As seasonal storms take many of us by surprise, it’s time to head for the certainty of indoors, and a decent book (or two). We have some really intriguing titles this month, including a profoundly odd-sounding book by a forest that shares author rights with humans, and some terrifying night terrors that may teach us a lot about our brains. Oh, and if you want to stop trying to control everything around you, try surrendering to a higher power – of your choice, naturally.

by Anna Lembke

In a complex world, the pressure to control your life is immense: from removing annoying noises around you to slavishly avoiding missing out on living your best life, to keeping your relationship, children and health on track in every way imaginable. It’s overwhelming. Surely we can’t keep it up? According to Anna Lembke’s new book, Radical Surrender: Letting go in a world addicted to change, there is a way out. The word ”addicted” in the subtitle offers a clue here: this is the author of the bestselling book Dopamine Nation, in which she looked at pleasure and pain – and the critical task of finding a delicate balance between them, especially in an age of unprecedented high-reward, high-dopamine stimuli, mostly delivered digitally.

In this new book, we are promised tools to help us let go of our desire for control, but we have to follow Lembke’s advice and acknowledge a “power greater than ourselves, however we define it, and give our will over to that power: less mastery and more a return to mystery”. As an addiction medicine psychiatrist and head of Stanford University’s Addiction Medicine Dual Diagnosis Clinic in California, this “radical surrender” should be scientifically argued. Watch out for our review on 5 November.

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by Steven Strogatz and Alex Townsend

Let’s face it: our every move, from our next Google search to our latest Netflix selection, is utterly dependent on numbers, and AI is now an everyday reality. We have no choice but to face up to the overwhelming presence of mathematics, small, medium – or big. In Big Math: The hidden codes that run our world, Steven Strogatz and Alex Townsend (both leading mathematicians at Cornell University, New York) set out to show how relatively familiar concepts such as matrices, vectors, Markov chains, linear algebra and the like lie at the heart of computer science and quantum computing – essential for us all to know, say its publishers, if we’re to “comprehend the changes sweeping the world”.

The best new popular science books of September 2026

Dive into new titles from major names including Carlo Rovelli, Maggie Aderin, Xand van Tulleken and Jim Al-Khalili, as well as a new biography of Stephen Hawking

by Amy Crawford

For some while now, we’ve known that the story of invasive species is complex, but just how complex is the stuff of Amy Crawford’s Undesirable: Invasive species, humans, and where we all belong. Blundering all over the world, we have accidentally (as well as deliberately) carried species with us on our adventures – and often created great incidental damage to the recipient environments, ranging from destroyed habitats to changes in the climate. Then there is the accidental introduction of blow-in species over relatively short stretches of water, or those dropped by migrating birds. After hundreds of years, it’s still not entirely clear where the gains or losses to local biodiversity really land.

“Whether it’s garlic mustard spreading through American forests or brushtail possums allegedly decimating the flightless birds of New Zealand,” Undesirable is a “multi-faceted story”, say its publishers. On top of that, exactly how to hold ourselves to account remains an open question. And apparently, the young field of “invasion biology” has been “wracked by controversy and haunted by ethical quandaries as it has sought to destroy some species for the benefit of others”. Crawford, a freelance writer and long-time contributor to Smithsonian magazine, looks set to give us plenty to chew on here.

by Robert Macfarlane, Cosmo Sheldrake, Giuliana Furci, César Rodríguez-Garavito, Los Cedros Cloud Forest. Illustrated by Paula Terán Ospina

Look closely at the list of creators on the cover of this book, aimed at a 5+ age group, about a cloud forest within the Intac valley in northwestern Ecuador, and along with nature writer Robert Macfarlane and other experts, you’ll spot a more unusual contributor: Los Cedros Cloud Forest itself. As the publishers (probably correctly) point out, this is the first time a forest has been included in the creation of a book. To celebrate that fact – and the anniversary of a court decision recognising Los Cedros’s right to exist and flourish in the future – this is apparently “more than a book”, in that by making it, “we are recognising the forest’s moral rights as the co-creator of a literary work”. When you open Song of the Cedars, the flora, fauna and fungi of Los Cedros Cloud Forest jump off the page in a panoramic scene, which can be read or displayed as you wish. All the royalties from sales of the book, the publishers say, will be used to support the protection of Los Cedros. Fighting talk!

by Angèle Christin

What’s it like to make your money as a content creator? Angèle Christin, a digital studies scholar at Stanford University, California, takes us inside that world in her new book. The things these influencers post on social media range “from dance routines to political commentary, makeup tutorials to carpentry DIY”. She looks far and wide to explore what she calls their “golden dreams of passion, autonomy, and monetary returns”. No spoiler alert needed: the outcome for these creators and their followers shows how this digital work tends to fuel precarity, inequality – and much more. Christin’s bottom line: it’s more than time to rethink the economic structure of social media.

