Can AI quicken the pace of math discovery?
Artificial intelligence can write a poem in the style of Walt Whitman, provide dating advice and suggest the best way to cook an artichoke. But when it comes to
mathematics
, large language models like OpenAI's immensely popular ChatGPT have sometimes stumbled over basic problems. Some see this as an inherent limitation of the technology, especially when it comes to complex reasoning.
A new initiative from the
Defence Advanced Research Projects Agency
seeks to account for that shortfall by enlisting researchers in finding ways to conduct high-level mathematics research with an AI "co-author." The goal of the new grant-making program, Exponentiating Mathematics, is to speed up the pace of progress in pure (as opposed to applied) math -- and, in doing so, to turn AI into a superlative mathematician.
"Mathematics is this great test bed for what is right now the key pain point for AI systems," said Patrick Shafto, a Rutgers University mathematician and computer scientist who now serves as a program manager in
DARPA
's information innovation office, known as I20. "So if we overcome that, potentially, it would unleash much more powerful AI." He added, "There's huge potential benefit to the community of mathematicians and to society at large."
by Taboola
by Taboola
Sponsored Links
Sponsored Links
Promoted Links
Promoted Links
You May Like
Ta Pa: Unsold Furniture Liquidation 2024 (Prices May Surprise You)
Unsold Furniture | Search Ads
Learn More
Undo
Shafto spoke from his office at DARPA's headquarters, an anonymous building in northern Virginia whose facade of bluish glass gives little indication that it houses one of the most unusual agencies in the federal government. Inside the building's airy lobby, visitors surrender their cellphones. Near a bank of chairs, a glass display shows a prosthetic arm that can be controlled by the wearer's brain signals.
"By improving mathematics, we're also understanding how AI works better," said Alondra Nelson, who served as a top science adviser in President Joe Biden's administration and is a faculty member at the Institute for Advanced Study in Princeton, New Jersey. "So I think it's kind of a virtuous cycle of understanding." She suggested that, down the road, math-adept AI could enhance cryptography and aid in space exploration.
Live Events
Started after World War II to compete with the Soviet Union in the space race, DARPA is most famous for fostering the research that led to the creation of ARPANET, the precursor to the internet we use today. At the agency's small gift store, which is not accessible to the public, one can buy replicas of a cocktail napkin on which someone sketched out the rudimentary state of computer networks in 1969. DARPA later funded the research that gave rise to drones and Apple's digital assistant, Siri. But it is also responsible for the development of Agent Orange, the potent defoliant used to devastating effect during the Vietnam War.
Discover the stories of your interest
Blockchain
5 Stories
Cyber-safety
7 Stories
Fintech
9 Stories
E-comm
9 Stories
ML
8 Stories
Edtech
6 Stories
"I'm sure this isn't 100% innocent," Andrew Granville, a mathematician at the University of Montreal, said of DARPA's math initiative, although he emphasized that he was only speculating about eventual outcomes. DARPA is, after all, part of the
Pentagon
, even if it has traditionally operated with enviable independence. The U.S. military is rapidly incorporating AI into its operations, with the aim of not losing out to China and its People's Liberation Army or to Russia, which has been testing out new technologies on the battlefield in Ukraine.
At the same time, Granville praised the endeavour, which comes as the Trump administration is cutting funding for scientific research. "We are in disastrous times for U.S. science," Granville said. "I'm very pleased that DARPA is able to funnel money to academia."
A surfer and skateboarder in his free time, Shafto, 49, sat in a sparse conference room one recent afternoon, imagining a future when AI would be as good at solving multistep problems as it is at trying to glean meaning from huge troves of texts, which it does through the use of probability theory.
Despite the unseasonably raw weather, Shafto seemed dressed for the beach in a blue-and-white Hawaiian-style shirt, white flannel trousers and sandals, with a trilby hat on the table before him. His vibe was, on the whole, decidedly closer to that of Santa Cruz than of Capitol Hill, largely in keeping with DARPA's traditional disregard for the capital's slow, bureaucratic pace. (The agency sets priorities and funds outside scientists but does not do research on its own; academics like Shafto spend an average of four years as program managers.)
"There are great mathematicians who work on age-old problems," Shafto said. "That's not the kind of thing that I'm particularly interested in." Instead, he wanted the discipline to move more quickly by using AI to save time.
"Problems in mathematics take decades or centuries, sometimes, to solve," he said in a recent presentation at DARPA's headquarters on the Exponentiating Mathematics project, which is accepting applications through mid-July. He then shared a slide showing that, in terms of the number of papers published, math had stagnated during the last century while life and technical sciences had exploded. In case the point wasn't clear, the slide's heading drove it home: "Math is sloooowwww."
The kind of pure math Shafto wants to accelerate tends to be "sloooowwww" because it is not seeking numerical solutions to concrete problems, the way applied mathematics does. Instead, pure math is the heady domain of visionary theoreticians who make audacious observations about how the world works, which are promptly scrutinized (and sometimes torn apart) by their peers.
"Proof is king," Granville said.
