Jake Peterson is Lifehacker’s Tech Editor, and has been covering tech news and how-tos for nearly a decade. His team covers all things technology, including AI, smartphones, computers, game consoles, and subscriptions.
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In the mid-1980s, an unexpected discovery sparked one of the most frenzied episodes in scientific history. The finding in question was of materials that turned into superconductors – materials that conducted electricity with zero resistance – at much higher temperatures than had ever been seen before. Almost overnight, labs the world over shelved their existing research programmes and jumped on the bandwagon to find other examples. Newspapers heralded an impending age of lossless power transmission, floating trains and extraordinary supercomputers. A Nobel prize was handed out within a year.
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Amid all the fuss, it was easy to overlook another odd property of the new materials. Even when they were too warm to actually superconduct, they still conducted electricity in an odd way, with an unusual type of resistance that no theory could explain. What became known as strange-metal behaviour was an intriguing mystery for many researchers in the field, but was nonetheless a sideshow to the main drama of resistance disappearing entirely.
Fast forward 40 years, and we still don’t understand high-temperature superconductivity, nor have we managed to find materials that exhibit this property at room temperature and pressure. But the associated strange-metal behaviour has been steadily coming to the fore. Attempts to understand it have forced physicists to question key assumptions about how electricity flows – employing a raft of outlandish concepts along the way, from quantum soups to black holes.
Now, experiments might finally be inching us closer to a resolution. And increasingly, it seems that this will take us beyond strange metals themselves – and that understanding their peculiar conductivity will help us explain superconductivity, too. “There must be something about it that gives the answer,” says theorist Subir Sachdev at Harvard University.
The usual explanation for why metals conduct electricity is that they are full of individual, negatively charged particles known as electrons, which can freely roam. There are a lot of them: just 1 centimetre of ordinary household wire contains roughly as many free-flowing electrons as there are grains of sand on a beach. Attach a battery, and those electrons will be repulsed from the negative terminal and attracted towards the positive one, generating a current.
That is the rough picture many of us learned at school. For physicists, a more nuanced conception of current derives from work by theorist Lev Landau in the 1950s involving the concept of quasiparticles. To imagine these, think of a crowd in a stadium doing a Mexican wave: any one individual is moving only up and down, but, collectively, they create a swoosh that sweeps longways. Landau’s ideas say that the thing that conducts electricity isn’t an electron, pure and simple, but rather an electron-like quasiparticle – an excitation that sweeps through materials thanks to the way all the internal particles interact.
Like their fundamental counterparts, electron quasiparticles can collide and scatter like billiard balls, but calculations involving them are much easier – and phenomenally accurate. For 70 years, quasiparticles have helped us correctly predict pretty much any property of materials we like, from their heat capacity to their electrical conductivity and magnetic susceptibility. Their success has led theorists to believe that all material physics, including conduction and resistance, must boil down to the interactions of individual particle-like objects. “The entire electronics industry – including the iPhone in your pocket – is based on the success of this theory,” says Sachdev.
Quasiparticles don’t travel unimpeded through a material. At room temperature or thereabouts, vibrations in the atomic structure interrupt them, generating resistance, while at lower temperatures, resistance instead mostly comes from the quasiparticles scattering off each other. The exciting discovery in the 1980s was that certain materials could superconduct even at temperatures where quasiparticle scattering should still have been significant.
Strange metals
The strange-metal behaviour was more subtle. In most conductors in cold conditions, resistance rises with the square of the temperature – that is to say, doubling the temperature gives four times the resistance. To the average materials scientist, this seems intuitive because temperature should determine two key factors that influence resistivity: the number of electrons available to collide and the number of places those electrons can end up afterwards. Two temperature dependencies, hence temperature squared.
As such, if you plot a graph of how a metal’s conductivity should vary with temperature, you inevitably get an upward-sweeping curve. Yet in strange metals, the resistance-temperature plot is a straight line (see chart below). There was no obvious quasiparticle-like behaviour that could generate such a trend, and the more physicists dwelled on it, the more mystified they became. There is “no operator or process that would [be able to give] this power of the temperature”, the late theorist Joseph Polchinski once wrote. It was, he added, “the conductor from Hell”.
