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The Irish Sun
14-07-2025
- Science
- The Irish Sun
We went head-to-head with AI and LOST as 30 of Earth's top brains left ‘frightened' after secret battle with chatbot
A SUPER-SMART artificial intelligence (AI) chatbot has spooked mathematicians who believe tech companies are on the verge of creating a robot "genius". 30 of the world's most renowned mathematicians congregated in Berkeley, California in mid-May for a secret maths battle against a machine. Advertisement 3 The bot uses a large language models (LLM), called o4-mini, which was produced by ChatGPT creator OpenAI Credit: Reuters The bot uses a large language models (LLM), called o4-mini, which was produced by ChatGPT creator OpenAI. And it proved itself to be smarter than some of the human geniuses graduating universities today, according to Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting. It was able to answer some of the toughest math equations out there in mere minutes - problems that would have taken a human expert weeks or months to solve. OpenAI had asked Epoch AI, a nonprofit than benchmarks AI models, to come up with 300 math questions whose solutions had not yet been published. Advertisement READ MORE ON AI This meant the AI couldn't just trawl the internet for the answer; it had to solve it on its own. The group of mathematicians, hand-selected by Elliot Glazer, a recent math Ph.D. graduate hired by Epoch AI , were tasked with coming up with the hardest equations they could. Everyone who participated had to sign a nondisclosure agreement to ensure they only communicated through secure messenger app Signal. This would prevent the AI from potentially seeing their conversations and using it to train its robot brain. Advertisement Most read in Tech Only a small group of people in the world are capable of developing such questions, let alone answering them. Each problem the o4-mini couldn't solve would grant its creator a $7,500 reward. By April 2025, Glazer found that o4-mini could solve around 20 percent of the questions. Father of murdered girl turned into AI chatbot warns of dangers of new tech Then at the in-person, two-day meeting in May, participants finalised their last batch of challenge questions. Advertisement The 30 attendees were split into groups of six, and competed against each other to devise problems that they could solve but would stump the AI reasoning bot. By the end of that Saturday night, the bot's mathematical prowess was proving too successful. "I came up with a problem which experts in my field would recognize as an open question in number theory — a good Ph.D.-level problem," said Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting, reported by Early that Sunday morning, Ono alerted the rest of the participants. Advertisement "I was not prepared to be contending with an LLM like this," he said. "I've never seen that kind of reasoning before in models. That's what a scientist does. That's frightening." Over the two days, the bot was able to solve some of the world's trickiest math problems. "I have colleagues who literally said these models are approaching mathematical genius," added Ono. Advertisement "I've been telling my colleagues that it's a grave mistake to say that generalised artificial intelligence will never come, [that] it's just a computer. "I don't want to add to the hysteria, but in some ways these large language models are already outperforming most of our best graduate students in the world." Just 10 questions stumped the bot, according to researchers. Yang Hui He, a mathematician at the London Institute for Mathematical Sciences and an early pioneer of using AI in maths, said: "This is what a very, very good graduate student would be doing - in fact, more." Advertisement 3 Over the two days, the bot was able to solve some of the world's trickiest math problems Credit: Getty 3 Just 10 questions stumped the bot, according to researchers Credit: Getty Read more about Artificial Intelligence Everything you need to know about the latest developments in Artificial Intelligence What is the popular AI How do you use Google's latest AI chatbot What is the AI image generator How do you use Snapchat's My AI tool? What are the What are the
Scottish Sun
14-07-2025
- Science
- Scottish Sun
We went head-to-head with AI and LOST as 30 of Earth's top brains left ‘frightened' after secret battle with chatbot
