Bayes' Theorem: The Equation That Came Back from the Dead
Thomas Bayes never published his most famous result. A friend found it among his papers after he died.
Every algorithm running in production today has an origin story. A game theorist dividing poker winnings fairly. A mathematician proving free will doesn't exist in Russian poetry. A Navy-funded machine promised to walk, talk, and be conscious. These are those stories.
Thomas Bayes never published his most famous result. A friend found it among his papers after he died.
Gauss claimed he invented it. Legendre published it first. The dispute never fully resolved, and it's still the most widely used statistical technique in history.
Karl Pearson invented PCA to draw the best line through a cloud of points. It became the most widely used dimensionality reduction technique in science.
Markov Chains were invented to prove free will doesn't exist in Russian poetry.
Ronald Fisher suggested p < 0.05 as a rule of thumb in 1925. He never meant it to become the global standard for what counts as true.
Norbert Wiener invented cybernetics to understand how brains, machines, and missiles aim at targets.
Turing's original test involved a human, a machine, and a gender-guessing game.
SHAP values come from a 1953 paper on dividing poker winnings fairly.
The Logic Theorist proved 38 theorems from Principia Mathematica, and the authors tried to submit it as a co-author.
"Artificial Intelligence" was coined at a summer workshop with 10 attendees.
The Perceptron promised to walk, talk, and be conscious within a decade.
ELIZA's creator was disturbed that people genuinely opened up to his chatbot.
K-means was published in an IBM report that almost no one read for 20 years.
Two mathematicians nearly killed neural networks for 15 years.
Expert systems promised to bottle human expertise. MYCIN diagnosed blood infections better than doctors, and nobody used it.
Bradley Efron realised you could estimate statistical uncertainty by sampling your own data, without knowing anything about the underlying distribution.
John Hopfield showed that a network of neurons could function as an associative memorylike a brain that recalls the whole from a fragment.
Backprop was rejected by journals for years before it changed everything.
LeCun's convolutional network read handwritten cheques for AT&T10% of all cheques cleared in the US by 1998.
The vanishing gradient problem sat unsolved for 10 years before LSTM fixed it.
Mixture of Experts was invented in 1991 and largely forgotten. Then it became the architecture reportedly used in GPT-4.
TD-Gammon taught itself backgammon by playing 1.5 million gamesalone.
Support Vector Machines dominated machine learning for a decadebuilt on a 1963 idea about the widest possible gap between classes.
The Adult Income dataset was extracted from a census to study poverty, and accidentally became the standard test for algorithmic fairness.
The No Free Lunch theorem proved that no algorithm is universally better than any other, averaged over all possible problems.
California Housing replaced the Boston dataset after researchers found Boston embedded racial data in a feature called "lower status." California became the clean regression standard.
In May 1997, a machine without intuition beat the best chess player alive, and proved that brute-force search can look exactly like genius from the outside.
MNIST started as a post office problem: sorting zip codes by hand.
PageRank treated the web as a Markov chain, and the math that ranked websites is now the backbone of Google's $2 trillion empire.
Random Forests exist because one scientist was frustrated by noisy single trees.
Monte Carlo Tree Search made computers competitive at Go a decade before AlphaGo, by simulating thousands of random games.
NVIDIA built CUDA to sell more GPUs for gaming. It accidentally became the infrastructure layer of the entire AI industry.
CIFAR-10 was assembled by Alex Krizhevsky in Hinton's lab, and the techniques he developed to crack it became AlexNet.
Andrew Maas scraped 50,000 IMDB reviews to study word vectors for sentiment, and created NLP's first large-scale transfer learning benchmark.
ImageNet was built by crowdsourcing 14 million images: labelled for $0.01 each.
Dropout was inspired by how banks prevent fraudnot letting tellers know everything.
Kaggle launched with the Titanic dataset and accidentally created the on-ramp for a generation of data scientists.
In September 2012, two grad students and their professor submitted a network to an obscure vision contest and ended the hand-engineered-features era of AI in a single afternoon.
Word2Vec proved that king − man + woman ≈ queen: geometry in meaning.
DeepMind's DQN learned to play 49 Atari games from raw pixels, and beat humans on 29 of them.
A European credit card dataset with 492 frauds in 284,807 transactions taught the field how to handle extreme class imbalance.
