But there is a new kid on the coding block. The new styles of code that have emerged—deep learning and machine learning—see code written from the bottom up. Code is allowed to change and mutate, up-date itself with interaction with new data. This learning process results in code that does things that might surprise even the humans that initiated the code’s journey. And it’s that element of surprise that allows this new type of code to be creative. ¹

A definition of creativity proposed by the cognitive scientist Margaret Boden requires three characteristics to be present: novelty, surprise and value. ² Novelty is something we can judge objectively, but surprise and value are much more subjective. Surprise is about engaging our emotions and making us look at the world in a new way. But a truly creative act doesn’t just shock us with its surprise for shock’s sake but should provide a new perspective that gives us value in the long run. Humans have embedded these subjective qualities of surprise and value in works of art over the centuries. Therefore, there is data for code to learn what might offer new surprises and value for the current generation.

Intelligence is multi-dimensional

With the explosion of AI in the last few years, many people have become quite fearful of the impact this new technology will have on society. Hollywood has generated much of this fear, peddling a dystopian narrative of AI and robots taking over the world. Talk of “the singularity”—a moment when AI will overtake human intelligence—also plays into this narrative. But this thinking falls into the trap of assuming intelligence is a one-dimensional phenomenon. The idea of a graph showing a trajectory of AI intelligence souring upwards until it passes the line of human intelligence. The human intelligence trajectory has either plateaued or, as some believe, has started creeping downwards as we waste our hours on mindless social media, a clever trick probably created by AI to advance the singularity.

But this misses the point that intelligence is, by nature, hugely multi-dimensional. We already talk about some people having high emotional intelligence compared to cognitive intelligence. And what we are seeing emerge in this new world of AI is code that is better than us at some things but that there are still many places where humans will be superior. And this is why the Hollywood narrative misses the great opportunity that lies ahead. This is not about competition—people being put out of a job by AI—but about collaboration. This is a wonderful new tool to help humans to do new things.

What if we translate the letters ‘AI’ not as artificial intelligence but rather as augmented intelligence, additional intelligence or alternative intelligence? When Turing began the journey of AI, he was interested in understanding how the human brain worked. ³ What was it about the way our brains operated that gave rise to our intelligence? For him, the interesting challenge was to explore whether one could recreate in technology something that matched our intelligence. The ‘A’ in AI was about artificially reproducing something that resembled our intelligence so that we could better understand the way the brain works. But things have moved on since those first forays into AI. Far more interesting is to try to produce intelligence different from our own, that will complement our style of thinking. That’s why that ‘A’ in AI needs to be updated. It’s my belief, that this alternative intelligence might ultimately help us as humans be more creative, not less.

Many creative people repeat behaviours that have worked for them in the past. The reason that you can recognise a jazz musician is often because they have got stuck in one style of playing their instrument. But interacting with AI trained in your creative output provides the opportunity for the AI to show you new ways of working with your material. Take the jazz pianist Bernard Lubat who allowed an AI to train in his improvisation style. The code that emerged, called the Jazz Continuator⁴ , shocked Lubat with its musical responce. “The system shows me ideas I could have developed, but that would have taken me years to actually develop. It is years ahead of me, yet everything it plays is unquestionably me.”

The Continuator had learned to master Lubat’s sound world, but rather than simply throwing stuff back that he had done before, it was exploring new territory. It was pushing the artist whose work it had learnt, to be more creative by showing him aspects of his craft he had not accessed before. It’s as if we humans fall into the trap of repeating successful behaviours that have worked in the past and end up behaving like machines, repeating old formulas. The new emerging AI is kicking us out of the rut we’ve fallen into and pushing us to be more creative again as humans, offering us new, surprising, valuable perspectives.

The creativity of mathematics

As a mathematician, I have been particularly interested in what impact this new technology would have on my field. Many people assumed that mathematicians would be the first to be out of job with the advances of AI. After all, isn’t AI just code, which is just algorithms, which is just mathematics? If AI is built out of mathematics, then shouldn’t it find mathematical research a cinch?

