The world’s largest gathering of mathematicians convened in Seattle from Jan. 8 to Jan. 11 — 5,444 mathematicians, 3,272 talks. This 12 months this system diverged considerably from the its conventional kaleidoscopic panorama. An official theme, “Mathematics within the Age of A.I.,” was set by Bryna Kra, the president of the American Mathematical Society, which hosts the occasion in collaboration with 16 companion organizations. In one configuration or one other, the assembly, referred to as the Joint Mathematics Meetings, or the J.M.M., has been held roughly yearly for over a century.
Dr. Kra supposed the A.I. theme as a “wake-up name.” “A.I. is one thing that’s in our lives, and it’s time to start out desirous about the way it impacts your instructing, your college students, your analysis,” she mentioned in an interview with The New York Times. “What does it imply to have A.I. as a co-author? These are the sorts of questions that we have now to grapple with.”
On the second night, Yann LeCun, the chief A.I. scientist at Meta, gave a keynote lecture titled “Mathematical Obstacles on the Way to Human-Level A.I.” Dr. LeCun acquired a bit into the technical weeds, however there have been digestible tidbits.
“The present state of machine studying is that it sucks,” he mentioned in the course of the lecture, to a lot chortling. “Never thoughts people, by no means thoughts making an attempt to breed mathematicians or scientists; we are able to’t even reproduce what a cat can do.”
Instead of the generative massive language fashions powering chatbots, he argued, a “large-scale world mannequin” could be the higher wager for advancing and bettering the know-how. Such a system, he mentioned in an interview after the lecture, “can cause and plan as a result of it has a psychological mannequin of the world that predicts penalties of its motion.” But there are obstacles, he admitted — some mathematically intractable issues, their options nowhere in sight.
Deirdre Haskell, the director of the Fields Institute for Research in Mathematical Sciences in Toronto and a mathematician at McMaster University, mentioned she appreciated Dr. LeCun’s reminder that, as she recalled, “the best way we use the time period A.I. at the moment is just one means of presumably having an ‘synthetic intelligence.’”
Dr. LeCun had famous in his lecture that the time period synthetic normal intelligence, or A.G.I. — a machine with human-level intelligence — was a misnomer. Humans “wouldn’t have normal intelligence in any respect,” he mentioned. “We’re extraordinarily specialised.” The most popular time period at Meta, he mentioned, is “superior machine intelligence,” or AMI — “we pronounce it ‘ami,’ which implies good friend in French.”
Dr. Haskell was already offered on the significance of “utilizing A.I. to do math, and the massive downside of understanding the maths of A.I.” An skilled in mathematical logic, she is engaged on the equal of a textbook: a set of outcomes that can be utilized by A.I. programs to generate and confirm extra complicated mathematical analysis and proofs.
For Kenny Banks, an undergraduate on the University of North Carolina at Greensboro who attended the J.M.M., synthetic intelligence doesn’t attraction as a device for guiding exploration. “I feel the arithmetic that folks at present love is pushed by human curiosity, and what computer systems discover attention-grabbing can’t be the identical as what people discover attention-grabbing,” he mentioned in an electronic mail. Nevertheless, he regretted not squeezing any A.I.-related talks into his itinerary. “The math + A.I. theme was positively of curiosity, it simply ended up not working with all of the issues I had deliberate!”
Here are another highlights from the mathapalooza in Seattle:
Day 1
At 6 p.m. on Wednesday, Jan. 8, after a ribbon-cutting and awards ceremony, attendees stampeded to the grand-opening reception in an exhibit corridor. The draw was a) free meals, and b) exhibitor cubicles occupied by publishers and purveyors of varied mathy wares. At Booth 337, Robert Fathauer was promoting a powerful stock of cube — together with the brand new “5-Player Go First Dice,” a colourful set of 5 60-sided cube that share no quantity in frequent, permitting 5 recreation gamers an equal shot after they roll to find out who begins first. Dr. Fathauer, who relies in Arizona, was additionally co-organizer of the assembly’s artwork exhibit and contributed two ceramic sculptures of his personal, “Hyperbolic Helicoid” and “Cubic Squeeze.”
The exhibit’s award-winning artwork submissions had been “Saddle Monster,” crocheted in wool, copper and nylon, by Shiying Dong of Greenwich, Conn., a mathematical artist with a Ph.D. in physics …
… and “Twisted” and “Untwisted,” created utilizing a vector graphics app on an iPad, by Rashmi Sunder-Raj, a mathematical artist in Waterloo, Ontario.
Rebecca Lin, a Ph.D. pupil in laptop science at M.I.T., acquired an honorable point out for a laser-cut engraving on paper titled “Disintegrating (State of Mind).”