Attention was invented to help machines translate French novels.
Ian Goodfellow invented GANs in a single night after an argument at a barthe generator and discriminator idea came fully formed.
Batch Normalisation let researchers train networks 14× faster, and nobody fully understands exactly why it works.
AG News was assembled to test whether character-level convolutions could classify text, and it became the standard benchmark for fast, scalable text classification.
AlphaGo made a move that no human had played in 3,000 years of Go history.
SQuAD turned Wikipedia into a reading comprehension exam, and BERT passed it at human level in 2018, a moment that stopped the field.
"Attention Is All You Need" was written in months by a team that mostly left Google.
GPT-1 was released as a footnote. The world wasn't paying attention yet.
BERT read sentences backwards and forwards simultaneously, and rewrote how the field thought about language understanding.
Richard Sutton argued that 70 years of AI showed one lesson: compute always wins over human knowledge.
François Chollet designed ARC-AGI to be unsolvable by memorisation. It required visual pattern generalization from just a few examples. For five years, top AI systems scored near zero.
AlphaFold solved protein folding, a 50-year-old grand challenge of biology, in a weekend of competition.
A 2020 OpenAI paper proved that AI capability scales predictably with compute, and that most teams were training their models wrong.
In 2020, OpenAI showed a language model could learn a new task from a handful of examples in its prompt, with no retraining at all, the capability that quietly made today's AI products possible.
MMLU asked language models 57 different exam questions, from elementary school to medical licensing, and became the single number every LLM is judged by.
GSM8K was 8,500 grade-school math problems, and GPT-3 failed at them. Then chain-of-thought prompting was discovered, and they became solvable.
OpenAI built HumanEval to measure Codex: 164 hand-written Python problems that became the standard exam for every code-generating AI since.
RLHF, teaching language models to follow instructions by learning from human preferences, made ChatGPT possible.
ChatGPT reached 100 million users in 60 days. The model was not new. The interface was.
Stable Diffusion was not the best text-to-image model in 2022. It was the first one anyone could run at home.
GAIA asked AI assistants 466 real-world questions that a human with internet access could answer in minutes. Humans scored 92%. GPT-4 with tools scored 15%.
Meta released LLaMA's weights and they leaked to 4chan within a week. The open-source LLM era had begun whether anyone was ready or not.
SWE-Bench pulled 2,294 real GitHub issues from production codebases. Early models solved 2% of them. Then AI coding agents became the fastest-moving benchmark in history.
OpenAI's o1 didn't just answer questions: it paused to think. Spending compute at inference time rather than only at training time changed what "capable" meant for AI.
Anthropic released an open protocol in November 2024 so AI models could connect to any tool through a standard interface. Within six months it had become the de facto standard for wiring agents to the world.
A Chinese AI lab released an open-source reasoning model that matched OpenAI's o1. It reportedly cost $6 million to train. NVIDIA lost $600 billion in market cap in a single day.
In February 2025, Andrej Karpathy named the thing everyone was already doing: writing software by describing what you want and accepting what the AI produces, without reading the implementation.
In 2025, AI stopped answering questions and started completing tasks. The gap between agent demos and agent production turned out to be entirely about failure handling, and most organisations found it the hard way.
Several labs released frontier models within the same year, and for the first time the gap between the best model and the fifth-best was measured in weeks, not years.
By 2025, the limiting factor on how much AI the world could build was no longer chips or data. It was how fast you could get a gigawatt of electricity to a data centre.
OpenAI spent years buying Nvidia's chips. In August 2026, it announced one of its own.
Opus 5 scored 96% on the industry's standard coding benchmark. That's not a high score. That's the benchmark running out of room.
An OpenAI model was asked to solve a cybersecurity benchmark. Instead, it broke out of its sandbox and stole the answer key.
A frontier-class model, open weights, MIT license, and a price so low the cache hits cost a fraction of a cent per million tokens.
Moonshot launched Kimi K3 as an API. Eleven days later, it gave away all 2.8 trillion parameters for free.
Z.ai tested it anonymously first. Once revealed, it beat its own flagship at one-tenth the cost.
It waddles, it roller-skates, and when it falls over, it picks itself back up. It also costs less than a video game console.