AlphaEvolve: How AI-Human Team Solves 18-Year Math Puzzle

In a world where technology moves at lightning speed, the boundaries between artificial intelligence and human ingenuity are blurring like never before. Nowhere is this collaboration more exciting—or more surprising—than in the realm of mathematics, that ancient and enigmatic discipline. Recently, a stunning event shook the global math community: between May and early June 2025, a team led by legendary mathematician Terence Tao and DeepMind’s AI system AlphaEvolve joined forces to make not one, but three historic breakthroughs on a problem that had resisted progress for 18 years. The result? A new milestone in additive combinatorics, and a glimpse into the future of scientific discovery itself.

Understanding the Sum-Difference Problem

To appreciate the significance of this breakthrough, let’s first take a quick tour of the so-called “sum-difference problem.” In additive combinatorics, mathematicians study relationships between two sets of integers, A and B, by looking at their sum set (A+B) and their difference set (A−B). The sum set contains all possible results of adding any element from A to any element from B, while the difference set contains all possible results of subtracting elements. For example, if A = {1, 2} and B = {3, 4}, then A+B = {4, 5, 6} and A−B = {−1, −2, −3} (after removing duplicates).

The challenge for mathematicians has been to construct special sets where the sum set is relatively small, but the difference set is as large as possible. The main metric for this is an exponent θ, with a theoretical upper limit of 4/3 (about 1.3333). The goal? To push the lower bound of θ ever higher.

Back in 2007, Gyarmati, Hennecart, and Ruzsa set a record by constructing a set of about 30,000 elements, pushing θ to 1.14465—a major breakthrough at the time. But for 18 years, progress stalled, and the problem became a daunting mountain for mathematicians to climb.

Enter AlphaEvolve: AI as a Mathematical Explorer

The turning point came on May 14, 2025. Enter AlphaEvolve, a new AI system developed by DeepMind, with Terence Tao’s guidance. Using an innovative evolutionary algorithm (inspired by natural selection, crossover, and mutation), AlphaEvolve scoured the vast space of possible integer sets. Think of it as a tireless explorer, rapidly testing millions of possibilities. The payoff? AlphaEvolve found a new set with 54,265 elements, boosting θ to 1.1584.

This result sent shockwaves through the mathematical world. For nearly two decades, human mathematicians with “pen and paper” had barely advanced the field—now, AI had leapfrogged ahead in a matter of weeks. It was the first time an AI system had made such a pure mathematical advance, showcasing the immense potential of AI in scientific research.

Human Ingenuity: The Art of Deep Refinement

But the story didn’t end there. Just a week later, on May 22, mathematician Robert Gerbicz picked up where AlphaEvolve left off. Instead of relying solely on AI, Gerbicz used traditional mathematical insight to meticulously analyze and fine-tune the AI’s construction. With deep understanding and precise adjustments, he nudged θ even higher, to 1.173050—an achievement that required both mathematical mastery and careful intuition.

As Terence Tao observed, it’s precisely this complementarity—AI’s broad, brute-force search and human depth of understanding—that drives rapid progress. AlphaEvolve provided new directions, while human mathematicians transformed those hints into theoretical breakthroughs.

The Third Breakthrough: Theory, Not Just Computation

Just as the community was marveling at Gerbicz’s advance, Fan Zheng struck again on June 2 with a new paper on arXiv. This time, the approach was even more elegant: instead of relying on AI’s raw computational power, Zheng set certain parameters to “infinity” and used a concept from probability theory called measure concentration. With careful analysis and computer-assisted calculations, Zheng pushed θ to 1.173077.

The difference may look tiny—just 0.000027—but in mathematics, every decimal point can represent a leap in understanding. More importantly, this breakthrough signaled a new research paradigm: AI provides the initial direction, then human creativity and theory drive deeper discoveries.

A New Era for Math—And Science

These three advances are more than just incremental improvements; they mark a major shift in how math is done. In the past, AI and humans were often seen as competitors—think of AlphaGo defeating the world’s best Go players. But here, the story is one of partnership: AlphaEvolve lights up hidden patterns in the darkness, while humans provide deep insight, abstraction, and innovation.

This is not just about using AI as a tool; it’s about forming a true partnership. AI becomes a source of inspiration and a catalyst for new ideas, while human mathematicians push the boundaries of theory. As Terence Tao notes, future math will increasingly blend computer assistance with traditional “pen and paper,” each amplifying the other’s strengths.

Beyond Math: The Future of Discovery

This chase for θ isn’t just a triumph for mathematics—it’s a sign of things to come in all sciences. As AI rapidly evolves, more and more fields—physics, chemistry, biology—are benefitting from AI-human collaboration. The combination of AI’s data processing and pattern recognition with human creativity and logic is rewriting the rules of research.

At the same time, these breakthroughs remind us that while AI is powerful, human ingenuity remains irreplaceable. For now, AI mostly offers tools and suggestions. The deepest leaps still come from human thought and creativity. Only by working together—AI and people side by side—can we reach new heights.

As Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” Today, those giants include not just the great minds of the past, but also powerful AI systems like AlphaEvolve.