by Ashley Ward

Ocean water is nearly four times saltier than human blood, yet it has been central to our evolution – the  “amniotic fluid of life itself”, as the publishers of Saltwater: A natural history of the sea describe it. In this book, author Ashley Ward, a marine biologist, will bring readers face to face with the deep secrets of marine life. There will be jousting rival humpback whales, and claustrophobic journeys in a submersible to 600 metres deep to see an aurora of bioluminescence. We will also apparently encounter the complex seabird cities that develop along coasts, where auk fathers train their chicks to become skilful divers. And there’s mention of the ethereal song of a pod of belugas carrying across a fjord in the Arctic archipelago of Svalbard. Ward could hardly be better placed to deliver all this and more, given his background as a biologist at the University of Sydney, Australia, and as head of its Animal Behaviour Lab.

by Baland Jalal

A sneak peek at the introduction of Baland Jalal’s The Phantom Mind: Insights from the borderlands of sleep shows what we can expect from a researcher often billed as the leading expert in sleep paralysis. “One morning in my teenage years, I awoke gripped by terror… In horror, I realized a demon was on my bed. It grabbed my legs and began tossing them up and down in the air, while crushing my chest and squeezing my neck. While being strangled to death, I could somehow telepathically read the mind of the monster. It had one – and only one agenda: to destroy me.”

This terrifying no man’s land between REM sleep and wakefulness became the territory of his research for the next decade or so. There are plenty more great stories in this highly accessible book, including one featuring Jalal’s mentor, the eminent neuroscientist V.S. Ramachandran, who appears as a sleep-paralysis ghost to Jalal – and leads him off on a new train of thought about exactly how the ghostly figures people see in sleep paralysis are formed. The borderlands of sleep turn out to be a rich seam to mine for those hoping to discover more about the waking mind. And watch out for our interview with Jalal, in our 14 November issue.

by Erica McAlister, illustrated by Natalie McIntyre

This is the latest in the Chicago University Press’s Day series. Earlier in the year, we enjoyed marine biologist Helen Scales’s Shell Day and behavioural ecologist Marty Crump’s Snake Day. Insect Day: A story of 24 hours and 24 hexapod lives follows the same pattern, acting as an hourly guide, this time following insects as they hunt for food, mates or just plain safety from predators. Author Erica McAlister is a curator at London’s Natural History Museum who studies flies. She starts at midnight in Africa with a female mosquito, Anopheles gambiae, which is out for the blood of any unwitting sleeper and may unintentionally transfer malaria. Who knew, by the way, that the males have no taste for blood?

By 7am, we’ve moved on to the Arctic circle, where a queen of Bombus polaris, the Arctic bumblebee, is basking within the flowers of the Arctic poppy. She can also keep warm simply by vibrating. Throughout the day, we meet the yellow-legged saddle casemaker (Agapetus ochripes), the blue-winged helicopter (Megaloprepus caerulatus), the Peruvian shield mantis (Choeradodis rhombicollis), the ferocious water bug (Abedus herberti) and Grote’s bertholdia (Bertholdia trigona). In its closing pages, Insect Day delivers a final punch: we’ve just toured insects, but there may be as many as 30 million more yet to describe.

by Richard Dawkins

A new Richard Dawkins book is always a bit of a treat, and 42 Tales from Life: A modern bestiary looks set to be no exception. This is a collection of animal tales, explaining how they evolved into the extraordinary, intriguing and often beautiful forms they have, with a colourful backdrop of illustrations by 19^th-century naturalist, morphologist and artist Ernst Haeckel. According to the publisher, Dawkins reveals “the fundamental truths behind even the most unfathomable animal behaviours”, such as the galloping of fish, the shape of the rhinoceros’ horn, the surprising similarities between horses and lizards, and why hummingbirds glow so brilliantly. The book starts with “The Cephalopod’s Tale” and “The Hummingbird’s Tale”, ending with “The Bat’s Tale” and “The Frog’s Tale”. They are accompanied by Haeckel’s art, whose depictions of plants, sea creatures and other animals turn out to have fascinated Dawkins all his life.

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OpenAI, the maker of ChatGPT, claims its AI models have disproven the exponential time hypothesis – a fundamental assumption that underpins computer science.

“This came as a complete surprise, a shock,” says at the University of Bergen in Norway. “Nobody I know expected it.”

Proposed nearly 30 years ago, the exponential time hypothesis (ETH) tries to put a limit on how quickly computers can solve certain logical puzzles.

The simplest way would be to try every possible combination of true or false for each part of the puzzle. ETH proposes that, although it may be possible to do this quicker with shortcuts, the amount of work needed has to grow exponentially as the puzzle gets bigger.