Each problem the o4-mini couldn't solve would grant its creator a $7,500 reward CHAT'S TERRIFYING We went head-to-head with AI and LOST as 30 of Earth's top brains left 'frightened' after secret battle with chatbot Click to share on X/Twitter (Opens in new window) Click to share on Facebook (Opens in new window) A SUPER-SMART artificial intelligence (AI) chatbot has spooked mathematicians who believe tech companies are on the verge of creating a robot "genius". 30 of the world's most renowned mathematicians congregated in Berkeley, California in mid-May for a secret maths battle against a machine. Sign up for Scottish Sun newsletter Sign up 3 The bot uses a large language models (LLM), called o4-mini, which was produced by ChatGPT creator OpenAI Credit: Reuters The bot uses a large language models (LLM), called o4-mini, which was produced by ChatGPT creator OpenAI. And it proved itself to be smarter than some of the human geniuses graduating universities today, according to Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting. It was able to answer some of the toughest math equations out there in mere minutes - problems that would have taken a human expert weeks or months to solve. OpenAI had asked Epoch AI, a nonprofit than benchmarks AI models, to come up with 300 math questions whose solutions had not yet been published. This meant the AI couldn't just trawl the internet for the answer; it had to solve it on its own. The group of mathematicians, hand-selected by Elliot Glazer, a recent math Ph.D. graduate hired by Epoch AI, were tasked with coming up with the hardest equations they could. Everyone who participated had to sign a nondisclosure agreement to ensure they only communicated through secure messenger app Signal. This would prevent the AI from potentially seeing their conversations and using it to train its robot brain. Only a small group of people in the world are capable of developing such questions, let alone answering them. Each problem the o4-mini couldn't solve would grant its creator a $7,500 reward. By April 2025, Glazer found that o4-mini could solve around 20 percent of the questions. Father of murdered girl turned into AI chatbot warns of dangers of new tech Then at the in-person, two-day meeting in May, participants finalised their last batch of challenge questions. The 30 attendees were split into groups of six, and competed against each other to devise problems that they could solve but would stump the AI reasoning bot. By the end of that Saturday night, the bot's mathematical prowess was proving too successful. "I came up with a problem which experts in my field would recognize as an open question in number theory — a good Ph.D.-level problem," said Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting, reported by Live Science. Early that Sunday morning, Ono alerted the rest of the participants. "I was not prepared to be contending with an LLM like this," he said. "I've never seen that kind of reasoning before in models. That's what a scientist does. That's frightening." Over the two days, the bot was able to solve some of the world's trickiest math problems. "I have colleagues who literally said these models are approaching mathematical genius," added Ono. "I've been telling my colleagues that it's a grave mistake to say that generalised artificial intelligence will never come, [that] it's just a computer. "I don't want to add to the hysteria, but in some ways these large language models are already outperforming most of our best graduate students in the world." Just 10 questions stumped the bot, according to researchers. Yang Hui He, a mathematician at the London Institute for Mathematical Sciences and an early pioneer of using AI in maths, said: "This is what a very, very good graduate student would be doing - in fact, more." 3 Over the two days, the bot was able to solve some of the world's trickiest math problems Credit: Getty
The Sun
14-07-2025
- Business
- The Sun
We went head-to-head with AI and LOST as 30 of Earth's top brains left ‘frightened' after secret battle with chatbot
A SUPER-SMART artificial intelligence (AI) chatbot has spooked mathematicians who believe tech companies are on the verge of creating a robot "genius". 30 of the world's most renowned mathematicians congregated in Berkeley, California in mid-May for a secret maths battle against a machine. 3 The bot uses a large language models (LLM), called o4-mini, which was produced by ChatGPT creator OpenAI. And it proved itself to be smarter than some of the human geniuses graduating universities today, according to Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting. It was able to answer some of the toughest math equations out there in mere minutes - problems that would have taken a human expert weeks or months to solve. OpenAI had asked Epoch AI, a nonprofit than benchmarks AI models, to come up with 300 math questions whose solutions had not yet been published. This meant the AI couldn't just trawl the internet for the answer; it had to solve it on its own. The group of mathematicians, hand-selected by Elliot Glazer, a recent math Ph.D. graduate hired by Epoch AI, were tasked with coming up with the hardest equations they could. Everyone who participated had to sign a nondisclosure agreement to ensure they only communicated through secure messenger app Signal. This would prevent the AI from potentially seeing their conversations and using it to train its robot brain. Only a small group of people in the world are capable of developing such questions, let alone answering them. Each problem the o4-mini couldn't solve would grant its creator a $7,500 reward. By April 2025, Glazer found that o4-mini could solve around 20 percent of the questions. Father of murdered girl turned into AI chatbot warns of dangers of new tech Then at the in-person, two-day meeting in May, participants finalised their last batch of challenge questions. The 30 attendees were split into groups of six, and competed against each other to devise problems that they could solve but would stump the AI reasoning bot. By the end of that Saturday night, the bot's mathematical prowess was proving too successful. "I came up with a problem which experts in my field would recognize as an open question in number theory — a good Ph.D.