There are some who think the answer isn’t actually that complicated. After all, linear temperature behaviour isn’t totally unheard of: copper exhibits the trend at room temperature, when vibrations running through the metal are by far and away the dominant source of resistance. These vibrations are generally seen as simple attenuators, and the higher the temperature, the more the material vibrates – hence a linear relationship. Last year, Eric Heller at Harvard University and others argued forcefully that these vibrations could be behind strange metals. But most other physicists remain unconvinced: at low temperatures, where strange-metal behaviour persists, the vibrations have long been predicted to freeze out.
A slightly more radical approach to explaining strange metals involves their electrons being caught between different forms of order. This can happen close to a phase transition, when a material reorganises itself – for instance, in such a way that a quantum property of electrons called spins collectively point in one direction, as in a magnet. On the brink of such a transition, when there is no definite preference for one order over another, the electrons are thought to produce fleeting patterns, like the murmurations of starlings in flight. And, crucially, the strength of these critical fluctuations is usually driven by temperature, linearly. “It could be the fluctuations that produce resistance,” says Stephen Hayden at the University of Bristol, UK.
This year, Hayden and his colleagues used a beam of neutrons at Rutherford Appleton Laboratory in Didcot, UK, to study electron-spin fluctuations in a strange metal. Having angular moments themselves, but no charge to complicate matters, neutrons are excellent probes of electron spin. Hayden’s team found that the spin fluctuations speed up and slow down in lockstep with temperature – providing some of the strongest evidence to date that critical fluctuations are behind strange-metal behaviour.
It may have been a telling result, but this case is far from closed. “The big question for us is whether it can be put into a theory,” says Hayden. This is where it gets tricky – and indeed where strange-metal behaviour challenges our deepest notions of what electricity and electrical resistance should be. A murmuration isn’t about individual starlings; it is about the behaviour of the flock as a whole. Likewise, if fluctuations are driving resistance in strange metals, the crucial actors are no longer quasiparticles – or, for that matter, anything particle-like – but collective patterns involving all the electrons at once. What, then, is electrical resistance if not individual collisions of some sort?
Sachdev’s attempts to answer that question with an alternative theory originate in the early 1990s, in collaboration with Jinwu Ye, who is now at Mississippi State University. The two theorists imagined a deliberately simplified system with no spatiality, no atomic structure at all – basically just a dot, in which every electron is connected to every other. In their model, any electrical disturbance fades at a rate proportional to temperature, despite there being no individually acting particles, or indeed any space for them to travel through. But it hardly resembled a real metal, and Sachdev recalls the idea being met with some scepticism: “My colleagues would think, is this just some curious thing Subir is amusing himself with?”
While Sachdev and Ye’s model languished, the strange-metal problem became ever more urgent. In the beginning, it was limited to “cuprates”, or copper-oxide materials. Then, in 2009, Louis Taillefer at the University of Sherbrooke in Canada and his colleagues spotted it in another class of materials called iron pnictides. Ten years later, a team led by Andrea Young at the University of California, Santa Barbara, and Cory Dean at Columbia University in New York spotted it in twisted layers of graphene. Then, just a few years ago, compounds called nickelates were added to the list by Harold Hwang at the SLAC National Accelerator Laboratory in California and his colleagues. But theorists were still struggling to come up with descriptions of resistance that didn’t involve particles.
Then, a hint of progress came from an unexpected corner of theoretical physics. In the late 1990s, string theorists discovered a mathematical trick that allows everything in a certain volume of space to be perfectly described by the physics taking place on a shell enclosing it. This “holography” was a strange idea, but it provided a new window onto some very difficult problems, including the nature of black holes. According to holography, everything happening inside a black hole can be completely encoded on its event horizon – the threshold within which even light is sucked in.
Cuprates are copper-oxide-based ceramics that exhibit superconductivity at high temperatures
Phil Degginger/Alamy
Black holes are a far cry from strands of metal in the lab, yet theorists such as Sean Hartnoll at the University of Cambridge believed there could be a link. Beginning in the late 2000s, he and others showed that in certain holographic models, an electric current inside a strange metal could be treated akin to light travelling around an event horizon, steadily losing some of its momentum to the inner black hole.
Nobody thought strange metals were black holes, but all this did suggest that holography might give us a foothold in terms of finding out how they work. In 2015, Alexei Kitaev, a theorist at the California Institute of Technology, presented a talk about one particular holographic model that, others later realised, looked remarkably similar to Sachdev and Ye’s early work. Now taking that work more seriously, theorists built on it, creating a family of “SYK” models – after the initials of Sachdev, Ye and Kitaev – that increasingly resembled real materials. “Suddenly, our original paper started getting several hundred citations every year,” says Sachdev.
