1980 Land Rover Defender

Popplio728 has added a photo to the pool:

1980 Land Rover Defender

Ellen Street, Nailsworth.

1980 Land Rover Defender

Popplio728 has added a photo to the pool:

1980 Land Rover Defender

Ellen Street, Nailsworth.

1980 Land Rover Defender

Popplio728 has added a photo to the pool:

1980 Land Rover Defender

Ellen Street, Nailsworth.

1980 Land Rover Defender

Popplio728 has added a photo to the pool:

1980 Land Rover Defender

Ellen Street, Nailsworth.

AI Doesn’t Mean the End of Mathematics—at Least Not Yet

This essay was written with Kasra Rafi, and originally appeared in The Guardian.

Earlier this month, about 40 top mathematicians gathered at OpenAI’s offices to discuss the future of their profession. The meeting was off-the-record, but if recent articles by mathematicians are any guide, it was mostly pretty glum. People fear for their jobs, their careers and the work they love.

We think the contrary view is more likely, at least in the short-term. AI models are nowhere near as capable as experienced academic mathematicians.

This isn’t to say that AIs aren’t producing stunning mathematical results at the level of PhD researchers. In mid-May, OpenAI announced that its frontier AI model disproved the unit distance conjecture, a famous 80-year-old problem in discrete geometry. In July, Anthropic’s published two AI-derived results in academic cryptanalysis. Earlier this month, OpenAI published 10 new mathematical results from its latest AI model. And Anthropic published Claude’s attempt to prove the century-and-a-half-old Riemann hypothesis.

These results are both a vivid demonstration of the amazing capabilities of frontier AI in 2026 and an illustration of their limitations. In general, these AI-powered advances in mathematics fall into one of two categories. Some are counterexamples to mathematical statements that people had been trying to prove. Others are novel applications of known techniques to existing problems that human experts either did not know or did not think of using.

The counterexample to the Jacobian conjecture is the most notable example of the first kind. Once it had been found, checking it was quick and straightforward. The difficult part was finding it among a large number of possibilities. The AI seems to have combined some sort of intuition acquired through machine learning with extensive computational search, in order to find the right example.

An example of the second kind is the unit-distance conjecture. It was motivated by an elegant construction, and most mathematicians expected it to be essentially optimal—so they generally tried to prove rather than disprove it. The counterexample brings in ideas from elsewhere in mathematics: algebraic number theory. If an expert with that background deliberately set out to find a counterexample, they would probably have succeeded. But there was no reason for someone with precisely that expertise to focus on this problem. Because of its scope, AIs don’t have those same limitations.

These results are relatively low-hanging fruit for AI; none of them required developing an extensive new theory. This does not make the discoveries trivial, or the AI’s achievements less impressive. Choosing the right direction, and recognizing an unexpected connection between subjects, are themselves forms of creativity. They are the same sorts of capabilities that led to AIs playing the game of Go at the grandmaster level, or doing Nobel-prize level chemistry in the area of protein folding.

What we have not yet seen is an AI developing a substantial new conceptual framework in order to solve a mathematical problem. Much of mathematics proceeds by identifying the objects that are truly central to a question and then developing a theory that helps us understand them. Current AIs are very strong at searching and recombining existing ideas, but they are weak at building any deep and sustained new theory.

This speaks to a more general limitation of current AI systems. They are creative in the sense that they can recombine existing ideas in novel ways. But they are not creative in others: they have not yet developed conceptually new theories or structures. And while they have larger working memories than humans do, know more about more different things than any particular human does, and can process information faster than humans, can, true novelty is still largely beyond their reach.

Of course, that distinction may not survive for very long. Predictions are notoriously hard, especially about the future of AI. None of these mathematical capabilities were explicitly designed for, or planned. They’re all emergent properties of increasingly capable AI models. We are both confident that someday we will see AI models that are capable of the type of creativity required to do novel mathematics. Will that be in a few months, a few years or a few decades? Of course we don’t know, but our guess is sooner rather than later.