-level problem," said Ken Ono, a mathematician at the University of Virginia and a leader and judge at the meeting, reported by Live Science. Early that Sunday morning, Ono alerted the rest of the participants. "I was not prepared to be contending with an LLM like this," he said. "I've never seen that kind of reasoning before in models. That's what a scientist does. That's frightening." Over the two days, the bot was able to solve some of the world's trickiest math problems. "I have colleagues who literally said these models are approaching mathematical genius," added Ono. "I've been telling my colleagues that it's a grave mistake to say that generalised artificial intelligence will never come, [that] it's just a computer. "I don't want to add to the hysteria, but in some ways these large language models are already outperforming most of our best graduate students in the world." Just 10 questions stumped the bot, according to researchers. Yang Hui He, a mathematician at the London Institute for Mathematical Sciences and an early pioneer of using AI in maths, said: "This is what a very, very good graduate student would be doing - in fact, more." 3 3
Sustainability Times
03-07-2025
- Science
- Sustainability Times
'Prime Numbers Had a Hidden Code': Mathematician Cracks 2,000-Year-Old Mystery That Could Rewrite Number Theory
IN A NUTSHELL 🔍 Mathematician Ken Ono discovered a surprising link between prime numbers and integer partitions , reshaping our understanding of these elusive integers. and , reshaping our understanding of these elusive integers. 🛡️ Prime numbers play a crucial role in modern cryptography , underpinning secure communications and transactions through their inherent complexity. , underpinning secure communications and transactions through their inherent complexity. 🔗 The discovery connects two distinct mathematical fields, bridging the gap between combinatorics and number theory with innovative equations. and with innovative equations. 🔮 This breakthrough opens new research avenues, prompting questions about its potential applications to other numerical structures and the future of mathematical exploration. The world of numbers has often been a realm of mysteries and discoveries, and nothing epitomizes this better than prime numbers. These elusive integers, only divisible by themselves and one, appear randomly along the number line, defying prediction and order. Yet, a recent breakthrough may change our perspective on these fundamental components of arithmetic. Mathematician Ken Ono and his team have uncovered an unsuspected link between prime numbers and a completely different mathematical field: integer partitions. This connection could revolutionize our understanding of prime numbers and unveil a hidden pattern in what was once considered pure randomness. The Ancient Quest for Primes: Revisiting the Sieve To appreciate the significance of this breakthrough, we must journey back to the third century BCE. It was then that the Greek scholar Eratosthenes devised an elegantly simple method to identify prime numbers—known today as the 'Sieve of Eratosthenes.' This technique involves systematically eliminating the multiples of each integer, leaving only those that remain indomitable: the primes. Despite its antiquity, the sieve remains one of the most effective tools for sifting through these unique integers. This enduring relevance underscores the complexity of the problem at hand: even after more than 2,000 years of research, no straightforward algorithm or universal formula can predict where the next prime number will appear. This ancient method highlights the persistent challenge prime numbers pose. While it is a rudimentary yet powerful tool, the quest to fully comprehend primes continues, emphasizing their profound mystery and significance in mathematics. 'Like a Floating Magic Carpet': Newly Discovered Deep-Sea Creature Stuns Scientists With Its Surreal, Otherworldly Movements Why Prime Numbers Matter Today Beyond their theoretical allure, prime numbers hold immense practical importance in our modern lives. Every time you send an encrypted message, complete a secure transaction, or connect to a website via HTTPS, you rely—perhaps unknowingly—on their power. Modern cryptography, particularly the RSA system, is based on the difficulty of factoring large prime numbers. This complexity is crucial for cybersecurity, yet it also makes primes frustratingly elusive for mathematicians. The difficulty in factoring these numbers ensures the security of our digital communications, highlighting the dual nature of primes as both a challenge and a protector in the digital age. The paradox of prime numbers lies in their dual role: they are both a foundational mathematical enigma and a critical component of our digital security infrastructure. 