In one of the most special and emotional moments I have witnessed during a mathematics conference, Benedict (Dick) Gross’s face unexpectedly appeared on all three of the large screens of the auditorium 10-250 and, after some initial surprised gasps, the audience went completely silent. For the duration of the video (about ten minutes), the number theorists gathered at MIT for the “Gross–Zagier formula, 40 years later” conference watched quietly, and some of us with teary eyes, while Gross explained to us how the formula came to be, in a collaboration that already is a beautiful and critical moment in the history of mathematics.
The conference, which was probably conceived over two years prior, was meant to celebrate the iconic Gross-Zagier formula and showcase recent related achievements on the arithmetic of L-functions, but when Dick Gross passed away (at 75) on December 19, 2025, it was clear that the conference would serve as well as a timely celebration of Gross’s mathematics and legacy. On August 6th, 2026, Don Zagier was slated to speak at the conference on “Higher Green’s Functions” and his talk began with his own recounting of the tale of how the two of them arrived at the consequential formula. Many of us thought that Zagier’s talk was the main event of the day (the main event of the conference, in fact) and I suspect many attendees were there just to listen to Zagier’s lecture (mea culpa), but the organizers had a touching surprise in store for the unsuspecting audience. When Zagier’s talk ended, and after a boisterous round of applause, Ben Howard (one of the co-organizers) told us to stay put because there was a very special short talk added to the schedule before we broke for lunch.
Howard explained: in the fall of 2025, Gross’s health was quickly deteriorating and foreseeing that he may not be able to be with us at MIT by August 2026, he decided to record a short video to be played during the event. Dick recorded the video in his office, looking directly into the camera, with his familiar affable demeanor. In the video, he proceeds to re-tell once more his account of how the formula came to be in his usual captivating and humorous way. Clearly, Gross was unwell in the recording, and he struggled at times to get the words out, but his expression brightened at times discussing mathematics, and telling us his best anecdotes of what it was like to work with Don.
The video came to an end and the audience at MIT 10-250 went from stunned silence to erupting in applause in a final goodbye and thank you to Gross for all of his delightful talks over the years. I stayed in my seat for a minute just trying to contain my emotions. I did not know Dick well, but I did interact with him several times during previous conferences, enough to verify that he was a fantastic human being, in addition to a stellar mathematician. When I heard the news, I felt very sad to hear about his passing. Death and I have had some recent encounters both my dad and my father-in-law passed away within months of each other almost a couple of years ago now and while I was not close to Dick, I know many were, and many considered him their mathematical father or close relative in some way or another.
Besides the painful thoughts that discussing death brings to my head, there is something else that came to my mind after watching Gross’s last talk. And that’s the invaluable human contributions of some mathematicians and, in this case, the community’s immense human loss. Dick’s generosity towards students and collaborators was widely known, as was his friendly demeanor to anyone and everyone: the kind of larger-than-life persona that makes just every conference, department, or gathering better and more welcoming… to other humans. Needless to say, his mathematical contributions have already carved a well-deserved place for him in the history of number theory, but his wonderful community-building contributions will certainly not be forgotten either for years to come. Hopefully never, as long as we continue to highlight and cherish them. Incidentally, Dick Gross was a student of John Tate, another outstanding human and mathematician who was also known to be extremely generous to his students and the community.
Thinking back at the reasons why I wanted to be a mathematician in the first place, clearly the beauty of mathematics itself was the main reason, but the legends of certain mathematicians were too tantalizing not to attempt to follow in their footsteps even if my steps are tiny compared to their mighty stride. The towering talent of mathematicians such as Andrew Wiles amazed me growing up, but so did their perseverance and tenacity in the face of a seemingly insurmountable proof. For example, my favorite scenes in the Nova documentary “The Proof” are those moments of Wiles recounting his emotions, and getting misty-eyed on camera thinking back at the moment when he knew he had it, letting his own humanity be on full display. Similarly, the documentary “N is a number” shines not because of Paul Erdős’s mathematics, but because of his persona, his charisma (his aura as kids would say these days), and mostly because of the emotions and personal anecdotes recounted with such joy by those who met and collaborated with Erdős.
But no other documentary is as touching as the deeply moving portrait of Maryam Mirzakhani in “Secrets of the Surface“. Her immense mathematical legacy (worth a Fields medal) is almost eclipsed by the human legacy that she left behind. Indeed, some of the most beautiful moments of the film show us how Maryam’s tenacity and humanity have inspired not only her friends and collaborators, but an entire generation of Iranian girls (and continues to inspire many of us too).