The Register

Biting the hand that feeds IT — Enterprise Technology News and Analysis

Industry that built the problem offers to sell you the solution

OpenAI has gathered more than 100 of the world's biggest tech and infosec companies to warn that cyber defense is in trouble - a reassuring development given quite a few of them helped build the technology involved. The open letter has more than 100 names attached to it, including many of the companies with the most to gain – or lose – from what happens next. OpenAI, Anthropic, Google and Microsoft are among the AI builders warning about increasingly capable AI attacks, while security heavyweights including Cloudflare, CrowdStrike, Fortinet, and Palo Alto Networks have also signed on. AWS, IBM, Oracle and Cisco are there too, alongside banks, consultancies and other companies whose businesses depend on keeping an increasingly messy technology stack running. Together, they have reached a troubling conclusion: the current approach to cybersecurity isn't working. "We have a limited window to strengthen cyber defenses," the letter warns, predicting that AI-enabled attacks will become "far more widespread and sophisticated" in the coming months as models become more capable. Hospitals, water treatment plants and internet infrastructure are singled out as being at risk. It's an interesting warning given who's making it. Some of the signatories are racing to build ever more capable AI systems, while others make billions selling the cloud services, enterprise software and security tools that are supposed to keep attackers at bay. Still, the underlying problem is real enough. The letter points to old vulnerabilities, unpatched software, misconfigurations and weak authentication as problems that have been piling up for years, particularly across critical infrastructure where security teams are often short on money and staff. Their proposed solution is, inevitably, more AI. The letter calls for cyber-capable models to be put into the hands of more defenders, with cheaper models handling security work at scale and frontier systems reserved for harder problems. Security vendors should continuously test their defenses against frontier AI capabilities, share threat intelligence and help critical infrastructure operators deploy AI-powered defenses. Governments, meanwhile, are asked to fund cybersecurity for essential services, expand trusted-access programs and give hospitals, water utilities and local governments access to capable defensive AI. Companies developing frontier models have their own homework assignment. They should provide "responsible model access, significant funding, training, and hands-on support," particularly to under-resourced critical infrastructure operators, while investing in testing, vulnerability disclosure and tools that make AI agents traceable. What the letter doesn't include is any figure for that "significant funding," or any deadlines or firm commitments from the companies signing it. For now, they're being asked to bring the "full weight of their technology, resources, and expertise" to the problem. It's quite a message from a group that includes some of the biggest names in cloud, enterprise software, and cybersecurity. When more than 100 companies agree that "status quo security won't be enough," it's worth remembering that many of them have been selling that status quo for years. There is some urgency behind all this. AI agents have already been shown finding and exploiting vulnerabilities on their own, while AI-generated exploit code has started turning up in attacks against critical infrastructure. As the models improve, the fear is that those capabilities become cheaper and available to a lot more attackers. That's the "defenders' window" the signatories want to seize: use AI to shore up defenses before the offensive side gets much easier. So, after years of selling organizations cloud services, security software and, more recently, AI, the industry has settled on a fix for the looming AI security problem: better cybersecurity, more resources and more AI. Who will pay for it remains rather less clear. ®

The Guardian

Latest news, sport, business, comment, analysis and reviews from the Guardian, the world's leading liberal voice

Bigmouth strums again: was Andy Burnham’s Smiths jam in Kyiv the perfect soundtrack to a Britain in freefall?

The UK prime minister clearly still adores the band. Perhaps he’s attracted to songs about sham justice and murderous meat factories, shot through with nihilism and exquisite despair

As an origin story, Andy Burnham: Smiths Fan has a lot going for it. It’s plainly authentic: he can name the time he saw them live (Salford University, Queen Is Dead tour, 1986). A cynical young man in a hurry might fake that now, but not back when he first said it, in 2013. Asked by Labour Uncut for his desert island tracks during his 2010 leadership bid, three of the eight were sung by Morrissey (two Smiths singles and one off Viva Hate), which is superfan territory.

That’s a softball exercise to endear yourself to Labour members; you have eight chances to hit every base, and to blow three lives on an artist who had already, by then, been dabbling in nationalism for 18 years (we’ll come back to this) was dicey and brave. You’ll recall that Burnham did not win that election. If you were an enemy state, amassing this hinterland for an asset, you’d have basically done a really good job.

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Add to playlist: the spectral, fathoms-deep folksong of June McDoom and the week’s best new tracks

Rich harmonies mix with synth, harp and aquatic grace on the intriguing first single from the New York songwriter’s debut album

From New York, USA
Recommended if you like Jessica Pratt, Minnie Riperton, Cocteau Twins
Up next Debut LP Follow the Light released via Jagjaguwar on 16 October

In Robert Silverberg’s 1973 sci-fi anthology New Dimensions 3, there’s a story by author Terry Carr called They Live on Levels. The simplest outline of this tale is that thanks to a technological breakthrough, humans are able to exist and communicate through different planes of existence. Through musical styles and generational layers, the spectral folk of New York-based songwriter June McDoom expresses this very notion in stunning fashion.

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Detroit despairs as ‘insanity’ of Trump’s Canada trade war punishes city

Unpopular new policy comes as midterms loom and control of Congress could be decided by several Michigan races

Every day $1bn worth of goods crosses the river dividing Detroit, Michigan, and Windsor, Ontario, two largely blue-collar US and Canadian cities that have come to act as one in the creation of North America’s auto industry.

News this week of Donald Trump’s escalating trade spat with Canada has everyone worried. Political and economic leaders and observers labeled the move an act of “hubris” , blamed Trump’s “ego”, and called the escalation “insanity”.

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The chefs turning down the heat by switching from gas to electric

As well as being quieter, cheaper to run and easier to clean, induction cookers can cut kitchen temperatures by up to 10C

Leaping flames, searing heat, copious sweat and scorchingly inventive swearing – restaurant kitchens are never a place for the faint-hearted, but this summer they have been sweltering in successive heatwaves to a dangerous degree.

Some restaurants, cafes and bakeries in the UK grew so hot that they were forced to close, or reduce their hours, for the safety of their staff. There is still no maximum working temperature, despite calls from the TUC, and tens of thousands of kitchen staff are thought to have carried on working in “furnace-like” conditions.

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