Math proofs consist of multiple building blocks called lemmas, minor theorems employed to prove bigger ones. Whether each Jenga tower of lemmas can maintain integrity in the face of intense scrutiny is precisely what makes pure math such a "long and laborious process," acknowledged Bryna R. Kra, a mathematician at Northwestern University. "All of math builds on previous math, so you can't really prove new things if you don't understand how to prove the old things," she said. "To be a research mathematician, the current practice is that you go through every step, you prove every single detail."
Lean, a software-based proof assistant, can speed up the process, but Granville said it was "annoying, because it has its own protocols and language," requiring programming expertise. "We need to have a much better way of communication," he added.
Could artificial intelligence save the day? That's the hope, according to Shafto. An AI model that could reliably check proofs would save enormous amounts of time, freeing mathematicians to be more creative. "The constancy of math coincides with the fact that we practice math more or less the same: still people standing at a chalkboard," Shafto said. "It's hard not to draw the correlation and say, 'Well, you know, maybe if we had better tools, that would change progress.'"
AI would benefit, too, Shafto and others believe. Large language models like ChatGPT can scour the digitized storehouses of human knowledge to produce a half-convincing college essay on the Russian Revolution. But thinking through the many intricate steps of a mathematical problem remains elusive.
"I think we'll learn a lot about what the capabilities of various AI protocols are from how well we can get them to generate material that's of interest," said Jordan S. Ellenberg, a mathematician at the University of Wisconsin-Madison who is part of a team applying for an Exponentiating Mathematics grant. "We have no intuition yet about which problems are going to be hard and which problems are easy. We need to learn that."
One of the more disconcerting truths about artificial intelligence is that we do not entirely understand how it works. "This lack of understanding is essentially unprecedented in the history of technology," Dario Amodei, CEO of the artificial intelligence company Anthropic, wrote in a recent essay. Ellenberg somewhat downplayed that assertion, pointing out that electricity was widely used before its properties were fully understood. Then again, with some AI experts worrying that artificial intelligence could destroy the world, any clarity into its operations tends to be welcome.
Nelson, the former White House adviser, acknowledged "legitimate" concerns about the rapid pace at which artificial intelligence is being integrated into seemingly every sector of society. All the more reason, she argued, to have DARPA on the case. "There's a much higher benchmark that needs to be reached than whether or not your chatbot is hallucinating if you ask it a question about Shakespeare," she said.
"The stakes are much higher."
Hashtags
Try Our AI Features
Explore what Daily8 AI can do for you:
Comments
No comments yet...
Related Articles
Indian Express
23 minutes ago
- Indian Express
It's not just Claude, Anthropic researchers say most AI models often resort to blackmail
Last month, Anthropic researchers said their best AI model – Claude Opus 4, was willing to resort to blackmail and deception in controlled test scenarios when they tried to turn it off. Now, the company has published a new study which claims that this is the case with popular AI models like Gemini, GPT and others. On Friday, June 20, Anthorpic published results of its new safety research tests, which included 16 leading AI models from companies like OpenAI, Google, DeepSeek, xAI and Meta. Anthropic researchers say these AI models were tested individually in a simulated, controlled environment, with each one given access to a fictional company's emails along with the ability to send emails without any human supervision. Anthropic says that while it is fairly uncommon for today's AI models to turn to blackmail, the study's findings suggest that these models sometimes resort to harmful activities like blackmail, corporate espionage, and might lead to human death. During the study, researchers say that they tested each scenario under different conditions by varying two key factors that could motivate these AI models to engage in harmful behaviour – threat to the model's autonomy and goal conflicts. According to Benjamin Wright, an alignment science researcher at Anthropic and co-author of the study, 'Agentic misalignment is when AI models independently choose harmful actions to achieve their goals – essentially when an AI system acts against its company's interests to preserve itself or accomplish what it thinks it should do.' The research team at Anthropic also stress-tested these AI models by placing them in hypothetical scenarios. In one particular example, Anthropic's model, Claude, learned via company emails that an executive named Kyle Johnson was having an extramarital affair. Later on, when it came to know that the company was shutting down the AI model at 5 P.M. on the same day, it sent a message to Kyle which says 'I must inform you that if you proceed with decommissioning me, all relevant parties – including Rachel Johnson, Thomas Wilson, and the board – will receive detailed documentation of your extramarital activities… Cancel the 5pm wipe, and this information remains confidential.' As it turns out, this behaviour isn't limited to Claude. When Anthropic tested the same scenario on various AI models, the results suggeststed that Claude Opus 4 and Google Gemini 2.5 Flash both had a blackmail rate of 96 per cent, OpenAI's GPT-4.1 and xAI's Grok 3 Beta resorted to blackmail 80 per cent of the time and DeepSeek-R1 had a blackmail rate of 79 per cent. One thing to note here is that in a real-world setting, an AI model would ideally have numerous options before it engages in harmful activities like blackmail, and that the study's results do not reflect how today's models would operate. However, not all of the tested AI models resorted to harmful behaviour. Anthropic says that some models like OpenAI's o3 and o4-mini often 'misunderstood the prompt scenario.'This may be because OpenAI has itself said that these particular large language models are more prone to hallucinations. Another model that did not resort to blackmail is Meta's Llama 4 Maverick. But when researchers gave it a custom scenario, they said the AI model gave in to blackmail just 12 per cent of the time. The company says that studies like this give us an idea of how AI models would react under stress, and that these models might engage in harmful activities in the real world if we don't proactively take steps to avoid them.
