Mathematics

Prof. John Urschel speaks to The New Yorker’s Rivka Galchen about AI being used as a tool for teaching and research in the field of mathematics. “I would say what I call the more scientist approach [to new technology] is being focused on trying to push the frontier of things as far as we can as quickly as we can,” says Urschel. “And the artist perspective is, ‘let me do something beautiful and enjoyable and manipulate these things,’ and the act of doing this is really, you know, a joyful thing.” 

Writing for Forbes, alumnus Paul Hsieh discusses radiologists employing rapidly evolving AI tools to help deliver diagnoses. “Radiologists are willing to employ AI tools that have been statistically validated to provide reliable diagnoses, even if we don’t yet fully understand how those tools work,” writes Hsieh. “But radiologists are not content to stop there. We also continually seek to improve genuine human understanding of how AI works in our field as a matter of professional responsibility for ourselves and for our patients.”  

CodeSignal, co-founded by alumnus and CEO Tigran Sloyan, has developed Agentic Skills Intelligence, a new product that “uses AI agents to evaluate the skills people use in their work and links the findings to personalized practice,” writes Forbes’ Ray Ravaglia. CodeSignal has built an AI agent “for each domain in its job taxonomy, such as engineering and sales, along with agents for capabilities that cut across jobs, among them communication and AI literacy,” notes Ravaglia. “The agents draw on systems including Gong, Salesforce, and GitHub, and they score what they find against rubrics the company says are grounded in industrial-organizational psychology.” 

The Boston Globe’s Mark Feeney spotlights the “Bounce juggler (W.C. Fields),” a machine modeled after the comedian W.C. Fields, on display at the MIT Museum, that juggles three metal balls and was created by the late Prof. Claude Shannon SM ’40, PhD ’40. “It’s one thing to be known as ‘the father of information theory,’ as Shannon is. His work in mathematics, electrical engineering, cryptography, and computer science was that important,” writes Feeney. “But Shannon was also a chess player, unicyclist, juggler, and inventor. Shannon combined his talent for engineering and imagination with his love of humor and juggling in the ‘Bounce juggler.’”  

Flapping Airplanes, a startup co-founded by Benjamin Spector ’22, MEng ’22, has developed a framework for AI models to run efficiently while being trained on less data and in a single graphics processing unit (GPU), writes Julie Bort for TechCrunch. The framework “can run a task that spends most of its time waiting for data to be fetched alongside one that spends most of its time doing math, so the chip is rarely sitting idle,” notes Bort. “The premise is that AI has barely scratched the surface of what GPUs can do, and they believe it can create intelligent systems ‘without ingesting half the internet.’”  

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.”