OpenAI, however, says its models have devised an algorithm that can beat the previously assumed speed limit for solving logical puzzles, apparently proving ETH false. “Assuming that it is confirmed, this is an enormous breakthrough,” says at the University of Oxford.

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Many computer science findings assume ETH is true. If it isn’t, the conclusions they establish about computational limits become useless. “It would require a complete revision of several areas of algorithms and complexity,” says Fomin, who says a textbook he wrote on the subject would become obsolete if the finding holds.

ETH is linked to a long-standing maths problem known as P versus NP, which concerns whether a problem whose answer is easy to check is also easy to solve. If ETH were true, it would have implied that the answer was no. But disproving ETH wouldn’t mean the answer is yes. “This doesn’t have a direct impact on P versus NP, so we should not view it as progress towards P versus NP,” says Goldberg.

The result was announced alongside other breakthroughs in maths and physics on 26 October.

In mathematics, OpenAI says its AI has proved a 1991 conjecture that waves cannot remain intensely focused for long. If confirmed, this would also answer enduring questions about how thin a shape can be while also containing line segments that point in every direction, as well as how waves spread.

In theoretical physics, OpenAI claims to have proven that quantum field theories – including quantum chromodynamics, which describes the strong force holding quarks together – make sense mathematically, rather than just producing predictions that match experiments. The findings also touch on the existence of pure Yang–Mills theory, part of a million-dollar mathematical problem, but don’t resolve the entire challenge. That work hasn’t been released publicly while an external group led by Nobel laureate David Gross examines it.

Hannah Fry: How OpenAI has caused an existential crisis in mathematics

OpenAI has been throwing everything at solving long-standing maths problems. This should have been a glorious moment for mathematicians – but instead we’re having a massive collective wobble, says New Scientist’s new columnist, Professor Hannah Fry

OpenAI says it verified the ETH result using Lean, a piece of software that checks mathematical proofs. at TU Wien in Austria has looked at what OpenAI has released and says he expects it to withstand scrutiny, although he says researchers still need to check that the formally proven statement means what its authors say it means.

To do so, OpenAI has commissioned an independent group, including Russell Impagliazzo and Ramamohan Paturi, both at the University of California, San Diego, who helped propose ETH, to examine the findings. In , the group says it could “change an important part of theoretical computer science”.

The speed at which AI is solving maths problems and the way AI firms are releasing their findings have concerned some academics. at Royal Holloway, University of London, describes the phenomenon as “mathematics done by press”, worrying that proprietary models can suddenly overturn months of researchers’ work.

at the Eindhoven University of Technology in the Netherlands describes OpenAI’s work on ETH as “ingenious”, “spectacular” and “awe-inspiring – but also humbling.” “It really makes you think about the future of mathematics, algorithms and academia,” he says.

at the University of Sydney says proving something and understanding why it is true aren’t the same thing. “The web collapsed, and we looked behind,” he says of the network of findings relying on ETH. “We have no idea why yet.”

OpenAI says it is experimenting with an approach in which independent academics organise efforts to verify and explain the results. But Fomin welcomes the disruption. “This result destroys a lot, but it also opens many new opportunities and new questions that nobody expected,” he says. “One shouldn’t complain about having too many interesting mathematical breakthroughs to try to digest,” says Wahlström.

The hall hummed with joyous curiosity at this year’s New Scientist Live at Excel London, which ran from 10 to 12 October and attracted thousands of visitors of all ages.

With topics including the search for extraterrestrial life, what AI is teaching us about consciousness and the maths behind Pokémon, there was a delightful range to explore. Highlights included physicist Jim Al-Khalili diving into the deepest mysteries of time and psychologist Kimberley Wilson on how to build lifelong brain health. Other packed talks ranged from how we evolved, from anthropologist Alice Roberts, to a myth-busting take on supplements by doctors Chris and Xand van Tulleken.

Fans lined up to meet speakers, including naturalist Chris Packham, who shared moving thoughts on why science is crucial to tackling the climate crisis. Younger fans flocked for selfies with mathematician and YouTuber Tom Crawford, who fought a fierce maths battle with maths teacher and TV presenter Bobby Seagull.

On the show floor, people could journey through a giant inflatable gut, 3D-print organs and get hands-on with large insects. They also lined up to board a Chinook helicopter, or step into a hospital of the future. Plus, in virtual reality, they could swim through coral reefs and explore the body in 3D.

Visitors also saw New Scientist staff, including editor Catherine de Lange, predict the biggest scientific breakthroughs in the next 70 years. Plus, podcast editor Rowan Hooper hosted an emergency briefing on the climate crisis, joined by leading climate and biodiversity scientists.

