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Limited seats available, first come first served. Let us join together in the commitment to sustainability! [Click to register] On the deep night of February 4, 2017, Sun Zhiwei, sound asleep, suddenly felt "two streams of heat surging back and forth behind him." He woke with a start, threw on his clothes, and sat up, unable to sleep again. Later, recalling that moment, Sun Zhiwei said he had "suddenly seen the light." The inspiration that flashed through his mind that night was aimed at a classic mathematical theorem from over two hundred years ago — he decided to attach two restrictive conditions to the famous "Four Square Theorem." For this conjecture, he decided to offer a bounty of $2,400 out of his own pocket. The amount was not chosen arbitrarily: the conjecture was born on February 4, and the conditions involved the number 24, so he simply named it the "24 Conjecture." Now, nine years have passed, and this bounty still hangs quietly in the fog of the mathematical world, unsolved to this day.
Like this imaginative new mathematical conjecture, this professor from the Department of Mathematics at Nanjing University, who speaks with a thick Huai'an accent, has proposed over a thousand of them one after another. In the kingdom of mathematics, those who prove theorems are often revered as heroes. For over thirty years, in research on Hilbert's Tenth Problem restricted to a bounded number of unknowns over the ring of integers, Sun Zhiwei has long maintained the best results. But what he enjoys more is staring at the unresolved blank spaces beyond those theorems.
In 2026, Sun Zhiwei completed a special manuscript. It is a thick "problem collection" of over 400 pages, recording 1,000 unsolved conjectures he personally proposed. Some conjectures are derived from the "Four Square Theorem" proved by the French mathematician Lagrange over two hundred years ago. For more than two centuries, the world has generally felt that the Four Square Theorem had been brought to a satisfactory conclusion. But Sun Zhiwei was not satisfied with that. In his "24 Conjecture," the Four Square Theorem has more restrictive conditions: every natural number is the sum of the squares of four natural numbers x, y, z, and w, and one can further require that x and x+24y are both perfect squares. In his "1-3-5 Conjecture," the requirement is that x+3y+5z is a perfect square.
This kind of questioning stems from his "picky" attitude toward textbooks. "We only say, this is a beautiful theorem, and once it's proved, that's the end of it. We never discuss whether the theorem is strong enough, whether it has limitations," Sun Zhiwei said. "Textbooks often only talk about greatness, not defects." Professor Hou Qinghu from the School of Mathematics at Tianjin University was deeply impressed by Sun Zhiwei's highly divergent thinking: "Many of Teacher Sun's conjectures are extremely challenging, and classical methods are almost powerless to solve them." Taking Sun Zhiwei's conjecture on integer partitions as an example, merely making simple combinations of square numbers with specific multiples makes it difficult for existing number theory tools to reach. Such conjectures precisely strike the blind spots of existing mathematical tools.
Before the age of 44, Sun Zhiwei was almost a pure "problem solver" — "others proposed conjectures, and I was responsible for proving them." The turning point in his fate occurred around 2005 when he went to the United States as a visiting scholar. At that time, Sun Zhiwei met an American professor skilled at using mathematical software to find patterns, while at that point he did not even know computer programming. After helping this professor crack a conjecture that had troubled him for years, Sun Zhiwei suddenly woke up: times had changed, and mathematical tools were undergoing a qualitative leap.
In 2009, at the age of 44, Sun Zhiwei began teaching himself Mathematica programming. In the past, when an idea popped into his head, either he had no time to calculate by hand, or pen and paper simply could not handle the computation; now, the computer could verify tens of thousands of examples for him. If it did not pass, he could revise it at any time; if it ran through, it became the prototype of a new conjecture. "From that year on, I suddenly saw the light, and I had so many wonderful ideas," Sun Zhiwei said. Where did these wonderful ideas come from? Many came precisely from ordinary, trivial life.
One day in 2013, he passed by the display window of the Nanjing University Mathematics Department, where a notice about reimbursement for medical expenses for faculty children was posted. The reimbursement principle was: "male odd, female even" (reimbursed at the father's workplace in odd years, at the mother's workplace in even years). These four words made Sun Zhiwei stop. What others saw was a reimbursement rule, but what he thought of was number theory. "In mathematics, except for 2, all prime numbers are odd, while another class of richly structured 'practical numbers' are basically even. Why can't I compare prime numbers to males and practical numbers to females?" In his imagination, prime numbers are like the "father of multiplication," while practical numbers are like the "mother of addition." Following this line of thought, he began to re-examine Goldbach's Conjecture: since even numbers greater than 2 can be expressed as the sum of two primes p and q, could these "prime couples" appear hand in hand, and could the corresponding practical numbers also satisfy a similar relationship? Thus, he proposed the "Couple's Version of Goldbach's Conjecture": even numbers greater than 4 can be written as p+q=(p-1)+(q+1), where p and q are primes, and p-1 and q+1 are practical numbers. Not only that, he also conceived the "Sandwich Conjecture" and the "Pork Belly Conjecture" based on this. Sun Zhiwei believes that the "Pork Belly Conjecture" is even far more difficult than the Twin Prime Conjecture. "I don't believe humanity will be able to prove it in a short time."
"Personification is my important magic weapon for discovering mathematical patterns," he said. "However complex human society is, the world of numbers is just as complex." Sun Zhiwei describes his working state as "wisdom born of urgency": when desk chores pile up and his mood is anxious, inspiration sparks are most likely to burst forth. "The more urgent it is, the more sparks fly. And once inspiration comes, everything else takes a back seat. I always insist on inspiration first." Philosophy, intuition, life experience, and high-speed computation mixed together form his crucible of inspiration. Sometimes he even finds it incredible: "Some patterns are so simple they're unbelievable. By rights, they should have been discovered long ago by Fermat, Euler, or Gauss. How could they have been left to today, to me?"