The challenge for AI mathematics is that doing mathematical research requires a huge amount of creativity. That word has always been my protective shield against AI matching the mathematical output of my colleagues at the mathematics department at Oxford. There’s an idea that the goal of mathematics is to prove all the true statements about numbers and geometry; to create a mathematical Library of Babel, like Borges’s library, that contains every book possible to write.⁵

But such a library contains everything and nothing. Because no one has made any choices. The Bodleian Library in Oxford, in contrast to Borges’s library, contains only those books that we humans have chosen to elevate to the status of literature. The authors have made choices of those strings of letters that are worth reading. Similarly, mathematical journals contain the theorems that we humans find exciting, that make us look at the world in a new way, that entertain and move us. We make choices about the theorems that we elevate into the mathematical canon. A computer can churn out a long complex proof that might match the proof of Fermat’s Last Theorem for its complexity but that is simply not interesting because it doesn’t tell a story that will transform our vision of the mathematical world in the way that the proof of the Last Theorem did. ⁶

The interesting thing is how we humans pick up that subtle difference between proof that will move our colleagues versus proof that leaves them cold. We go through a very similar process to the code that learns by being exposed to data. My trajectory as a mathematician has been to read the proofs and theorems of the past, absorbing the themes and ideas that the mathematicians of previous generations have valued. That has informed my own direction as a mathematician producing new theorems. So it doesn’t seem beyond the realms of possibility that an AI could learn in a similar way.

AI’s problem with time

AI currently has a problem that is holding it back from being a great creator of proofs. One of the very interesting limitations that AI creativity has at the moment is the idea of a sustained narrative line that extends beyond a few paragraphs. We have seen an extraordinary explosion of, for example, text generation algorithms. GPT-3 and ChatGPT from OpenAI⁷ have been heralded as game changers, and the text they can generate is certainly remarkable. But the ideas generally fizzle out beyond a few interesting pages of text. It certainly offers the human interacting with the code some very provocative new perspectives but sustaining a narrative over chapters rather than paragraphs still seems a challenge too far. It’s almost as if the temporal element demanded by the narrative is a limiting factor.

The same limitation is revealed by the Jazz Continuator. The AI is very convincing in the short term but listening to more than five minutes of it improvising away, and the listener becomes bored. It feels like it is meandering. It doesn’t know where it’s going. It has nothing really to say. I get the same feeling with GPT-3. It can produce an extraordinary stream of consciousness and gives us a fascinating insight into the data that it has learnt but it still feels like something is missing.

Pharmako-AI, a book created through the collaboration between human artist K Allado-McDowell and AI GPT-3⁸, is a fascinating read. But ultimately, it doesn’t transcend the hallucinatory feeling of two voices tripping away. There is even a wonderful moment when GPT-3 stops the human from exploring thoughts on code and rather, wants to discuss the experiences of taking the drug ayahuasca. Given that the AI is unembodied, this is something that it will only be able to understand at a distance. That sense of meandering has limited the power of AI to come up with interesting mathematical proof, the mathematician’s novel. But that’s not to say it can’t be a powerful new weapon in the mathematician’s arsenal.

AI: a new telescope on the digital world

Mathematical research often consists of two important strands. One of those is coming up with proofs of conjectures about the way numbers and geometries behave. But an equally important, if not more important, part of being a mathematician is coming up with these conjectures—hunches about what might be true. Fermat first had to suggest that his equations might not have solutions. That guess set the rest of us off on the 350-year journey to prove his hunch correct.

AI might not be good at constructing the journey of proof, but it seems that it might be rather adept at coming up with new conjectures. This was demonstrated by work from DeepMind published in Nature at the end of 2021⁹. My colleague in Oxford, Mark Lackenby, who works on knots, believed that there exists an undiscovered relationship between the hyperbolic and algebraic invariants of a knot, two different ways of looking at these mathematical objects. By letting a supervised learning model roam over calculations of these two invariants, the AI could detect the existence of a pattern between the two, which had not been observed before. This new pattern offered a conjecture to the human mathematician that set us off on a new journey of discovery.

This is a perfect example of the powerful potential of working together with AI. The AI emerging at the moment is powerful enough to construct the type of proof that human mathematicians can produce. That ability requires a lot of intuition and creativity built up over years of exposure to mathematical ideas. That’s not to say AI won’t eventually acquire that intuition, it likely will, but it is not evident yet.

But the AI can be exposed to mathematical data and pick out new patterns that are opaque to the human eye. This new tool is like the moment Galileo picked up a telescope, which allowed him to see deeper into our solar system than anyone had before and see new things in the night sky. The new AI emerging is like a digital telescope allowing us to see deep into the digital universe revealing patterns that had gone unseen before.

Any new technology brings with it anxiety and fear about the impact it might have. But we mustn’t let that dystopian narrative pedalled by Hollywood obscure the vast potential these tools have to stimulate creativity by humans aided by AI. The future is about collaboration, not competition.