Some insist that AI already demonstrates creativity, while others, like me, argue that creativity remains uniquely human. Part of the difficulty lies in how we define creativity. What one observer hails as a creative achievement, another might dismiss as merely computational or imitative.

Defining creativity: The Lovelace Test

A rigorous approach to defining creativity comes from Selmer Bringsjord’s Lovelace Test: a computer program can be called creative if it produces a result beyond the explanation or intent of its programmer.

So far, no AI has demonstrably met this standard.

That said, creativity — like beauty — can be a matter of subjective judgment, and interpretations vary widely. Current transformer models like Grok & ChatGPT are doing what was intended by the readers of the 2017 paper that introduced the algorithm. The results these chatbots generate can be surprising, but surprising results do not always originate in creativity. Programmers are sometimes surprised by the results of their code, but the computer is doing what the programs instructed it to do.

A Higher Bar: Solving Unsolved Problems

While these subjective measures are interesting, a more objective standard is possible. An undeniable final test for AI creativity is its ability to solve an open problem in mathematics — a problem that has resisted solution despite extensive human effort. Such achievements require not just computation, but genuine insight and creativity.

Here are some examples from recent history where human ingenuity has solved difficult open problems in mathematics:

Example 1 – Hannah Cairo

Recently, Hannah Cairo disproved the Mizohata-Takeuchi conjecture, a 40-year-old open problem dealing with the harmonic analysis of the behavior of wave-based functions on curved surfaces. This required original thinking, creative problem-solving, and a deep understanding of advanced mathematics.

Remarkably, Hannah Cairo is a 17-year-old home-schooled student. Expect her to be nominated for the Fields Medal — the Nobel Prize for mathematics.

Example 2 – Grigori Perelman

In July 2023, Russian mathematician Grigori Perelman solved the Poincaré Conjecture, a 99-year-old problem about the nature of closed three-dimensional manifolds. His proof confirmed that every simply connected, closed 3D manifold is topologically equivalent to a 3D sphere.

Perelman famously declined the prestigious Fields Medal for his work.

Example 3 – Andrew Wiles

In 1994, Andrew Wiles solved Fermat’s Last Theorem, a problem that had stood for 357 years. Fermat’s Last Theorem says that it’s impossible to find three whole numbers that — when each is raised to the same power greater than two — add up exactly to one another. Wiles was ineligible for the Fields Medal because recipients must be under 40, and he was 41 at the time.

These examples represent what many would consider true creativity — generating entirely new, correct solutions to longstanding intellectual challenges.

Current unsolved problems — Can AI solve them?

A number of famous unsolved problems in mathematics remain open today. A list can be found on Wikipedia. The most celebrated examples include:

1. Goldbach’s Conjecture – Every even integer greater than 2 can be expressed as the sum of two primes. First proposed by Christian Goldbach in 1742.
2. Twin Prime Conjecture – Are there infinitely many pairs of primes that differ by two (e.g., 5 and 7, 11 and 13, 521 and 523)? First proposed in 1849.
3. Collatz Conjecture – Iteratively applying a simple function to any positive integer appears always to converge to 1, but no proof exists. Lothar Collatz proposed his conjecture in 1937.
4. Riemann Hypothesis – Concerns the distribution of zeros in the Riemann zeta function. First proposed by Bernhard Riemann in 1859.

These problems have resisted human effort for decades or even centuries. Proving or disproving any of them without human assistance would be a definitive demonstration of AI creativity.

Interestingly, it could be that no proofs exists for some unsolved problems in mathematics. They might be true simply because they are true.

Can AI help, without actually creating anything?

AI can assist mathematicians in many ways — scanning through massive datasets, testing conjectures for special cases, or searching millions of possible solutions quickly. But the conceptual leap — the spark that narrows down the search space to a promising idea — still comes from a human mind.

If you were to ask today’s AI systems to “prove Goldbach’s Conjecture” or “prove the Riemann Hypothesis,” you would not get a solution — only an acknowledgment that no proof exists. AI does not, at present, originate the kind of deep insight required to solve a open mathematical problem.

The verdict

For now, AI remains a powerful assistant but not a genuine originator of new mathematical truths. The day an AI independently solves a long-standing unsolved problem in mathematics — without human guidance — will mark a historic turning point. That will be the day skeptics must acknowledge that AI has achieved creativity in the fullest, most undeniable sense.

Until then, creativity remains, for the most part, solely in the  human domain.