Intriguingly, SYK models didn’t only predict a resistance that rises linearly with temperature. At a deeper level, they suggested that in strange metals, electrical current somehow loses momentum at a rate depending merely on temperature and Planck’s constant, the fundamental quantity that sets the scale of quantum effects. It was as though resistance was butting up against a universal quantum speed limit. The chemistry of a particular strange metal didn’t seem to matter at all.
The discomfiting implication of this is that there may not be an easily interpretable answer to what electricity is in strange metals. At best, the SYK model requires physicists to be content to think of it as a kind of “quantum soup”, beholden only to distant, universal laws that don’t involve individual particles. In a way, this is a return to a 19th-century picture of conduction, when scientists thought that electricity was like a fluid. In time, atomic theory filled in the details of that view, showing how to predict certain key properties such as viscosity; since then, physicists have grown accustomed to all macroscopic behaviour resting on a clear and intuitive foundation of microscopic physics. Removing the latter now, says Sachdev, “is like the rug being pulled out from under our feet”.
Physicists may have to abandon having an intuitive microscopic model of electricity, settling for a kind of strange quantum fluid
Chris Malbon
The question is whether conduction in strange metals really is indifferent to individual particles, or whether holographic physics is a mask for something more fundamental and particle-like that we have yet to uncover. And it turns out there may be a way to know for sure.
Typically, when a small current passes through a conductor, it should create a certain level of electrical crackle, or “shot noise”. The idea is that each charge-carrying particle arrives like the pitter-patter of raindrops on a window – if the current is indeed carried by particles. If not, “you’ve got a very soupy situation,” says experimentalist Doug Natelson at Rice University in Texas. “You should basically get no shot noise at all.”
In 2023, Natelson’s group tried to measure shot noise in very pure wires of a well-known strange metal. However, the result was slightly ambiguous: the shot noise was far less than they would have expected, but not zero. A quantum soup with the occasional electron crouton, you might say. “It’s really interesting,” says Natelson. Other research groups, such as Anindya Das at the Indian Institute of Science and his colleagues, are currently attempting to repeat the experiment for different materials. Theorists remain divided over what it means. Some, such as Sachdev, see the suppressed shot noise as evidence that strange metals really are a quantum soup. Others argue that it can still be explained in terms of fleeting patterns, as implied by Hayden’s experiments.
And then there is the bigger question, the one that had scientists so excited back in the 1980s. If we are reaching for a new picture of conduction in strange metals, can that tell us anything about how to obtain room-temperature superconductivity?
Maybe. A few years ago, Sachdev and colleagues found that a refined SYK model was able to predict both strange-metal resistance and a colder superconducting phase in the same system. Sachdev is now trying to reintroduce physics specific to certain materials, such as cuprates, in the hope that it will show that strange-metal behaviour and superconductivity are two manifestations of the same underlying quantum soup. But, crucially, his model doesn’t yet predict at what temperature superconductivity will kick in, or what sort of material will exhibit it closest to room temperature.
Still, 40 years after the discovery of high-temperature superconductivity and strange metals, physicists have a raft of ways to think about them. From collective fluctuations to holography, the mystery no longer looks quite as impenetrable as it once did. “Hopefully, some combination of these, put together in the right way, will ultimately shed some light on what is going on,” says Hartnoll. %!s()
Matthew Mercer returns behind the screen for Critical Role's bleak new Daggerheart adventure
Critical Role's next nightmare begins with the first Age of Umbra trailer
Image: Critical Role
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Age of Umbra: Sallowlands, the latest tabletop role-playing miniseries from the minds of Critical Role, is almost upon us. After months of various teasers, the creepy, gothic series trailer has been revealed exclusively to Polygon — and we’re happy to share that it’s just as spine-chilling as the previous Age of Umbra series.
Critical Role revealed its five adventurers at the heart of the miniseries in mid-June. They are Sister; Dillwyn and her companion Badger; Caguama; Alphonse; and Mercy, played by Critical Role co-founder Laura Bailey, Jennifer English, Abubakar Salim, Vico Ortiz, and Zachery Renauldo, respectively. Matthew Mercer, who took a break from serving as Critical Role’s Dungeon Master during Campaign 4, will return to guide these new players in this Daggerheart miniseries.
