Good morning. In today’s edition:

• 🟰 AI solves 80-y.o. math problem
• 🧠 Human brain cells play Doom
• 🌫️ There’s something living inside fog

…and much more.

Ready, Set, Go: Today’s news should be a ~3.85-minute read (1,024 words).

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In Monday’s send, we mixed up a few details in the Did You Know section. Mt. Everest’s height was initially measured to be 29,000 feet in 1852 by Indian surveyor Radhanath Sikdar, and published as 29,002 feet in 1856 by his boss, Surveyor General Colonel Andrew Waugh, who added two feet to make it look more credible.

Thanks to Jason for bringing this to our attention.

"The greatest deception [humans] suffer is from their own opinions."

–Leonardo da Vinci (1452–1519)

For 80 years, mathematicians tried to crack a math problem that an OpenAI model recently solved in roughly the amount of time it takes to binge-watch your favorite season of a TV show.

It marks the first time a prominent open problem that’s central to a field of mathematics has been solved autonomously by AI.

Let’s break it down

The challenge was the "unit distance problem," first posed in 1946 by legendary mathematician Paul Erdős. We’ll spare you the head-spinning details and skip straight to the “Give it to me in plain English” part:

• If you put n dots on a sheet of paper, how many pairs of dots can be exactly one unit apart?

Erdős believed he knew the best possible arrangement. And for nearly 80 years, nobody could prove him wrong—until OpenAI came along with a new solution.

Well, kind of…Instead of confirming Erdős's hunch, the model found something even more surprising: a counterexample showing how his conjecture was wrong. The AI model’s answer was checked by a group of actual mathematicians, who then wrote a 19-page companion paper explaining that yes, the robot is right.

Why didn't humans solve it first?

There are multiple theories, according to experts.

1. The solution is highly counterintuitive, as most people sought to prove Erdős’ conjecture rather than disprove it.
2. Modern math rewards specialization, while AI can pull concepts from across its entire knowledge base—in this case, the unrelated fields of algebraic number theory and discrete geometry.
3. AI has the time, attention, and persistence to stick with certain methods that other researchers might abandon, which proved particularly useful for this problem.

Bottom line: The answer to Erdős’ conjecture took OpenAI’s model less than 32 hours and $1,000 in tokens, per some back-of-the-envelope math by a former researcher.

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Earth’s temperature forecast is apparently stuck on “slightly concerning with a chance of sweating through your shirt.”

There’s an 86% chance that at least one year between 2026-2030 will surpass 2024 as the hottest on record, per a new UN World Meteorological Organization report.

• Scientists also project a 75% chance the average global temperature across that five-year stretch will exceed 2.7°F above pre-industrial levels.
• That figure is the threshold at which countries pledged to try keeping temperatures below in 2015, when signing the landmark Paris Climate Accords.

What’s stoking the heat?

Researchers point to rising fossil fuel emissions as a main driver of rising temps, since carbon dioxide traps heat in the atmosphere. A potential El Niño event later this year could also turbocharge global temperatures, meaning the next record annual temperature may arrive as soon as 2027.

Many climate experts argue the findings show why countries should accelerate clean-energy investment to reduce their fossil fuel usage, since the heat it adds to Earth’s atmosphere leads to more extreme droughts, storms, heatwaves, and other weather patterns.

At the same time: Many policymakers caution against treating climate projections as evidence the world will experience apocalypse-level events, arguing that human adaptations like better infrastructure, improved forecasting, and technological innovation can help blunt many future impacts.

BUSINESS & MARKETS

• 🛒 Amazon dethrones Walmart as the Fortune 500's No. 1 company in terms of revenue for 2025, ending Walmart’s 13-year reign atop the list.
• 🏘️ Home sellers are pulling their listings off the market at the fastest pace since March 2020, with 5.8% of all home listings nationwide being pulled in April, per Redfin.
• 🏦 Morgan Stanley will soon allow external AI agents to connect directly with its stock administration platforms, per CNBC; it’s the first major Wall Street bank to open its platforms to external AI tools.