The truth is that on August 6th, 2026, the main reason why I attended the MIT conference on the Gross-Zagier formula was to enjoy the whirlwind experience of a Don Zagier talk. Much like Erdős, the human mathematical intelligence of Zagier is something to behold and fascinating to watch. His talks are immensely entertaining because of his humor, wit, charisma, candor, and devilish pace. And without fail, you are left with a sense of awe at his capacity to realize brilliant connections where most of the rest of us would only see noise in numbers. If you want to see just one example of Zagier’s antics, I just happened to record a bit of his lecture at Harvard during Dick Gross’s 60th birthday conference back in 2010, and in this clip the self-proclaimed “hitman of mathematics” figures out an exact formula for the number
-7.483708229911735369141145
to the great amusement of the dazzled audience.
Gross, Zagier, Wiles, Erdős, or Mirzakhani are just a handful of examples from the rich field of mathematics, a field that has yielded generation after generation many crops of impressive humans. A field also has weeds and invasive species, and it needs love and care to keep producing healthy crops no doubt! but I think those in our field love the community because of the many fantastic humans that populate it.
In the age of AI, some argue vociferously that artificial quasi-intelligence artifacts, in the near future, will be able to solve any problem that humans could solve by themselves. While this possibility is uncertain and may never actually come to pass, we mortal mathematicians have always had the sneaky suspicion that someone like Zagier could solve any problem we could solve, in a fraction of the time. But this has never deterred us, because mathematics has never been a competition: it is, rather, an art the art of understanding the amazingly beautiful mathematical realm. And this mathematical art form is a human endeavor that no machine will be able to accomplish for the simple reason that it is the understanding of mathematics that drives us human understanding by humans for humans. Further, if we asked Zagier for help with a problem, undoubtedly he would selflessly help us solve it but most importantly, understand it, and co-author a paper with us with authors listed in alphabetical order (therefore likely placing Zagier’s name last).
In a sense, we are captivated by the intelligence of people like Gross or Mirzakhani because they have been able to understand mathematics (not produce mathematics) at a much higher level than most of us may ever be able to. We are most thankful and inspired by them, though, when they take us along for the ride, and manage to explain the beautiful mathematical worlds they have discovered. Even when their explanation is beyond our understanding, it is their emotions and excitement that may be enough for us to be energized to learn more on the subject until we can glimpse the same beauty they have discovered.
Unfortunately, but not surprisingly, AI/LLM-driven discoveries have received the polar opposite reception than other recent human achievements. Instead of energizing the field, instead of producing new insights, instead of inspiring new generations of Iranian girls, some mathematicians are quitting academia and many students now question whether they should pursue their dream of a PhD in Mathematics.
Why?
Because AI proofs, without being humanized, without human understanding and digestion, and without human mathematicians telling us why and how the proof works, are just totally devoid of the artistic craft that we love in the mathematics of humans. An AI proof is at first the equivalent of a bad parenting response:
“Why? Because I say so.”
Only a posteriori mathematicians may digest the proof, mold it, modify it, improve it and make it appealing to other mathematicians, after some badly needed human touch. Do not get me wrong. We have already seen some surprising insights produced by an LLM, as it was in the case of the disproof of the unit-distance conjecture. But most of us were more interested in the commentary by other human mathematicians, that is, the humanization of the proof, than by the allegedly LLM-generated mathematics. Incidentally, almost immediately a human (Will Sawin) discovered a way to improve the proof and the result.
Will artificial quasi-intelligent systems be able to solve any problem a mathematician can solve? It seems doubtful to me, even if AI companies want us to assume that is the case: I am referring to a recent event put together by Open AI where the premise, as Daniel Litt wrote in his blog entry “The End of Mathematics“, was as follows:
The premise of the workshop (which we took as a starting point, rather than subject to debate, for the sake of productive discussion) was that AI will become robustly superhuman at mathematics.
Or as Alex Kontorovich put it:
The whole premise of the meeting was: Assume math is “solved”, that is, any problem solvable by human+AI is also solvable by AI alone.
Such a premise seems just as un-useful as it is presumptuous (but of course a company would want you to believe that their product will be superhuman: “Invest now! Invest early!“). Instead, what seems to be settled by the recent advancements is that artificial quasi-intelligence will never be able to replace the great human mathematicians in our community: the Grosses, Zagiers, Wileses, and Mirzakhanis, that have inspired us and move us to follow their footsteps to try to add our own little hand-crafted pieces of mathematical art to the subject that we love.
If we want to make sure that mathematics survives the AI era, and if we want our field to continue to attract human talent and humans hoping to build a better and stronger community, then we need to heavily invest in humans, and vociferously celebrate – more than ever the human contributions by the great people that have built our community piece by piece, just like, for example, Dick Gross or Maryam Mirzakhani did.
Received 18 August 2026.
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