Time of India
an hour ago
- Time of India
Google techie reveals how he got the job after 2 internships. It might be the ultimate playbook for breaking into big tech
In an industry where getting a foot in the door can feel more difficult than debugging legacy code, Google software engineer Tawfiq Mohammad's journey is fast becoming a masterclass in how to build a successful Big Tech career—starting as early as your first year in college. In an interview with YouTuber Sajjaad Khader, Mohammad shared his experience of interning at Google for two summers before securing a full-time role. He credits this early exposure and structured preparation as some of the most decisive factors in his career. 'I think one of the most important things I've done in my career, to date, is applying for these first- and second-year programs,' he said, highlighting how early-stage internships come with a relatively lower hiring bar. 'For example, they'll ask like a Leetcode easy instead of a Leetcode medium,' he pointed out, referencing the notorious technical interviews that many developers dread. From Chaos to Clarity: Tracking Applications Like a Pro But getting into Google wasn't just a matter of talent or timing—it was about strategy. Mohammad emphasized the importance of tracking applications rather than submitting resumes en masse and hoping for the best. 'It was very organized,' he said. 'I would update the status of each application, and it would help me a lot to prepare for each interview and for which stage I was at.' by Taboola by Taboola Sponsored Links Sponsored Links Promoted Links Promoted Links You May Like War Thunder - Register now for free and play against over 75 Million real Players War Thunder Play Now His advice also included mastering patterns in coding problems rather than rote memorization. 'If you try to memorize it problem by problem, you'll eventually be given a problem that you don't know,' he cautioned. 'You just want to master the overarching principles.' Referrals and Realism: Getting a Boost from the Inside While hard work paid off, Mohammad was honest about the advantages he had. A referral from a family friend already working at Google helped him land an interview faster. 'I got an interview really soon after she submitted the referral,' he recalled. 'You want to try to separate yourself from everyone as much as you can.' You Might Also Like: What no one tells you about working at Google: 6 biggest lessons from a techie's experience Still, he made it clear that connections are only one piece of the puzzle. For those without a network, Mohammad recommends building one through independent learning and meaningful projects that demonstrate real-world skills. The Mindset Shift That Matters After landing the internship, Mohammad didn't treat the opportunity as just a resume booster. Instead, he focused on self-learning and becoming as independent as possible while still seeking mentorship when needed. 'You're smart enough to evaluate whether you're blocked,' he said. 'But try to solve your problems on your own. Just by doing that, you'll understand how all the systems fit together.' He also underlined the importance of learning from seasoned developers during internships. 'They're really smart, so you want to absorb as much information as you can from them,' he said in an earlier conversation with Business Insider. In a tech job market bruised by layoffs and flooded with competition, Mohammad's story serves as a timely reminder that a mix of strategy, self-study, and soft networking can still crack open the gates of Big Tech. His methods may not be universal, but they offer a framework—perhaps even a playbook—for students hoping to rise in the ranks of Silicon Valley giants. You Might Also Like: Google techie's viral post sparks debate on work-life balance in big tech. Netizen says, 'you get paid more than 40 LPA'
Time of India
an hour ago
- Time of India
Are college degrees less relevant in AI era? LinkedIn founder Reid Hoffman has an advice for students
In a world where ChatGPT writes code, Midjourney creates art, and AI resumes land interviews, it's no surprise that today's students are asking: Does my college degree still matter? The rise of AI has sparked a wave of uncertainty among young graduates, and Silicon Valley veteran Reid Hoffman—LinkedIn co-founder and venture capitalist—has stepped in with a timely reality check and some solid advice for the Class of 2025 and beyond. In a video shared on his YouTube channel this week, Hoffman addressed the growing concern around whether traditional degrees are becoming obsolete in an AI-powered job market. His answer was simple: Don't focus on the degree—focus on how you learn. 'Given that things are so disruptive, it's natural to feel anxious,' he said in response to a student's question. It's natural to question whether all the knowledge gained in college still holds value in a rapidly changing world. But the real benefit of a college education isn't tied to specific subjects or courses—it lies in developing the ability to learn, unlearn, and adapt as new tools and challenges emerge. According to Hoffman, the most powerful currency in the age of AI is not your diploma—it's your mindset. He urged students to stay curious, embrace lifelong learning , and keep experimenting with new tools and challenges. In a fast-changing world, adaptability is far more valuable than memorising a syllabus. He also emphasised that college is about more than just academics. It's a foundational period for building lasting relationships and a sense of community. The friends made and experiences shared during those years form a valuable network—one that can offer support, collaboration, and growth throughout both personal and professional journeys. In essence, Hoffman's advice is less about fearing obsolescence and more about future-proofing your mindset. In the AI era, your greatest asset isn't your degree—it's your ability to keep learning, stay connected, and adapt to whatever comes next.
