Matematici e AI: insieme contro i problemi irrisolti
The Appeal of Tackling the Impossible
There's something almost addictive about mathematical problem-solving. Mathematicians don't just stumble upon conjectures—they chase them down, lose sleep over them, and occasionally earn Fields Medals for conquering them. The longer a problem stands unsolved, the more prestigious its eventual solution becomes.
In June, something interesting happened. Teams from London to Berkeley got together to create a new list of 50 problems with one key constraint: every single one had to be verifiable through automated checking. This wasn't just about keeping things neat—it actually bridges the gap between human intuition and machine verification, creating a space where AI and mathematicians can genuinely collaborate.
Yang-Hui He, a mathematician at the London Institute for Mathematical Sciences, brought his young son to one workshop. While a child happily ate cake in the corner, mathematicians worked together to submit problems spanning knot theory, algebra, topology, and number theory. There's something wonderfully human about that image—centuries-old mathematical tradition meeting the next generation.
Problems That Haunt Mathematicians
The resulting list reads like a collection of mathematical nightmares. Here are a few highlights:
The Sum of Three Cubes
Can you express a number as the sum of three cubes? The equation x³ + y³ + z³ = k has puzzled mathematicians for decades. In 2020, Andrew Booker and Andrew Sutherland cracked the case for k=42, using up 1.3 million computing hours across thousands of volunteer home computers. Next target? 114. But here's the kicker—the smallest solutions probably involve around 30 digits, and solving it through brute force could run up a $100 million bill.
Proving Irrationality the Apéry Way
Irrational numbers—those decimals that refuse to become clean fractions—hold deep secrets. We all know pi and √2, but proving irrationality is notoriously tricky. It took humanity two millennia to prove pi was irrational. Then in 1978, Roger Apéry demonstrated that ζ(3) (the sum of 1/n³) was irrational using something called a "sandwiching" technique. When questioned about his breakthrough, Apéry claimed he'd found it in a flower pot. That mystery still remains unsolved.
The Lonely Runner Conjecture
Here's a problem that sounds almost playful: imagine runners on a circular track, each moving at their own constant speed. The conjecture suggests that at some point, each runner will be maximally distant from everyone else—their "loneliest" moment. Simple to understand, brutal to prove.
When AI Joins the Conversation
The most intriguing part of this project is how it connects to artificial intelligence. Epoch AI created this list specifically to benchmark AI progress. The timing is worth noting—OpenAI recently claimed to have solved the Navier-Stokes problem, one of the seven Millennium Prize Problems worth $1 million each.
By late September, a few problems on this new list had been solved, though the official collection still overflows with challenges. OpenAI has announced that its unreleased internal AI model has solved more than 100 open questions, though exactly how many belong on this specific list remains unclear.
Why This Should Matter to Tech People
You might be wondering what centuries-old mathematical conjectures have to do with modern software development or cloud hosting. More than you'd expect.
First, mathematical problem-solving pushes computational innovation forward. The brute-force attack on the "sum of three cubes" problem for k=42 required distributed computing across thousands of volunteer machines—a glimpse of modern cloud infrastructure. Second, the intersection of AI and formal verification impacts software reliability across the board. When mathematicians demand problems be "automatically checkable," they're practicing what software engineers call formal methods—the same principles that make secure systems trustworthy.
Third, and perhaps most importantly, the spirit of tackling impossible problems drives all technological progress. Whether you're solving the Riemann Hypothesis or building the next scalable hosting platform, the approach stays consistent: identify constraints, find elegant solutions, verify your work.
The mathematical community's collaboration with AI organizations marks a new chapter in discovery. These 50 problems aren't just academic curiosities—they're benchmarks for human-AI partnership in intellectual pursuit. And in an era where we're building AI-assisted development tools and exploring vibe coding platforms, watching AI tackle mathematics' toughest challenges offers a preview of the future we're creating.
The flower pot mystery remains unsolved. But somewhere, an AI might be getting closer to understanding how Apéry found his proof.