SPORTS, MEDIA & ENTERTAINMENT

• 🏀🏆 NBA Finals: New York Knicks defeat the San Antonio Spurs 105-95 in Game 1 after finishing on an 11-0 run; Game 2 is Friday in San Antonio.
• 📺 CBS News fires 60 Minutes correspondent Scott Pelley following a tense meeting with Nick Bilton, the program’s new executive producer.
• 🏈 QB Russell Wilson, a 10-time Pro Bowler who won a Super Bowl and the Walter Payton Man of the Year Award, announces his retirement from the NFL after 14 seasons; Wilson also confirmed plans to start working a CBS Sports analyst.

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SCIENCE, SPACE & EMERGING TECH

• 💉 GLP-1 weight-loss drugs linked to a 30% lower risk of developing or dying from breast cancer, two new studies show; third study finds patients with breast, lung, bowel, or liver cancer who take GLP-1s were up to 50% less likely to see their disease spread.
• 🍔 Ultraprocessed foods are associated with a 58% higher risk of dementia and a 46% higher risk of cognitive impairment among people who eat the highest amount of such foods, per new study.
• 🧠 First-ever invasive brain-computer chip approved for commercial use in China, helping some paralyzed patients write, grasp objects, and perform other daily tasks.| Human brain cells grown on a computer chip learned to play video game Doom, in new milestone for biological computing.

US, WORLD & POLITICS

• 💥 US and Iran exchange some of their heaviest fighting since April's ceasefire, as diplomatic negotiations remain at a standstill; US Central Command says the ceasefire is still on following the latest clash.
• ⚖️ Supreme Court allows Alabama to use a Republican-favored congressional map in this year's elections, overturning a lower court order to use the state's 2024 map.
• 🧓 Social Security checks could be cut by an average of $500/month (a 24% decrease) if the program's retirement trust fund becomes insolvent, which is currently projected for the end of 2032, new report finds.

☝️ Cristiano Ronaldo was the highest paid athlete in 2025-26 for a fourth straight year, per new data from Forbes. The top-50 athletes overall earned a collective $4.1 billion, down slightly from $4.2 billion last year but still the second-highest total ever measured.

🤔 Did you know? Scientists have found that people who reason through a problem in a foreign language tend to make more rational, less emotionally-based decisions compared to doing so in their native tongue—a phenomenon dubbed the “foreign language effect.”

📰 Worth a read: The small businesses trying to prop up the tandem bike industry

🖱️ What we’re clicking:

• There’s something living inside fog, scientists find
• Why Spielberg thinks there are aliens living among us
• Gladiator diets were mostly vegetarian

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Yesterday we covered how a growing number of US states are legalizing the medical aid in dying—aka physician-assisted suicide—for certain terminal patients, with the practice soon to be legal in 13 states plus D.C.

❓ Our question to you: Do you think medical aid in dying (MAID), or physician-assisted suicide, should be legal?

• Yes: 70%
• No: 19%
• Unsure/other: 11%

Click here to read some of the most thoughtful longform responses.

+Note on sample size: We received 734 votes and 122 longform responses.

🎢 Coasting into first: Check out the new roller coaster in Texas that’s set to break six different world records.

📚 Find your next read: Literature Map takes your favorite author(s) and provides dozens of similar recommendations, ranked by how likely you are to enjoy them.

🏈 Can anybody beat Brady?...Ranking the NFL’s 30 strongest contenders for greatest player of all time.

❓ Want to discover a delightful dose of trivia in your inbox each day? Now I Know is a daily newsletter packed with quirky history, curious science, and fascinating word origins. Subscribe today.*

*A message from our partners

Which Nordic country was the filming location for the Battle of Hoth in Star Wars: The Empire Strikes Back?

🐢 A beach day turned into a rescue mission when an 8-year-old girl spotted a little sea turtle in trouble. It turned out to be one of the world’s most endangered species, a Kemp’s ridley sea turtle, and her quick thinking saved its life.

+Note: This story previously appeared in Positive DONUT, our weekly newsletter surfacing all the good things you don't hear about in the news.

Norway

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