'Time Breaks Down at Quantum Scale': New Scientific Discovery Shocks Physicists and Redefines the Laws of the Universe An Unexpected Connection: Prime Numbers and Integer Partitions Here is where the story takes an unexpected turn. Ken Ono and his team have found that prime numbers are not as chaotic as once believed. In fact, they can be detected through an infinite number of ways, using equations derived from a seemingly unrelated mathematical object: the integer partition function. But what exactly is an integer partition? It is a way of breaking down a whole number into the sum of positive integers. For instance, the number 4 can be expressed in several ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 Though simple in appearance, integer partitions conceal immense combinatorial complexity. These partitions are at the heart of the discovery. Researchers have shown that prime numbers can be identified as solutions to an infinite number of Diophantine equations, crafted from partition functions. This discovery not only bridges two previously distinct areas of mathematics but also opens new avenues for exploration. 'Google Just Changed Everything': This Ruthless New AI Reads 1 Million Human DNA Letters Instantly and Scientists Are Stunned A Breakthrough Celebrated by the Mathematical Community This groundbreaking discovery has been hailed by the mathematical community as 'remarkable.' Professor Kathrin Bringmann from the University of Cologne, an expert in the field, emphasizes the newfound capability of the partition function to detect prime numbers, opening entirely new fields of inquiry. In essence, this breakthrough is not just a theoretical accomplishment; it connects two previously distant mathematical territories, creating an unexpected bridge between combinatorics and number theory. This discovery is a testament to the evolving nature of mathematics, where long-studied concepts can yield new insights and cross-disciplinary connections. As we delve into the mysteries of prime numbers, new questions arise. Can this approach be used to gain insights into other numerical structures? Are there equivalents for composite numbers, arithmetic sequences, or other enigmatic objects? As is often the case in mathematics, each discovery opens a multitude of new chapters to explore. With quantum computing on the horizon, redefining our theoretical foundations is not merely an academic pursuit—it is a strategic necessity. Could this be the beginning of a new era in our understanding of numbers? Our author used artificial intelligence to enhance this article. Did you like it? 4.5/5 (27)
Yahoo
20-06-2025
- Science
- Yahoo
Mathematicians discover a completely new way to find prime numbers
When you buy through links on our articles, Future and its syndication partners may earn a commission. For centuries, prime numbers have captured the imaginations of mathematicians, who continue to search for new patterns that help identify them and the way they're distributed among other numbers. Primes are whole numbers that are greater than 1 and are divisible by only 1 and themselves. The three smallest prime numbers are 2, 3 and 5. It's easy to find out if small numbers are prime — one simply needs to check what numbers can factor them. When mathematicians consider large numbers, however, the task of discerning which ones are prime quickly mushrooms in difficulty. Although it might be practical to check if, say, the numbers 10 or 1,000 have more than two factors, that strategy is unfavorable or even untenable for checking if gigantic numbers are prime or composite. For instance, the largest known prime number, which is 2136279841 − 1, is 41,024,320 digits long. At first, that number may seem mind-bogglingly large. Given that there are infinitely many positive integers of all different sizes, however, this number is minuscule compared with even larger primes. Furthermore, mathematicians want to do more than just tediously attempt to factor numbers one by one to determine if any given integer is prime. "We're interested in the prime numbers because there are infinitely many of them, but it's very difficult to identify any patterns in them," says Ken Ono, a mathematician at the University of Virginia. Still, one main goal is to determine how prime numbers are distributed within larger sets of numbers. Recently, Ono and two of his colleagues — William Craig, a mathematician at the U.S. Naval Academy, and Jan-Willem van Ittersum, a mathematician at the University of Cologne in Germany — identified a whole new approach for finding prime numbers. "We have described infinitely many new kinds of criteria for exactly determining the set of prime numbers, all of which are very different from 'If you can't factor it, it must be prime,'" Ono says. He and his colleagues' paper, published in the Proceedings of the National Academy of Sciences USA, was runner-up for a physical science prize that recognizes scientific excellence and originality. In some sense, the finding offers an infinite number of new definitions for what it means for numbers to be prime, Ono notes. At the heart of the team's strategy is a notion called integer partitions. "The theory of partitions is very old," Ono says. It dates back to the 18th-century