your Health Records
On July 23, OpenAI relaunched a feature called Health in ChatGPT that connects the chatbot to your Apple Health data and, in the US, to medical records from supported hospital systems and services like One Medical. Once connected, ChatGPT can compare your lab results over time, summarize what changed since your last appointment, and spot patterns across your sleep, exercise, and daily activity. It is open to logged-in users 18 and older on both the free and paid plans.
This is a relaunch with wider access than the first test version. The trade is straightforward: more useful health analysis in exchange for handing sensitive medical information to another company. Observers noted that Apple's own assistant can keep that data on your device, while sending it to ChatGPT means sharing it outward.
What it all means: AI is moving into the most personal records you have, and it is doing it as an opt-in convenience rather than a mandate. The analysis can genuinely help you walk into a doctor visit better informed. The cost is that your medical history becomes one more thing living on a company's servers, and that is a choice worth making on purpose.
