A new Leiden Declaration, endorsed by the International Mathematical Union and published on June 2, 2026, warns that AI could undermine mathematics by flooding the field with plausible but flawed proofs, weakening attribution, shifting incentives, and giving tech companies too much influence over research priorities. "Mathematicians should find it quite striking that tech companies are suddenly interested in their work," said Kevin Buzzard, a mathematician at Imperial College London, in a statement. "The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space." Ars Technica reports: The Leiden Declaration, which has already drawn hundreds of signatories, warns that recent AI developments are threatening "characteristic values" of mathematical research, "often in ways that disproportionately affect students and early-career mathematicians, and hence the long term future of the discipline." First, it points out how AI models can "produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs." Such developments put reviewers under increasing pressure and are "jeopardizing our ability to implement traditional standards for the correctness, transparency, and independent verifiability of proof," the declaration warns. "Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong," said Leslie Ann Goldberg, head of computer science at the University of Oxford, in a statement. "Once that happens, the errors are likely to propagate as new results are built on faulty foundations." Second, the declaration highlights how "models trained on published works frequently return outputs that do not properly cite the human works they synthesize," while also pointing out that many current AI models were trained on data obtained through "exploiting licenses and access arrangements" or "simply violating copyright protections." Third, the declaration describes how the use of AI "may become incentivized for its own sake, disrupting our mechanisms for hiring, funding and recognition" while leaving out researchers who lack access or are "unwilling to use technologies controlled by organizations whose values they do not share." Fourth, the declaration warns against mathematics research "communicated through informal channels such as press releases or blog posts, often without any research paper or other disclosure of information necessary for scientific evaluation." Such communication strategies can lead to "oversimplification" in media reporting that overemphasizes AI tools' significance at the expense of prior human contributions, and "misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products." Fifth, the declaration describes "increasing involvement of technology companies in mathematical research" as threatening the "autonomy of mathematics," especially as university budgets are under pressure and researchers may feel greater professional incentive to collaborate with technology companies on "asymmetric terms." This also raises the risk that mathematics research questions amenable to AI-driven techniques may be prioritized. What can mathematicians do about this? The Leiden Declaration urges them to treat AI as a tool, not a substitute for human responsibility. Individual mathematicians should disclose AI use, remain accountable for the correctness of their work, continue crediting human authors, and use AI tools only when they align with the declaration's values. It also warns that mathematics can be applied to "warfare, oppression, mass surveillance, and the undermining of democracy," so mathematicians should weigh the ethics of tech-industry partnerships carefully. Professional organizations are encouraged to develop AI-use guidelines for publication and review, protect researchers from having their work used as training data without consent, support peer-reviewed publishing, and "actively prepare to become involved if major mathematical results are claimed using unconventional means." For policymakers, the recommendations are blunt: "protect the rights of authors," "regulate the artificial intelligence industry," and "invest in public computational infrastructure." The declaration also urges people to "don't believe the hype," warning that tech companies have "a strong commercial incentive... to overstate the capabilities of their products."

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ETH Zurich researchers say they have generated certified "perfect randomness" for the first time by using a quantum Bell-test setup with two entangled superconducting chips connected by a 30-meter cooled link. "In the long term, this work could play a similar role in digital security as atomic clocks do for timekeeping: a physically certified source of randomness that other systems can rely on," reports Phys.org. "Possible applications range from the encryption of sensitive communications and digital identities to public randomness services for lotteries and blockchain applications." From the report: They call their method randomness amplification. "This was made possible by an improved so-called Bell-Test with simultaneously high quality and high data rate," says [Renato Renner and Andreas Wallraff]. He and his coworkers use a complex setup that consists of two superconducting chips, which they cool down to very low temperatures close to absolute zero. Each chip represents a quantum bit or qubit, which can take on the states "0" or "1" or any arbitrary superposition of these states. A 30-meter-long tube, which is also cooled down, connects the two chips. Microwave photons can fly back and forth between them, thus creating quantum mechanical entanglement. This means that a quantum measurement on one qubit, which randomly yields the values "0" or "1," influences automatically and at a distance whether "0" or "1" is measured on the second qubit. The separation of 30 meters ensures that, during the measurement, even at the speed of light, no information can be exchanged between the qubits. This would disturb the perfect randomness. Wallraff and his team made the choice of the exact type of measurement (or "measurement basis" in technical jargon) on the two qubits depending on an imperfect random number generator. Renner's coworkers could then amplify the randomness of the measurement results further using a special algorithm. "The resulting sequence of zeros and ones is now really perfectly random, and we can even certify that," says Renner. He likens this result to crossing a ridge: "The technical improvements allowed us, for the first time, to create random numbers that will remain perfectly random for all eternityâ"no matter what analytical methods are used to assess their randomness." The findings have been published in the journal Nature.

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In Polymarket's prediction market, "most people end up losing money," reports the Washington Post — typically a few bucks. "Since Polymarket launched in 2022, a few thousand people have lost the bulk of the money... and an even smaller group — .05 percent of users — has gone home with most of the overall profits, according to a new analysis from finance researcher Pat Akey and colleagues." A lot of users aren't that good at predicting the future. They're losing money at roughly the same rate as online gamblers betting on sports and other real-life events at traditional sportsbooks, according to the U.K. gambling regulator's analysis of 2024 data. On Polymarket, the odds of making a profit are slightly higher on weather and tech markets — and a little lower on sports... On Polymarket, just 1,200 people took more than half the profits — $591 million, or more than $100,000 each. ["The top 1% of users capture 76.5% of all trading gains," the researchers write.] When you dabble in prediction markets, you're competing against these sophisticated players who consistently win. Most of those 1,200 big winners didn't place just a few smart bets. They appear to be pros making thousands of trades, mostly in the past year and a half, that were probably automated. One user made $3 million since January on more than a million trades about the Oscars, according to TRM Labs... The most profitable participants are also just good at picking what to bet on, Akey found, winning so often it was statistically unlikely to be dumb luck. They had some sort of edge — expertise, deep research or, perhaps, inside knowledge. "Our results suggest that the informational benefits of prediction markets come at a cost to unsophisticated participants," the researchers conclude.

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