Swiss mathematician Leonhard Euler, and it has continued to be expanded and refined by mathematicians over time. "Partitions, at first glance, seem to be the stuff of child's play," Ono says. "How many ways can you add up numbers to get other numbers?" For instance, the number 5 has seven partitions: 4 + 1, 3 + 2, 3 + 1 + 1, 2 + 2 + 1, 2 + 1 + 1 + 1 and 1 + 1 + 1 + 1 + 1. Yet the concept turns out to be powerful as a hidden key that unlocks new ways of detecting primes. "It is remarkable that such a classical combinatorial object — the partition function — can be used to detect primes in this novel way," says Kathrin Bringmann, a mathematician at the University of Cologne. (Bringmann has worked with Ono and Craig before, and she's currently van Ittersum's postdoctoral adviser, but she wasn't involved with this research.) Ono notes that the idea for this approach originated in a question posed by one of his former students, Robert Schneider, who's now a mathematician at Michigan Technological University. Ono, Craig and van Ittersum proved that prime numbers are the solutions of an infinite number of a particular type of polynomial equation in partition functions. Named Diophantine equations after third-century mathematician Diophantus of Alexandria (and studied long before him), these expressions can have integer solutions or rational ones (meaning they can be written as a fraction). In other words, the finding shows that "integer partitions detect the primes in infinitely many natural ways," the researchers wrote in their PNAS paper. George Andrews, a mathematician at Pennsylvania State University, who edited the PNAS paper but wasn't involved with the research, describes the finding as "something that's brand new" and "not something that was anticipated," making it difficult to predict "where it will lead." Related: What is the largest known prime number? The discovery goes beyond probing the distribution of prime numbers. "We're actually nailing all the prime numbers on the nose," Ono says. In this method, you can plug an integer that is 2 or larger into particular equations, and if they are true, then the integer is prime. One such equation is (3n3 − 13n2 + 18n − 8)M1(n) + (12n2 − 120n + 212)M2(n) − 960M3(n) = 0, where M1(n), M2(n) and M3(n) are well-studied partition functions. "More generally," for a particular type of partition function, "we prove that there are infinitely many such prime detecting equations with constant coefficients," the researchers wrote in their PNAS paper. Put more simply, "it's almost like our work gives you infinitely many new definitions for prime," Ono says. "That's kind of mind-blowing." The team's findings could lead to many new discoveries, Bringmann notes. "Beyond its intrinsic mathematical interest, this work may inspire further investigations into the surprising algebraic or analytic properties hidden in combinatorial functions," she says. In combinatorics — the mathematics of counting — combinatorial functions are used to describe the number of ways that items in sets can be chosen or arranged. "More broadly, it shows the richness of connections in mathematics," she adds. "These kinds of results often stimulate fresh thinking across subfields." Bringmann suggests some potential ways that mathematicians could build on the research. For instance, they could explore what other types of mathematical structures could be found using partition functions or look for ways that the main result could be expanded to study different types of numbers. "Are there generalizations of the main result to other sequences, such as composite numbers or values of arithmetic functions?" she asks. "Ken Ono is, in my opinion, one of the most exciting mathematicians around today," Andrews says. "This isn't the first time that he has seen into a classic problem and brought really new things to light." RELATED STORIES —Largest known prime number, spanning 41 million digits, discovered by amateur mathematician using free software —'Dramatic revision of a basic chapter in algebra': Mathematicians devise new way to solve devilishly difficult equations —Mathematicians just solved a 125-year-old problem, uniting 3 theories in physics There remains a glut of open questions about prime numbers, many of which are long-standing. Two examples are the twin prime conjecture and Goldbach's conjecture. The twin prime conjecture states that there are infinitely many twin primes — prime numbers that are separated by a value of two. The numbers 5 and 7 are twin primes, as are 11 and 13. Goldbach's conjecture states that "every even number bigger than 2 is a sum of two primes in at least one way," Ono says. But no one has proven this conjecture to be true. "Problems like that have befuddled mathematicians and number theorists for generations, almost throughout the entire history of number theory," Ono says. Although his team's recent finding doesn't solve those problems, he says, it's a profound example of how mathematicians are pushing boundaries to better understand the mysterious nature of prime numbers. This article was first published at Scientific American. © All rights reserved. Follow on TikTok and Instagram, X and Facebook.