As revealed in the Sallowlands trailer, the five survivors will explore the perilous Halcyon Domain. What was once a glorious, celestial landscape of the old world, ruled by the God-King Oethedias, has become decayed and joyless. The gods are gone, communities are shattered, and people are quickly losing hope. What makes matters worse is that the dead are often reborn as twisted nightmares, bringing destruction and rot that plague the land.
That changes when a rumor surfaces about a “gargantuan metropolis appearing out of nowhere.” The possibility of a new place, teeming with life and magic, fills our survivors with hope of a new world that could bring them salvation — and the first true sign of something glorious.
The official description of Sallowlands on the Daggerheart website notes that players will “encounter brutal adversaries and high stakes in this dark and emotional actual play, which explores themes of desperation, survival, and love in the face of overwhelming odds.”
Image: Critical Role
We expect plenty of violence in this grim fantasy world, but Critical Role is known for stories about finding hope even in darkness. Critters will see how much light the series offers when the first episode of Age of Umbra: Sallowlands debuts on July 9. %!s()
High court ruling 'magnificent vindication' of the Daily Mail’s journalism, publisher claims
We are getting a statement through from the Associated Newspapers Limited, the publisher of the Daily Mail, which celebrates the judgment ruling in its favour and says it will seek to recover costs. The statement, attributed to a spokesperson, reads:
…
double quotation markAssociated Newspapers welcomes today’s judgement, which is an overwhelming victory for the Daily Mail and its journalists, and for a free press generally.
“Mr Justice Nicklin today cleared the Daily Mail and The Mail on Sunday, and dismissed every single one of the 97 allegations made by the claimants. In every case, the Judge accepted the honesty of our journalists’ evidence on how they sourced their stories.
“This isa magnificent vindication of the Daily Mail’s journalism.
“For some of the most outrageous allegations made when the case was launched in a blaze of publicity four years ago - placing bugs in people’s cars and homes, listening to calls as they were made and illicitly accessing bank accounts - no credible evidence was ever presented.
“As we said at the time, these allegations were ‘lurid’ and ‘preposterous’, and were a fishing expedition by the claimants and their legal teams in a politically motivated campaign to muzzle the free press.
“The reputations of our decent and hard-working journalists were terribly impugned, and today they have been exonerated.
“As the judgement clearly shows, every single article was legitimately sourced.
“Associated Newspapers thanks Mr Justice Nicklin for the patience and wisdom he has displayed throughout this misguided legal action, which has wasted so much valuable court time and more than £50m in legal costs.
“We will look to resolve outstanding issues, including the recovery of the costs we have incurred while defending ourselves against this egregious litigation.
Key events
7d ago
Closing summary
7d ago
Judge said claimants could not rely on 'suspicion' to prove allegations
7d ago
High court ruling 'magnificent vindication' of the Daily Mail’s journalism, publisher claims
7d ago
Prince Harry and claimants lose case against Daily Mail publisher
7 Jul 2026
Buckingham Palace says Harry can no longer stay at royal residence on UK visit
7 Jul 2026
Ruling expected in Prince Harry's court battle with Daily Mail publisher
Closing summary
Prince Harry lost his high-profile case against the Daily Mail’s publisher ANL for alleged unlawful information gathering in yet another blow to the estranged royal as he begins a fraught five-day trip back to the UK. A written judgement by the High Court published following an 11 week trial earlier this year said the “claimants failed to prove their pleaded allegations... the claims are therefore dismissed”.
In an emphatic ruling that is likely to signal an end to new litigation relating to the phone-hacking scandal era, the high court dismissed all the group’s claims, stating that the claimants had not proved that any information had been obtained unlawfully.
The Duke of Sussex’s and others claims against the Daily Mail’s publisher over allegations of unlawful information gathering “should never have been brought to trial”, editor Paul Dacre has said. Following the judgment, ANL’s editor-in-chief Dacre described the ruling as “a momentous victory for the Mail” and “an overwhelming vindication of our journalism”.
Prince Harry and six other prominent figures now fave a legal bill of up to £50m after losing the case. ANL will try to recover its costs from the mammoth case. It potentially leaves the claimants with a bill of as much as £50m. It said the verdict represented “an overwhelming victory for the Daily Mail and its journalists, and for a free press generally”.
