AI just solved the 80-year-old Erdős problem, and mathematicians are amazed ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏
May 21, 2026—AI just solved a major conjecture in geometry, and mathematicians are wowed. Plus, SpaceX's megarocket launches tonight, and Ebola is still spreading in Africa.
—Andrea Gawrylewski
Chief Newsletter Editor
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A poster displaying Ebola emergency contact numbers is pinned to a tent at the Busunga border crossing between Uganda and the Democratic Republic of Congo in Bundibugyo, on May 18, 2026. BADRU KATUMBA/Getty Images
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After 80 years of struggle by human mathematicians with nothing to show, a chatbot has solved a major geometry conjecture, called the “unit distance” problem. The company OpenAI, maker of ChatGPT, announced the result yesterday, together with comments from a number of experts, who declared the artificial intelligence’s method “clever” and “elegant.” Chatbots have made some achievements in math in recent months, but this marks a true milestone that would warrant being published in a mathematics journal if humans had achieved it.
The conjecture: Draw nine dots on a sheet of paper. The goal is to get as many pairs of dots as possible to be an inch apart. For any number of dots, even billions or trillions, the problem asks: What’s the highest number of pairs you can get? In 1946 mathematician Paul Erdős used some sophisticated math to show that using precise spacing, you could get more pairs than by simply placing them in a grid (of 3 by 3 dots, for example). For 80 years, no one could disprove him.
What the AI did: OpenAI mathematicians fed the conjecture to an internal large language model (LLM), which produced, in hundreds of pages of calculations and reasonings, something very different from a square grid solution. It devised a higher-dimensional lattice of points with special mathematical symmetries that facilitate the separation of even more pairs by the same distance. The AI model then developed a way to map this otherworldly grid back down to the two-dimensional page, producing a flattened numerical “shadow.” In fact, the solution can’t be drawn on paper.
What the experts say: Independent mathematicians evaluated the LLM’s proof. What stood out to them was the chatbot’s patience and focus. “AIs have an edge: It’s not just that they can try all known methods,” says Jacob Tsimerman, a mathematician at the University of Toronto, who was not involved in the work but was part of a companion paper solicited by OpenAI. “They can play for longer and in more treacherous waters than mathematicians without getting overwhelmed.”
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The Intelligence-Depression Link
Psychology researchers typically find that as intelligence (measured by IQ) increases, a person’s mental health improves—until it hits an inflection point and starts to go down. However, a recent study cast some doubt on that relationship. It found that depression scales that measure a person’s mental health may not work the same for people with high IQs.
How it works: The researchers crunched data from two U.S. surveys that included an estimate of a person’s IQ and their responses to well-established mental health questionnaires. At first, the team found the classic bell curve pattern of mental health increasing with intelligence, then decreasing after it reaches a certain point. But then they used a statistical method to determine whether the mental health measures work the same for people at different intelligence levels, in part by calculating whether responses to individual questions reflect depression to the same extent for everybody. Both questionnaires failed this test, meaning they can’t be used to compare people with differing intelligence.
What the experts say: The conclusion that people with high intelligence are more depressed because they answer questionnaires that way is flawed because the questions likely aren’t working in the same way for every patient. “Very intelligent people may think about mental health differently and maybe experience symptoms differently,” says Nicole Beaulieu Perez, a psychiatric nurse at New York University not involved in the research. —Emma Gometz, Newsletter Editor
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Viticulture researcher Erna Blancquaert (right, with graduate student Sindiswa Zandile) starts work at dawn in the vineyards of South Africa’s celebrated Stellenbosch wine region. This time of day, before plant metabolism starts and the heat of the day sets in, is best for measuring the water status of grapevines and sampling fruit when its flavor is at its peak. Blancquaert and her team study the impact of sustainable and regenerative viticulture practices, such as using seaweed as a fertilizer and allowing cattle to graze in vineyards. Nature Africa | 3 min read
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The OpenAI large language model that solved the Erdős conjecture didn't use any special math or tools that didn't already exist. And, as noted in the article, without humans intervening to “clean up” the AI’s work, the result wouldn’t be so convincing. But AI did push out of natural human dimensions, which is something much harder for us to do. Being honest with ourselves about human limitations might help us see where AI can complement our strengths instead of merely surpassing them.
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—Andrea Gawrylewski, Chief Newsletter Editor
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