Research in mathematics is a deeply imaginative and intuitive process.
This might come as a surprise for those who are still recovering from high-school algebra.
What does the world look like at the quantum scale?
What shape would our universe take if we were as large as a galaxy?
What would it be like to live in six or even 60 dimensions?
These are the problems that mathematicians and physicists are grappling with every day.
This process relies on our intuition as much as our knowledge.
Machine intuition
Where does the intuition of a mathematician come from?
One can ask the same question in any field of human endeavour.
How does a chess grandmaster know their opponent is in trouble?
How does a surfer know where to wait for a wave?
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Something miraculous seems to happen in the human brain.
Moreover, this miraculous something takes thousands of hours to develop and is not easily taught.
The past decade has seen computers display the first hints of something like human intuition.
AlphaGo won 41, and experts observed that some of AlphaGos moves displayed human-level intuition.
One particular move (move 37) is now famous as a new discovery in the game.
How do computers learn?
Behind these breakthroughs lies a technique called deep learning.
At first, the networks output is useless.
Such ideas were tried in the 1970s with unconvincing results.
With the deep learning revolution of the 2010s, computers began performing well on these tasks.
AI has essentially brought vision and speech to machines.
Training neural nets requires huge amounts of data.
Whats more, trained deep learning models often function as black boxes.
At the induction ceremony in London I met Demis Hassabis, chief executive of DeepMind.
Over a coffee break we discussed deep learning, and possible applications in mathematics.
Could machine learning lead to discoveries in mathematics, like it had in Go?
This fortuitous conversation led to my collaboration with the team at DeepMind.
Mathematicians like myself often use computers to check or perform long computations.
However, computers usually cannot help me develop intuition or suggest a possible line of attack.
So we asked ourselves: can deep learning help mathematicians build intuition?
Amazingly, the computer was able to predict these Kazhdan-Lusztig polynomials with incredible accuracy.
The model seemed to be onto something, but we couldnt tell what.
This conjecture suggests a way forward on a problem that has stumped mathematicians for more than 40 years.
Remarkably, for me, the model was providing intuition!
Our paper reminds us that intelligence is not a single variable, like the result of an IQ test.
Intelligence is best thought of as having many dimensions.
