for foundational discoveries and inventions that enable machine learning with artificial neural networks
A memory is not stored anywhere. It is a hollow in a landscape.
Three notes drift out of a shop speaker and the whole song arrives, along with the weather on the day you first heard it. You didn't look the song up. Those three notes pulled you to it.
Computers before 1982 couldn't do that. They found things by address: you had to know which drawer something was in before you could take it out. Hand one half of a blurry photo and it has no idea which drawer to open.
The 2024 physics prize rewards a way to make a crowd of simple switches get pulled by content, and then to let them learn for themselves what should pull them where. The toolkit wasn't computer science. It was a century of physics about magnets and gases.
Machines modelled on neurons were not new. In 1943 the neuroscientist Warren McCulloch and the logician Walter Pitts proposed a mathematical model of how neurons cooperate. In 1949 the psychologist Donald Hebb guessed that when two neurons keep firing together, the link between them grows stronger. In 1957 Frank Rosenblatt built the "perceptron" to interpret images.
Then came the cold shower. In 1969 Marvin Minsky and Seymour Papert published an influential book showing that such simple networks could not even learn "one or the other but not both". The Nobel committee's scientific background is blunt: it led to a funding hiatus for neural-network research. Mainstream AI went on writing rules into programs, but recognising images needed more rules than anyone could compute.
Hopfield was a theoretical physicist who in the 1970s had brought a physicist's eye to electron transfer between biomolecules and to how cells correct errors in biochemical reactions. In 1980 he left Princeton for a chair in chemistry and biology at Caltech, where he had computers to experiment with freely. His question appears on a slide from his Nobel lecture:
How mind emerges from brain is to me the deepest question posed by our humanity.— John J. Hopfield · Nobel Lecture "Physics is a point of view" · 2024
Physicists know magnetic materials well. Each atom acts like a tiny compass needle, its spin, and neighbouring needles nudge one another. The whole material settles on its own into an arrangement that keeps most of them content: a state of lower energy.
Hopfield's 1982 paper in PNAS carried this over almost unchanged. Each node is 0 or 1, like a pixel in a black-and-white picture, every node is linked to every other, and the links have strengths. The network as a whole has an "energy", and the committee points out that his two key equations are the very ones textbooks use for magnets.
Storing a picture means tuning the links, Hebb-style, so that the picture sits at the bottom of a hollow. To recall, you feed in a damaged or noisy version. Each node looks only at its neighbours and asks: would flipping me lower the total energy? If so, it flips. No central controller; nodes flip one at a time until nobody wants to. Often the network has stopped on the original picture.
Picture hill country with a few lakes, one lake per memory. Wherever a raindrop lands, it runs downhill into one lake; a lake's catchment is every input "close enough" to call it up. The paper's abstract says the network recovers an entire memory "from any subpart of sufficient size". That is content-addressable memory: finding things by what they contain, not where they live.
The scale was tiny: 30 nodes, 435 links, fewer than 500 parameters. He tried 100 nodes and the computer of the day couldn't cope. But once the structure matched magnetic physics, physics tools applied directly: within a few years, the theory of spin glasses, "frustrated" disordered magnets, was used to work out analytically how many memories such a network can hold.
When Hopfield's paper came out, Hinton was at Carnegie Mellon in Pittsburgh, wondering whether a machine could, like a child, grow its own categories from examples. With Terrence Sejnowski and others he started from the Hopfield network and added two things.
The first was noise. A Hopfield network only ever goes downhill, so once it drops into a shallow dip it is stuck. Hinton let nodes decide with a bit of randomness: firm when the input is strong, a coin toss when it is weak. A "temperature" sets how jittery they are; start hot and cool down, and the network finds deeper hollows. The odds of each arrangement follow the formula of the nineteenth-century physicist Ludwig Boltzmann, so in 1985 the device was named the Boltzmann machine.