Faced with outsiders' questions about "why are you so obsessed with posing problems," Sun Zhiwei's answer was crisp and firm: "If a discipline has no more conjectures, people won't know what to do, and the discipline will approach stagnation." His conjectures span multiple peaks of pure mathematics, and have even attracted the attention and follow-up of many top international scholars, including the late Belgian mathematician Jean Bourgain, a Fields Medalist. New Zealand number theory expert Shaun Cooper lamented in his monograph: the large number of conjectures proposed by Sun Zhiwei has greatly broadened people's cognitive boundaries of Ramanujan-type series theory and activated a large amount of subsequent derivative research. But more often, the conjectures he proposes still lie quietly in the fog. To prove them, the mathematical community often first needs to nurture a next generation of entirely new theoretical weapons.
Sun Zhiwei has an independent view of contemporary mathematics: "Many people praise the brilliance of modern mathematics. Frankly speaking, I am different from others. I am not appreciating the brilliance of modern mathematics; I see its limitations. Some conjectures are designed precisely against the weaknesses of modern mathematics." He even jokingly calls some of the extremely difficult conjectures "alien conjectures" — "definitely impossible to solve on Earth." Someone once asked him in confusion: "What is the point of posing these problems that no one can solve?" Sun Zhiwei replied: "My motivation is not about whether you can solve them or not. I am simply pursuing truth. Whether modern tools are sufficient is another matter entirely."
In the public's stereotypical impression, the work of mathematicians is derivation: step by step, ultimately proving a theorem. Sun Zhiwei says the order is often reversed. "Mathematicians often first discover the result, and then supply the proof. They do not derive something step by step." In his view, the advancement of mathematics must rely on two legs: one is using intuition to discover problems, and the other is using logic to conquer problems. "Riemann, Poincare, and Ramanujan were all masters with superhuman mathematical intuition. Hardy once tried to help Ramanujan develop more standardized proof habits, and later realized that if he forcibly remolded him, Ramanujan's unique intuition might disappear."
To encourage peers to solve problems, Sun Zhiwei has offered various bounties out of his own pocket. Since research funds cannot reimburse such expenses, the prize money is entirely covered by his personal salary. The bounty amounts also carry a rich Sun-style humor: for example, the "520 Conjecture" offers a bounty of $520, not only because the series sum in the conjecture equals exactly 520 divided by pi, but also because May 20 happens to be the anniversary of his alma mater Nanjing University. So far, he has already paid out about five bounties. The "520 Conjecture" was jointly cracked by a Canadian mathematician and an American mathematician. Interestingly, the other party asked not to be paid in US dollars, hoping it could be converted and sent in RMB. They even left it untouched after receiving it, specially framing the certificate of problem solving signed by Sun Zhiwei and hanging it on the office wall. The largest bounty — $1,350 for the "1-3-5 Conjecture" — was ultimately won by a Portuguese professor and his doctoral student, attracting coverage from overseas media.
In the wave of artificial intelligence (AI), Sun Zhiwei is an enthusiastic embracer. He not only frequently uses AI to assist exploration, but has also written several essays on the subject, publicly lamenting on social media: "If you don't use AI anymore, you really will fall behind." Faced with the concerns about AI expressed by top scholars such as Terence Tao, Sun Zhiwei has his own more open-minded optimism: "In a great harvest era, it's understandable if you say farmers can't keep up. Tao says that in the AI era mathematical proofs will be excessive, and I understand that too, but that is not a reason to oppose it. If there is more grain, you can eat it slowly. Mathematicians previously spent a long time digesting Galois theory and digesting Perelman's proof of the Poincare Conjecture." He agrees with Tao's view: mathematics has entered an industrial era. But he believes: "If you do mathematics only for fame and fortune, you will worry that AI will steal your job; if you do it to pursue truth, you should welcome AI promoting mathematical progress."
Sun Zhiwei does not believe AI will replace mathematicians. "AI cannot solve all mathematical problems. Mathematicians have no need to panic; they can free up time to do what AI is not good at, such as developing new methods and creating new theories." He has even summarized a rather wise set of tactics for "taming" AI in daily use. For example, "forbid it from searching the internet, otherwise if it finds out this is an unsolved problem, it will refuse to do it." In Sun Zhiwei's view, AI is not an all-powerful machine, but more like an assistant that needs to be trained. "I see AI as a knowledgeable, diligent, and smart graduate student. When letting it attack difficult mathematical problems, you need to guide it appropriately, and when necessary, have it adjust its attack strategy."
"The outside world often says that we in China have more problem-solving-type mathematicians, reading others' textbooks, reading others' papers, following behind, and mostly being follower-type," Sun Zhiwei said. "But proposing new problems is different. You cannot run behind others; you must have your own original ideas and cannot blindly follow." "In the AI era, asking good questions is especially important." Sun Zhiwei advises young students that in addition to burying themselves in problem sets and studying literature, they must also leave open several windows for free thinking: "Mathematics is very rigorous, but creative exploration requires curiosity and imagination." Many years ago, when Nanjing University's Lily BBS was still lively, Sun Zhiwei's personal signature read: "Mathematics is a science rich in imagination, and also the most rational art."
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