The talks were all recorded and will be available to stream online for 12 months. See for details of how to get access.

A few years ago, when I first started talking about mathematics in public, a professor of algebraic number theory pulled me to one side and gave me some sharp words of warning: “The world fears mathematicians, Hannah. Let’s keep it that way.”

He was being, to put it mildly, a bit of a snob. Maths had an intimidating mystique to maintain, and I was apparently jeopardising it by titting around on the internet making videos and podcasts, rather than focusing on a perfectly respectable research career.

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I have thought a lot about that comment since. Partly because I have spent the intervening years doing everything I can to completely ignore him (and getting a New Scientist column feels like a rather lovely reward for doing so).

But buried beneath his snobbery, I have come around to the idea that he was right about something. And I have never felt that more than in the past few weeks, since a swarm of AI agents have been busy solving our most famous long-standing problems.

I’m talking, of course, about OpenAI’s announcements over the past few weeks that it has found proofs for hundreds of mathematics problems that had previously resisted human attempts to solve them.

The furore began, most notably, with a proof (by way of finding a counterexample) that the Navier-Stokes equations can break apart. This particular gem was such a big deal to the mathematical community that at the turn of the millennium, the Clay Mathematics Institute promised they’d give $1 million to whoever managed to solve it.

Those Navier-Stokes equations are what I did my PhD on. They are basically Isaac Newton’s second law of motion: F=ma, but applied to fluids. They are, in my not entirely unbiased opinion, staggeringly beautiful, able to articulate everything from the drip of a water droplet on a leaf and the churn of an entire atmosphere to the gases swirling around in a galaxy in the sky.

The thing is, these equations have a tricky little bit that pops out of the acceleration part, which contains a feedback loop within it. The faster fluid flows, the faster the gradient can get between two adjacent streams, and so the faster fluid flows. It’s a bit like the fluid version of putting a microphone next to a speaker. The feedback loop can get louder and louder until everything ends up breaking. Or, in the case of the Navier-Stokes equations, the speed of the flow heads off to infinity.

To be clear: no one was ever worried about fluid dynamics tearing open a black hole when you stir your tea or anything. It was just that the weird behaviour of this little term left the possibility that the equations themselves would break.

On the flip side, there’s another term in the equation – the viscosity – that acts as a brake and calms everything down, stopping the flow from getting completely out of control. So, the question was: does the brake always kick in?

If you have been following the story, then by now you will know what happened. Various groups of mathematicians had been using AI to circle in on this problem, finding special cases where the feedback loop goes crazy, without quite getting to the full Navier-Stokes.

But supposedly, once OpenAI heard that others were getting close, they threw everything at it: 10,000 AI agents, sending each other 3 million messages over 88 hours, costing millions of dollars in tokens, to find a single example where everything blows up. The Navier-Stokes equations do indeed fall. And an AI proved it.

This should have been a glorious moment of scientific exposition, but instead, mathematicians have spent the last few weeks having a massive collective wobble.

Part of the reason is that nobody yet understands the answer. The OpenAI solution is almost hilariously ugly. It is a proof that’s 166 pages long, accompanied by hundreds of thousands of lines of formal code – almost impenetrable symbols – slapped down on the table and left for the mathematicians to pick apart, while the AI labs move on to the next thing. They came for the glory without giving much back.

So, we are left with a proof that almost no one wants to read, a $1 million prize that no one will want to , and no one who can stand at a blackboard and explain why this particular vortex makes everything break, when nothing else we tried ever did.

And now, to top it off, the new tranche of proofs that landed last week claim to have polished off hundreds of other important, unsolved mathematical problems, including a big result in the biggest trophy in all of mathematics: the Riemann Hypothesis. All tipped onto the code-sharing website GitHub for someone else to check.

So, mathematicians are having their own existential crisis about their role and purpose, like Lee Sedol did after AlphaGo, Gary Kasparov before him with Deep Blue and probably every literature graduate, musician and artist since ChatGPT was launched.

Please don’t get me wrong. I want to use this column, at least in part, to talk about the incredible, world-changing things that are happening with AI in science. I know that there is some inevitability to machines outpacing the humans, and I know that at its best, AI has a great deal to offer.

But at its worst, AI is an engine of extraction. Not just text, or images or equations. The real sting in the tail is that OpenAI set its sights on mathematics because the prestige, the respect and the glory was just another thing that could be mined.

It didn’t need to be that way.

They so easily could have been open and collaborative. But the moment when one of humanity’s greatest intellectual traditions became vulnerable, they chose conquest over stewardship.

And so, I am left thinking about that professor again. He was right that there is a special mystique to mathematics, but wrong about who would puncture it. And I’m sorry to say that, while the world might fear mathematicians, the machines certainly don’t.