Other claimants in the case were Doreen Lawrence, the mother of the murdered black teenager Stephen Lawrence; the singer Elton John and his husband, David Furnish; the actors Elizabeth Hurley and Sadie Frost; and the former Liberal Democrat minister Simon Hughes.
In a comprehensive victory for the publisher, all the claims were dismissed by the court. The claimants’ case was seriously damaged after a key witness, Gavin Burrows, a private investigator turned apparent whistleblower, said before his trial that his witness statement was a forgery and that he had not carried out illegal activity for the Mail titles.
The Mail case is the last to be brought against newspaper groups by the prince, who is coincidentally in the UK for a series of charity engagements. He has been at the forefront of legal attempts to hold British newspapers to account for alleged past wrongdoing. He previously won substantial damages in his hacking case against the Daily Mirror, in which the judge found that 15 out of 33 articles related to Harry put to the court were the product of phone hacking or unlawful information-gathering.
Jessica Welch, partner in the reputation protection team at Simkins LLP, said: “This is a widely awaited decision given the subject matter and the claimants involved, but I don’t believe that the application of this judgment to privacy law generally should be overstated.
“Mr Justice Nicklin was clear that the court’s findings relate specifically to the 57 articles that formed part of the claim and the evidence available to the specific claimants. Much of the claimants’ case rested on inference from decades-old conduct – the kind of covert activity that, by its nature, arguably leaves few direct traces. In the end, the Judge found that given the seriousness of the allegations, the claimants failed to reach the higher evidential burden required to prove them.
“However, the Judgment does not disturb the underlying privacy law framework established in earlier privacy case law, as well as the finding against Mirror Group Newspapers in 2023 of “widespread and habitual” phone hacking and the public apology and settlement from News Group Newspapers in previous phone hacking cases, all of which stand as precedent that such claims can succeed.”
Simon Hughes, who lost his claim against Associated Newspapers (ANL) over claims of unlawful information gathering, said in a statement following Tuesday’s ruling: “The judgment in the case against ANL is naturally very disappointing for me, and I am sure for all other claimants.
“I shall take time to consider the lengthy judgment in detail and plan to make no further comment in the near future.”
Gideon Benaim, partner and head of the reputation protection team at Simkins LLP, said: “This is an important judgment, particularly given the profile of the parties and the allegations involved, but it appears on an initial reading to be highly fact specific.
“The court has concluded that the evidence before it didn’t meet the threshold required to prove that unlawful information gathering took place. As Mr Justice Nicklin said in his judgment, “suspicion, even understandable suspicion, is not proof”.
“Most privacy cases will continue to depend on whether the information is private, whether publication was justified in the public interest and, ultimately, the evidence available to the court. I don’t see this decision fundamentally changing that position.”
Dacre concluded: “Today’s verdict is not just a victory for Associated’s magnificent journalists – several of whom have had a terrible toll imposed on their health and lives – but a free press generally.
“Make no mistake. This was a conspiracy, supported by Hacked Off, to destroy a paper.
“Financed by the orgy-loving, racist Max Mosley and involving the actor Hugh Grant, it was also a sinister bid to resuscitate Leveson Two and impose statutory regulation on the press which, even now, is rearing its ugly head in Labour’s Media Green Paper.
“Some of the allegations made by Harry’s lawyers against the Mail involved Peter Mandelson and Jeffrey Epstein.
“They were rejected by the Court. But remember it was the power of the Mail’s journalism that, not once, but twice, resulted in Mandelson being sacked as a minister.
“And it was the Mail on Sunday’s exclusive picture of Prince Andrew, with his arm around 17-year-old Virginia Giuffre in Ghislaine Maxwell’s home, that, ultimately, resulted in justice for Epstein’s underage victims.
“Such justice only happened, as with Stephen Lawrence, because of the actions of a free press.”
In a statement after the ruling, Associated Newspapers Limited’s editor-in-chief Paul Dacre said: “Four years ago, lawyers for Prince Harry, Doreen Lawrence and Elton John accused the Mail, in a blaze of publicity, of placing bugs in homes, cars, cafés and landline phones.
“We described these charges – some related to stories that were over 30 years old – as ‘lurid and preposterous’.
