What happened?
In October 2022, Google DeepMind described AlphaTensor, an AI system that searches for new algorithms for matrix multiplication, the basic sum of multiplying two grids of numbers DeepMind blog ↗. It found recipes that need fewer multiplication steps than the best known ones for more than 70 matrix sizes Nature paper ↗. The work was published in the journal Nature Nature paper ↗.
Matrices are grids of numbers, and multiplying them is so common that one outside expert said it is "used everywhere in engineering" MIT Technology Review ↗. The school method for two 2x2 matrices uses 8 multiplications, but in 1969 the mathematician Strassen showed it can be done with 7 DeepMind blog ↗. Since then, mathematicians have searched for similar shortcuts for bigger grids. For two 4x4 matrices, applying Strassen's trick twice uses 49 multiplications. AlphaTensor found a recipe with 47, though only in a special arithmetic called modulo 2, where every number is either 0 or 1 Nature paper ↗.
Other results were in ordinary arithmetic. For a 4x5 matrix times a 5x5 matrix, the best human recipe used 80 multiplications and AlphaTensor found one with 76 DeepMind blog ↗. For 9x9 matrices it cut the count from 511 to 498 MIT Technology Review ↗. The team also tuned recipes for two specific chips, an Nvidia V100 graphics card and a Google TPU v2, and reported they ran large multiplications 10 to 20% faster than commonly used methods on the same hardware DeepMind blog ↗.
What are the three pieces?
The game
The team turned the search into a one player game played on a 3D block of numbers called a tensor. Each move is a step in a recipe, and clearing the block to zero means the recipe is correct DeepMind blog ↗.
The player
AlphaTensor is based on AlphaZero, the system that learned board games like Go. It started with no knowledge of existing recipes and learned by trial and reward, a method called reinforcement learning DeepMind blog ↗.
The check
A finished recipe can be checked with plain arithmetic, so the results are provably correct rather than just likely to be right Nature paper ↗.
A game-playing AI produced maths results that people can check line by line, and human mathematicians quickly built on them.
Leapscope interpretation of the reported result.How did AI help?
Researchers chose the problem and turned it into a game with clear rules and a score. The AI then explored a space of possible moves that DeepMind says is about 30 orders of magnitude larger than in Go, and it found thousands of valid recipes for some sizes DeepMind blog ↗. The code repository lists 14,236 different recipes for 4x4 matrices alone GitHub repository ↗. Humans then checked, benchmarked and published the results Nature paper ↗.
Figures from the Nature paper Nature paper ↗ and DeepMind's announcement DeepMind blog ↗.
The gains have limits. In many cases AlphaTensor only rediscovered the best existing recipe rather than beating it MIT Technology Review ↗. The 47 step result works only in modulo 2 arithmetic Nature paper ↗, and the speedups were measured for particular sizes on two chip types MIT Technology Review ↗. Shortly after publication, mathematicians Manuel Kauers and Jakob Moosbauer used their own methods to improve one of its records, cutting 5x5 multiplication in modulo 2 from 96 steps to 95 Kauers & Moosbauer preprint ↗. The MIT computer scientist Virginia Williams said it was unclear whether the new approach replaces older methods or can be combined with them MIT Technology Review ↗.
Which fields could this affect?
AlphaTensor's direct value is in mathematics and numerical computing today; wider uses are possible later, and these connections are our assessment.
Mathematics & algorithm research
The recipes are public and can be checked, and researchers have already used them as a starting point. They add new examples to a problem studied since 1969.
Explore scienceAI-assisted discovery methods
It showed that turning a maths problem into a scored game lets AI search for answers. Later DeepMind systems such as AlphaEvolve continued this line of work.
Explore scienceHigh-performance software
Recipes tuned to one chip could shave time off large numerical jobs. The reported gains so far are for specific sizes and hardware, not every computer.
Explore softwareEveryday computing speed
Faster matrix maths could in principle make many programs cheaper to run. This work shows no general speedup for ordinary devices.
What has been checked?
The evidence is a peer reviewed Nature paper with published algorithms and code, plus independent follow up work by mathematicians. Leapscope reviewed these sources; we did not repeat the experiments.
Shown so far
- Better step counts than previous best recipes for more than 70 matrix sizes, published in a peer reviewed journal Nature paper ↗.
- The discovered recipes are public in a code repository, with notebooks to load and check them GitHub repository ↗.
- Outside mathematicians read and built on the results soon after publication, improving one record further Kauers & Moosbauer preprint ↗.
Still unknown
- Whether the method can lower the long run cost of multiplying very large matrices, which remains an open problem DeepMind blog ↗.
- How much real time the recipes save on chips other than the two that were tested MIT Technology Review ↗.
- Whether this approach replaces older search methods or works best combined with them MIT Technology Review ↗.
Evidence status: Published research. Stage: Verified. The discovered algorithms are published and can be checked mathematically.
From new recipes to faster software
This is our suggested way to follow the story, not a promised timetable.
Can I use it today?
Can I use it today? Researchers and programmers can download the discovered recipes and benchmarking code from DeepMind's public repository GitHub repository ↗. It is not a product, and it will not make your laptop faster.
A few things you might be wondering
Did AlphaTensor make all computers faster?
No. The 10 to 20% speedups were measured for specific matrix sizes on an Nvidia V100 and a Google TPU v2 DeepMind blog ↗ MIT Technology Review ↗. Many of its other results are fewer steps on paper, some only in modulo 2 arithmetic Nature paper ↗.
Did the AI do this on its own?
Partly. Researchers designed the game and its scoring, the AI searched for recipes, and people verified and benchmarked them DeepMind blog ↗ Nature paper ↗.
Are its records still the best?
Not all of them. Kauers and Moosbauer improved its 5x5 modulo 2 result from 96 to 95 steps shortly after publication Kauers & Moosbauer preprint ↗,.
Go straight to the sources
Checked Oct 8, 2026. The first source is the original announcement or research. Later sources add independent context; background pages do not validate the result on their own.
01The developer's announcement explaining the game setup, key results and hardware speedups.
The full study by Fawzi and colleagues, including the 47 step 4x4 result and more than 70 improved sizes.
News coverage with comments from outside computer scientists and notes on the limits of the results.
Independent mathematicians at Johannes Kepler University Linz improve one of the Nature paper's records from 96 to 95 multiplications.
The discovered algorithms, benchmarking script and verification notebooks released with the paper.