Chinese mathematician Sun Zhiwei proposes 1,000 problems to challenge AI

In an era where AI is capable of providing solutions to intricate mathematical problems, Chinese mathematician Sun Zhiwei emphasizes the importance of curiosity and questioning over relying solely on existing formulas and theorems. As a 61-year-old professor at Nanjing University’s department of mathematics, Sun has developed an extensive pool of mathematical problems – over 1,000 so far – for the global research community to address.

Traditional mathematical education stresses comprehending established formulas and validating verified theorems. However, Sun argues that genuine advancement hinges on cultivating intuition to formulate new questions and employing logic to resolve them. Sun stated, "If a discipline lacks conjectures, individuals cease to understand what to do, and the field stagnates."

He reassures that AI cannot solve all mathematical conundrums, and mathematicians need not panic. Instead, they should utilize their time to develop novel methodologies and establish new theories. Sun perceives AI as an extremely knowledgeable, diligent, and intelligent graduate student. When assigning it challenging mathematical problems, he provides appropriate direction and, if necessary, prompts it to modify its approach.

He instructs the AI to disregard internet search access to prevent discovering that the problem remains unresolved and to cease endeavoring on it. Sun recounted that in his early career, he employed traditional problem-solving techniques, making substantial contributions to Hilbert’s Tenth Problem, posed in 1900. A 2005 visiting professorship at the University of California, Irvine, marked a pivotal moment when he encountered an American professor proficient in employing mathematical software to unearth patterns—a technique unfamiliar to Sun at the time.

After aiding the professor in resolving a conjecture that had eluded resolution for years, Sun acknowledged that mathematical tools were undergoing a qualitative transformation. In 2009, he began instructing himself on using the Mathematica program for technical computing. This enabled him to validate thousands of cases, a laborious and often impractical task accomplished through manual calculations previously.

"Following that year, I experienced an epiphany, and a plethora of eccentric ideas began to emerge," Sun recounted. This year, Sun compiled a collection of problems spanning more than 400 pages, encompassing 1,000 unsolved conjectures that he proposed. His academic webpage features a compilation of conjectures accompanied by monetary incentives for their proofs, financed by his salary.

Many of his problems surpass conventional milestones. For instance, Sun incorporated additional constraints to French mathematician Lagrange’s two-century-old four-square theorem, which posits that every natural number can be expressed as the sum of four integer squares, to devise new conjectures. "We merely declare a theorem 'beautiful,' and once the proof is completed, we consider the matter concluded.

We never deliberate upon whether the theorem is robust enough or it possesses limitations," Sun explained. "Textbooks frequently focus on greatness, not flaws." As AI reshapes scientific discovery, Sun advocated welcoming AI in advancing mathematics in the pursuit of truth. "If you pursue mathematics solely for fame and fortune, you might be apprehensive about AI usurping your profession, but if your objective is the pursuit of truth, you should embrace the manner in which AI advances the field," he remarked.

Sun designated some of his most challenging problems "alien conjectures," indicating that "Earthlings cannot solve them." When queried about the rationale for proposing unsolvable problems, Sun asserted that his motivation is not whether one can solve it or not; he is merely striving for truth. Whether modern tools suffice is another matter.