“Today, in what was a momentous victory for the Mail, the High Court dismissed every single one of the 97 claims. That is an overwhelming vindication of our journalism.”
He added:
double quotation markThe Mail’s famous front-page naming five thugs as Stephen Lawrence’s “MURDERERS”, could have seen me jailed for contempt of court.
Instead, it triggered the Macpherson Inquiry and the eventual jailing of two of the killers. Stephen’s father, Neville, says he owes the Mail everything.
Why Baroness Lawrence – for whom we have always had profound respect and sympathy – chose to turn on both the paper, and the brilliant reporter who campaigned for justice for her son for over two decades, is something I will never be able to comprehend.
PA Media is reporting that Prince Harry’s lawyer David Sherborne was seen entering Chatham House in central London to meet Harry on Tuesday afternoon, after the duke lost his case against the publishers of the Daily Mail.
Michael Savage
The claimants presented the court with 55 articles published between 1997 and 2015, and three incidents that did not lead to articles, that they claimed demonstrated unlawful information gathering.
A series of extraordinary claims of illegality at the Mail were made by the claimants’ legal team, which alleged “habitual and widespread” wrongdoing.
They included claims of phone hacking, landline tapping and bugging via private investigators, as well as making corrupt payments to police. All the claims were dismissed by the court.
You can read more here:
Hacked Off, a group which has long campaigned for tighter regulation of the British media, has reacted to today’s high court judgment. Hacked Off board director and phone hacking victim Jacqui Hames said:
double quotation markThe stories and conduct which formed the basis for the claims against the Mail were devastatingly intrusive, and included medical details, information about children, and other deeply invasive behaviour and coverage.
The Mail’s conduct fell well short of professional standards in the press, yet nothing has changed in the last twenty years and news publishers like the Mail still remain outside any independent form of regulation. Action to address standards in the press is long overdue, andmust be a priority for the incoming administration.
The courts are not the appropriate vehicle for investigating the allegations of wrongdoing against the Mail in their fulness, and the judgment was clear in stating that, focusing on a handful of individual articles, the court had not made findings on whether illegality was widespread at the Mail.
Now only a public inquiry can get to the bottom of what really happened.
Associated Newspapers Limited (ANL), which publishes the Daily Mail, Mail on Sunday and MailOnline, has consistently denied any wrongdoing.
Commenting on the overall evidence prince Harry gave during the trial in January, Mr Justice Nicklin said in his judgment:
double quotation markIn assessing Prince Harry’s evidence overall, it was apparent that he wished the court to understand the personal impact of the matters in issue.
At times, this led him beyond giving factual evidence into advancing arguments on the issues, and exchanges followed with Mr White KC (Antony White KC, for Associated) in that vein.
As I indicated to Prince Harry at the time, that is not uncommon: many litigants feel a strong instinct to argue their case themselves.
However, when giving evidence, that is not a burden they are required to carry. The responsibility for advancing the party’s case rests with the advocate.
Prince Harry hasn’t given a reaction to today’s judgment yet.
As we reported earlier in the blog, he arrived at an event for the Invictus Games in London’s Chatham House shortly before the judgment was published this afternoon.
Prince Harry arrives at Chatham House in central London on 7 July, 2026. Photograph: Justin Tallis/AFP/Getty Images
According to Sky News, he has been speaking since the judgment was published but has not mentioned the ruling, sticking to his pre-prepared script.
“What brings us together is far more important than what sets us apart,” he said.
“Each country represented here is writing its own chapter”.
The event is bringing together members of the Invictus community, leading experts and policymakers to discuss issues affecting injured and sick service personnel and veterans – all those eligible to take part in the paralympic-style games.
Judge said claimants could not rely on 'suspicion' to prove allegations
In the judgment, Mr Justice Nicklin acknowledged that the allegations were “serious”, noting that they included claims of dishonesty, unlawful conduct and deliberately false evidence.
Because they were civil (not criminal) claims being brought against Associated Newspapers Limited, he explained that the legal test was whether the allegations were proved on a balance of probabilities.
“The more serious and less likely an allegation is, the more convincing the evidence must be before a court can find it proved,” he wrote, noting in the summary that the claimants could not rely on “suspicion, even where understandable”.