The second was hidden nodes: some nodes receive the image, others see nothing directly and instead hold an "interpretation" of what is seen. The learning rule Hinton described in his Nobel lecture is almost naïvely simple:
Awake, clamp a real image on the visible nodes, let the network jiggle to equilibrium, and strengthen every link between two nodes that are on together. Asleep, clamp nothing, let the network "dream", and weaken those links a little. Over time, what the network dreams comes to resemble what it has actually seen. In his words, learning lowers the energy of interpretations of real data and raises the energy of the network's fantasies. A machine that can produce new examples on its own: an early generative model.
The price was speed. The 1985 paper admits the learning algorithm was "very slow". It became practical only after slimming down: drop links within a layer to get the restricted Boltzmann machine (RBM), add Hinton's 2002 approximate shortcut, and in 2006 stack RBMs layer by layer to pick up edges and corners from unlabelled data before fine-tuning with backpropagation. Deep, dense networks became trainable.
Hinton's own verdict, at the end of his lecture, is modest: stacked RBMs "were like an enzyme". They helped researchers cross into deep learning, and once across, they were no longer needed.
Many people stand between these two papers and the AI in your phone, and the committee's own background lists them: in 1986 Rumelhart, Hinton and Williams showed backpropagation could train networks with hidden layers (they reinvented a scheme others had used, and explained what hidden layers do); Yann LeCun's convolutional networks read handwritten digits on cheques for several American banks from the mid-1990s; neural networks were part of the analysis behind the 2012 Higgs discovery. The popular version offers a contrast: under 500 parameters in Hopfield's network, more than a trillion in today's large language models.
The Hopfield network itself has not gone stale. A 2020 paper titled "Hopfield Networks is All You Need" showed that a continuous "modern Hopfield network" retrieves a memory in one update, and that this update rule is equivalent to the attention mechanism in transformers.
As for "is this physics?", the award drew real argument: some physicists saw a prize for computer scientists as a sign of crisis in physics, while some computer scientists read it as physics claiming AI for itself. Hinton, woken at 2 a.m. in a California hotel, answered honestly:
I would say I am someone who doesn't really know what field he's in but would like to understand how the brain works.— Geoffrey Hinton · Nobel telephone interview · October 2024
The committee's case is concrete: the equations of both works are the equations of statistical physics. Rather than "AI won the physics prize", the award says that the collective behaviour of many simple units has always been physics' home ground.
The sharpest attack came from Jürgen Schmidhuber, co-creator of LSTM. His technical report, first posted in December 2024 and updated twice in 2025, is titled "A Nobel Prize for Plagiarism". He argues the laureates republished methods from Ivakhnenko in Ukraine and Shun-ichi Amari in Japan from the 1960s–70s without citing them. The committee's background does cite Amari's 1972 paper, and does say backpropagation had been used before.
Amari himself, in RIKEN's congratulations, was gracious: the origins of the field "can in part be traced to Japan", and "Physics has crossed boundaries."
Photo apps that group faces, voice typing, translation, chatbots: all are deep neural networks grown along this line. Hinton noted in his lecture that Netflix combined RBMs with other methods to predict which films users would like.
Harder evidence comes from hospitals. Sweden's MASAI randomised trial assigned 105,934 women in breast screening during 2021–2022 either to AI-supported screening (the AI triaged scans and flagged suspicious areas for radiologists) or to standard reading by two radiologists. Results published in 2025: 6.4 cancers found per 1,000 women with AI versus 5.0 without, no significant rise in false positives, and 44.2% less reading work for radiologists.
Already in clinical trials: jobs like screening, where you look at many images to find a few abnormal ones, are the likeliest to change first, pending longer follow-up. Still in research: the committee mentions networks standing in for costly quantum-mechanical calculations to screen solar-cell materials, and sharper climate models without extra computing power. Real results, but far from "AI invents new materials on its own".
It doesn't mean computers think. The committee's public explainer says so plainly: "Although computers cannot think", machines can now mimic functions such as memory and learning. Nor did these two invent neural networks (the first model dates from 1943), and today's chatbots are not Boltzmann machines: Hinton himself says RBM pre-training was later replaced by other methods.
When a problem is too fuzzy to write as steps, define a measure of "how bad", then find a rule by which every local part can judge for itself how to make things a little less bad. That is how a Hopfield network works without anyone in charge.