Will AI Ever Solve an Unsolved Math Problem and Prove Its Creativity?

Is AI Truly Creative? Here Is the Ultimate Test

The word “creative” gets thrown around a lot, but people mean very different things by it. To have a meaningful discussion, we need a clear, strict definition—and a test that follows from it.

Some claim AI already shows creativity, while others believe creativity remains a purely human trait. The core issue is that what one person calls creative, another might see as simply mechanical or imitative.

Defining Creativity: The Lovelace Test

A solid benchmark comes from Selmer Bringsjord’s Lovelace Test. It states that a computer program can only be called creative if it produces an output that goes beyond what its programmer intended or could explain.

No AI has passed this test yet. Sure, transformer models like Grok and ChatGPT produce surprising results, but those outputs still fall within the scope of their programming. Surprising doesn’t always mean creative. Programmers themselves often don’t predict every outcome, but the AI is just following instructions.

A Higher Bar: Solving Unsolved Problems

Beyond subjective judgments, there’s an objective way to judge creativity: solving open problems in mathematics that have resisted human efforts for decades or centuries. These require genuine insight, not just brute computation.

Here are some standout examples of human creativity tackling such challenges:

• Hannah Cairo: A 17-year-old home-schooled student who recently disproved the Mizohata-Takeuchi conjecture, a 40-year-old problem in harmonic analysis involving wave functions on curved surfaces. Her work demanded original thought and deep mathematical understanding. She’s a top candidate for the Fields Medal, often called the Nobel Prize of mathematics.
• Grigori Perelman: In 2023, he solved the Poincaré Conjecture, a 99-year-old puzzle about three-dimensional manifolds. His proof showed that any simply connected, closed 3D manifold is topologically equivalent to a 3D sphere. Perelman declined the Fields Medal for his achievement.
• Andrew Wiles: In 1994, Wiles cracked Fermat’s Last Theorem, a problem unsolved for 357 years. The theorem states there are no whole numbers that satisfy a specific equation for powers greater than two. Wiles missed out on the Fields Medal due to age rules but secured a place in math history.

These breakthroughs represent true creativity: new, correct solutions to problems that stumped generations.

Current Unsolved Problems — Can AI Solve Them?

Numerous famous problems remain open today. Some key examples include:

• Goldbach’s Conjecture: Every even number greater than 2 can be expressed as the sum of two primes. Proposed in 1742.
• Twin Prime Conjecture: Are there infinitely many prime pairs that differ by two? Proposed in 1849.
• Collatz Conjecture: A simple iterative process seems to always reach 1, but no proof exists. Proposed in 1937.
• Riemann Hypothesis: About the distribution of zeros in the Riemann zeta function. Proposed in 1859.

These problems have withstood human attempts for decades or centuries. If AI were to independently prove or disprove any of these, it would be a clear demonstration of genuine creativity. Interestingly, some may be true without a proof ever existing.

Can AI Help, Without Actually Creating?

AI can be a valuable assistant—scanning large datasets, testing cases, or exploring millions of possibilities quickly. But the crucial leap—the insight that narrows the search to a promising idea—still comes from humans.

Ask current AI systems to prove Goldbach’s Conjecture or the Riemann Hypothesis, and you’ll get no solutions, only acknowledgment of their unsolved status. AI doesn’t originate the deep insights needed to solve these open problems.

The Verdict

For now, AI acts as a powerful tool, not an originator of new mathematical knowledge. When AI finally solves a long-standing mathematical problem on its own, without human input, that will be the moment creativity can be said to have crossed into the digital domain.

Until then, creativity remains largely a human trait.