“The claimants had to prove that the information complained of had been obtained unlawfully. The court rejected the argument that, simply because information was private, and because Associated could not positively explain how it had been sourced, the relevant article must have been unlawfully sourced,” the judgment read.
Michael Savage
In a ruling that is likely to signal an end to new litigation relating to the phone-hacking scandal, the high court dismissed all the claims, stating the claimants had not proved information had been obtained unlawfully.
The written verdict from Mr Justice Nicklin said the court could not simply infer a story had been obtained unlawfully if there was a legitimate and realistic legal way in which they could have been sourced.
You can read more on the significance of the ruling from the Guardian’s media editor, Michael Savage, here:
In the summary, the judge said that a hearing will now take place on 29–30 July to hear arguments on “any points of dispute as to the consequential orders to be made” following today’s judgment.
The verdict potentially leaves the claimants with a huge bill for the case, which is thought to be as much as £50m.
High court ruling 'magnificent vindication' of the Daily Mail’s journalism, publisher claims
We are getting a statement through from the Associated Newspapers Limited, the publisher of the Daily Mail, which celebrates the judgment ruling in its favour and says it will seek to recover costs. The statement, attributed to a spokesperson, reads:
double quotation markAssociated Newspapers welcomes today’s judgement, which is an overwhelming victory for the Daily Mail and its journalists, and for a free press generally.
“Mr Justice Nicklin today cleared the Daily Mail and The Mail on Sunday, and dismissed every single one of the 97 allegations made by the claimants. In every case, the Judge accepted the honesty of our journalists’ evidence on how they sourced their stories.
“This isa magnificent vindication of the Daily Mail’s journalism.
“For some of the most outrageous allegations made when the case was launched in a blaze of publicity four years ago - placing bugs in people’s cars and homes, listening to calls as they were made and illicitly accessing bank accounts - no credible evidence was ever presented.
“As we said at the time, these allegations were ‘lurid’ and ‘preposterous’, and were a fishing expedition by the claimants and their legal teams in a politically motivated campaign to muzzle the free press.
“The reputations of our decent and hard-working journalists were terribly impugned, and today they have been exonerated.
“As the judgement clearly shows, every single article was legitimately sourced.
“Associated Newspapers thanks Mr Justice Nicklin for the patience and wisdom he has displayed throughout this misguided legal action, which has wasted so much valuable court time and more than £50m in legal costs.
“We will look to resolve outstanding issues, including the recovery of the costs we have incurred while defending ourselves against this egregious litigation.
Clarkson University researchers have developed an artificial intelligence tool that can uncover the mathematical equations governing complex and chaotic systems directly from data. The technology, called KANDy—short for Kolmogorov-Arnold Networks for Dynamics—is designed to help scientists understand systems that are difficult to describe using traditional methods because they are noisy, nonlinear or highly unpredictable.
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Most AI models excel at making predictions but often operate as "black boxes," offering little insight into why they behave as they do. KANDy takes a different approach. Rather than just providing predictions of future actions, KANDy aims to understand the equations governing the phenomenon.
Researchers can feed KANDy data from a complex physical system, and the model attempts to identify the mathematical rules driving that system's behavior. The result is an AI model that is both predictive and interpretable.
The new framework builds on a class of neural networks known as Kolmogorov-Arnold Networks, or KANs. By adapting the technology specifically for dynamical systems, the researchers created a model capable of discovering governing equations even in cases where existing equation-discovery methods fail.
The study, now available on the arXiv preprint server, was conducted by Research Associate Kevin Slote and Electrical and Computer Engineering Research Assistant Professor Jeremie Fish, led by Erik Bollt, who tested KANDy on a variety of challenging problems, including discrete and continuous dynamical systems and chaotic partial differential equations.
The model also successfully recovered important topological structure in a mathematical object known as the Hopf fibration, demonstrating its ability to capture deeper properties of complex systems.
The research highlights KANDy's potential for data-driven modeling of nonlinear dynamical systems, providing scientists and engineers with a new tool for understanding complicated physical phenomena from observed data.
To install the KANDy software and try it, see the installation instructions on GitHub.
Publication details
Kevin Slote et al, KANDy: Kolmogorov-Arnold Networks and Dynamical System Discovery, arXiv (2026). DOI: 10.48550/arxiv.2602.20413
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Researchers develop AI tool that finds the equations behind complex systems (2026, July 7)
retrieved 14 July 2026
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