Day 2
On Thursday, Jon Wild, a music theorist at McGill University in Montreal who does math on the facet, was invited to a session on utilized arithmetic to debate his investigations into “counting preparations of circles” within the airplane. Given sure constraints, there’s a technique to attract one circle, 3 ways to attract two circles, 14 methods to attract three, 173 methods for 4, and 16,951 methods to attract 5. (The enumeration of six circles is but to be computed.) Dr. Wild was stunned to study that this analysis was related to 3-D printing: that’s, to how a number of printer heads might every hint round arcs whereas avoiding collisions. “I used to be tickled,” Dr. Wild mentioned.
During a session on arithmetic and the humanities, Susan Goldstine, a mathematician at St. Mary’s College of Maryland, lectured about her “Poincaré Blues” craft challenge. Named for the French mathematician Henri Poincaré, the challenge concerned making a patchwork denim skirt from outdated denims. As she described in a write-up: “After noodling round with totally different patterns, I settled on the tiling of the Poincaré disk mannequin of the hyperbolic airplane by 30º-45º-90º triangles,” which was acquainted to her from an illustration by the classical geometer H.S.M. Coxeter (and which additionally impressed the Dutch artist M.C. Escher).
Day 3
At noon, the undergraduate poster session buzzed with expositions on subjects together with lunar time synchronization; the maths of piano tuning; loops in four-dimensional house; and a mannequin for wildfire containment, smoke unfold and their public well being penalties.
During one other session on arithmetic and the humanities, Barry Cipra, a mathematician from Minnesota, gave a speak about “gelbes feld” (“yellow subject”), a portray by the Bauhaus-trained Swiss artist Max Bill.
It could seem like a strong canvas of coloration, Dr. Cipra mentioned, however there’s a faint sample of contrasting dots, or, extra exactly, squares. “Let’s take a look at an summary model of Bill’s summary,” he mentioned. “Can you see what Bill is as much as?”
By Dr. Cipra’s evaluation, the artist encoded within the portray a traditional 3-by-3 magic sq. — a sq. array of numbers that type a logic puzzle whereby the sum of every row, column and diagonal equals 15.
Another peculiarity was that every row, column and diagonal had 5 pips (as on cube or dominoes):
Dr. Cipra famous, “It seems like Bill posed and solved an authentic arithmetic downside and hid it in a portray: Can you place the pips inside every sq. of the 3-by-3 magic sq. in order that there are precisely 5 pips alongside every row, column and foremost diagonal of the 9-by-9 subgrid?” The identical query might be requested for 5-by-5 and bigger magic squares of strange sizes, he mentioned. “But it’s removed from clear what the reply goes to be.”
Dr. Goldstine discovered Dr. Cipra’s discovery compelling. “I’m at all times excited when math turns up in a spot the place you wouldn’t count on it,” she mentioned in an electronic mail. “I typically use these shocking connections to get college students who is perhaps afraid of or bored by math to see a few of its magnificence.”
Day 4
The last day supplied numerous public occasions, together with a mini math pageant with hands-on puzzles and video games.
“Why is it math?” requested Aleksandra Upton, 7, of a geometrical puzzle.
“Because we are able to depend all of the totally different ways in which we put the shapes collectively,” mentioned her mom, Karolina Sarnowska-Upton, a software program engineering manager at Microsoft in Redmond, Wash.
In one public lecture, Ravi Vakil, a mathematician at Stanford and the incoming president of the American Mathematical Society, explored the concurrently playful and profound “arithmetic of doodling.”
In one other, Eugenia Cheng, a mathematician and pianist on the School of the Art Institute of Chicago, addressed “Math, Art, Social Justice.” One of her salient messages: “Pure arithmetic is a framework for agreeing on issues.” She sang a few of the lecture alongside a recorded video of herself enjoying the piano.
And there was a world premiere of a documentary movie, “Creating Pathways,” the second within the “Journeys of Black Mathematicians” sequence by the director George Csicsery. (It airs on public tv stations in February.) The movie’s senior advisor was Johnny Houston, an emeritus professor at Elizabeth City State University in North Carolina. After the screening, Dr. Houston remarked on the timeliness of the 2025 premiere: In 1925, Elbert Frank Cox grew to become the primary African American — and first Black particular person on this planet — to obtain a Ph.D. in arithmetic. Of his personal journey, and that of many Black mathematicians, Dr. Houston mentioned that with publicity, expertise and alternative, “we are able to do in addition to any mathematician in incomes a Ph.D. and past.”
The final of the talks wound down that night. By 3 a.m. the following morning, as some attendees headed to the airport, two mathematicians had been simply heading to mattress, however not earlier than using the elevator all the way down to the lodge foyer to ask reception for a late checkout.