Mathematics

Research led by Principal Research Scientist Neil Thompson suggests that AI is likely to be upend theoretical scientific fields within a few years, writes Wired’s Will Knight. “As with math, Thompson says, we should expect advances in other areas to have both positive and negative effects,” writes Knight. “He notes that theoretical advances sometimes drive practical advances in science and suggests that greater use of AI may mean that more progress happens this way.” 

Prof. Ankur Moitra and Prof. John Urschel share their thoughts with Forbes’ Alex Knapp about OpenAI releasing more than 700 math preprint papers online. “We’re used to landmark results being accompanied by new insights and theories,” writes Moitra. “But these feel different. The claims are spectacular, the papers are incomprehensible and there’s no punchline in sight that explains why the mysteries suddenly unraveled.” Adds Urschel: “It’s obvious that how we do and evaluate mathematics is going to have to change. What I think is constant is the fundamental idea of understanding that underpins our profession. And I’m excited to learn from these breakthroughs.” 

In an interview with Bloomberg, Prof. Justin Solomon discusses how mathematicians are responding to advances in AI in the wake of an AI platform solving the Navier-Stokes problem. “The really interesting part [of proof writing] is the modeling and figuring out which questions to ask and what insights they bring us to the universe, and the AI tools are not doing that,” says Solomon. “Writing the prompts is very much what we’ve been teaching our students to do for centuries now, and that skill, I think, persists.” 

Prof. John Urschel speaks with Wall Street Journal reporter Andrew Beaton about how he called an audible and pivoted from the NFL to a career in mathematics, delving into his time playing for the Baltimore Ravens, his graduate studies at MIT and the publication of his latest research, which proves a decades-old mathematical conjecture. “I feel like I bet on myself in a big way,” Urschel says. “I’m living my best life right now.” 

Prof. Virginia Vassilevska Williams speaks to the Scientific American’s Peter Hall and Joseph Howlett about AI assisting in faster matrix multiplications. “Matrix multiplication is needed all over the place,” says Williams. “But also, its complexity is one of the great mysteries in computer science. In a maybe diabolical sense, the advance on matrix multiplication can be seen as an attempt by the LLMs to speed themselves up.”  

The New York Times’ Siobhan Roberts highlights Prof. Frank Wilczek’s 1973 discovery of asymptotic freedom, a physical property that “allowed physicists to better understand the nuclear force,” according to Edward Witten at the Institute for Advanced Study, that may help solve the Yang-Mills Millennium Prize Problem. The discovery “indicated that proving the existence of quantum Yang-Mills theory in four-dimensional spacetime was central to understanding the mathematical framework of modern subatomic physics.”  

Prof. John Urschel found that the Gaussian elimination algorithm, used to calculate shared solutions to a group of equations, specifically linear equations, is close to 100 percent reliable, writes reporter Miriam Waldvogel for The Washington Post. “It just seems so interesting that the most fundamental algorithm we have in the field, we do not fully understand,” says Urschel. “I really love this question of why versus how, and this idea of understanding what’s going on.” Remarking on his previous career as an NFL player, he shares: “If a student thinks that’s cool and [it] gets them to come take my class, and they learn a lot of cool, numerical math, that sounds great to me.”

In a piece republished by Scientific American, reporter Manon Bischoff highlights MIT researchers proving in 2024, that “many newer games in the Super Mario series are mathematically maximally complex and therefore contain unsolvable problems.” “We don’t know how to prove that a game is fun,” says Prof. Erik Demaine, a co-author of the research. “But we can prove that it’s hard and that maybe gives some insight into why it’s fun.”  

The 2003 Cohn-Elkies method “for finding upper bounds on the density of sphere packings,” established by MIT Prof. Henry Cohn and Harvard University’s Noam Elkies, is highlighted by Jack Murtagh for the Scientific American. “Their recipe is almost mechanical: come up with a mathematical function, feed the function into their method, and an upper bound pops out,” writes Murtagh. “They provided the field with a machine: identify the right inputs, churn it through their method, and a breakthrough in sphere packing might emerge.” 

Prof. Shafi Goldwasser and Prof. Vinod Vaikuntanathan founded the Institute for Responsible Superintelligence (RESI), “to develop mathematical principles and protocols to ensure AI models behave as intended,” writes Aaron Pressman for The Boston Globe. “You patch them [AI models] up, you test them, you patch them to make sure that they can perform to the best ability, but also not do damage,” says Goldwasser. “That’s probably not enough attention, given the fact that these things are going to become what we call super intelligent.” 

Prof. Justin Solomon joins GBH’s “The Curiosity Desk" to explain the Navier-Stokes problem and the significance of this longstanding challenge being solved by an AI platform. “There are concerns and there’s excitement,” says Solomon. “Obviously, working on the Navier-Stokes equations and other open problems shows that these AI tools are capable of assisting with proofs, or at least counter examples in this particular case, of really hard questions that have been open for centuries.” 

Akamai will honor their late cofounder Danny Lewin SM ’98, a victim of the American Airlines Flight 11 on 9/11, by illuminating their headquarters in blue the evening of Sept. 11, write Jon Chesto and Shirley Leung for The Boston Globe. “Lewin remains revered at Akamai; its highest employee award is given out each year in his honor,” Chesto and Leung write.  

In a Scientific American article by reporter Joseph Howlett, Prof. Naomi Sweeting discusses the potential pitfalls of consulting artificial intelligence in mathematics. “I view math as part of a vast and beautiful human project,” says Sweeting. “It's this huge endeavor that puts us in communication with thousands of years of human thinking.” 

New Scientist’s Jacklin Kwan highlights Prof. Christoph Kehle’s work demonstrating that extremal black holes, a variety of black hole that has zero temperature, could exist. “Extremal black holes were thought of as an idealised, unattainable limit: something you could write down as a solution, but which could never be reached [through any real physical] process, but we proved that wrong,” says Kehle. 

Prof. Tom Leighton, CEO of Akamai, speaks to Fast Company reporter Victor Dey about his vision for a faster and cheaper AI grid that could serve as an alternative to large data centers, and more effectively route inference workloads. “Many inference tasks do not need the largest model or the largest cluster or the most expensive compute,” says Leighton. “What they need is the ability to marry the right model, in the right place, data and moment, at the most effective cost.”