The Myth about Maths

Marcus du Sautoy is on a mission. The Oxford mathematics professor and Charles Simonyi Professor for the Public Understanding of Science (a chair previously held by Richard Dawkins) spends most of his time trying to deconstruct myths around maths. From TED talks and podcasts, to YouTube videos, plays, TV and game shows, the professor has shone a light on subjects from the creativity of AI and its self-awareness, to code cracking and measuring the universe. A Carl Sagan for maths if you will, Marcus du Sautoy takes on some of the big questions of the day.

Why do so many people hate maths?

When I give talks about mathematics I often get the response ‘I didn’t realise that was mathematics. I like that!’ I often think we should teach two subjects: mathematical language, the boring stuff, and mathematical literature, full of all the great stories of mathematics about infinity, hyperspace and prime numbers. One of the challenges of teaching mathematics is that it is like building a pyramid. If you have one bad year at school, then trying to build anything on top of that becomes impossible.

One of the big influences on me as a student was A Mathematician’s Apology (1940) by GH Hardy. Mathematicians are storytellers; it’s just that our characters are numbers and geometry. The proofs we construct are meant to have strong narratives which move our audiences in the same way that great literature does.

What's the biggest myth about mathematicians?

That we are good at arithmetic. Actually, most mathematicians are rubbish at multiplication tables. Most people think that research mathematicians, like me, must do long division to a lot of decimal places. But actually, mathematics is the science of patterns, not calculations.

Your latest book Thinking Better: The Art of the Shortcut (2021) tells us how maths can solve everything from morbidity on a battlefield to measuring the earth, and two points on the globe. How might this apply to our everyday lives?

My book is a celebration of mathematics as the art of the shortcut. I want people to understand that there are wonderful ways of thinking, developed over the last two thousand years, that give us the ability to avoid boring, hard work. I called the book Thinking Better as a kind of homage to Daniel Kahneman’s book Thinking, Fast and Slow (2011). In his book, Kahneman illustrates how bad our fast, intuitive thinking is at solving problems; it constantly leads us astray. We need slow, analytical thinking to solve counterintuitive problems. But it doesn’t have to be slow. I argue that mathematics gives us fast ways to think analytically.

What’s the most exciting mathematical development of the 21st Century?

One of the most exciting mathematical breakthroughs in the last 20 years has to be the proof of the Poincaré Conjecture by Grigori Perelman. This was one of the seven Millennium Problems set at the beginning of this new century and it is the only one so far to be solved. It concerns the possible shapes our 3-dimensional universe might be.

Are concerns about the singularity and AI overtaking human intelligence, warranted?

Talk of the singularity ー the moment when machine intelligence overtakes human intelligence ー has oversimplified the discussion. It implies a very one dimensional view of intelligence 一 something that can be plotted on a graph which can at some point, overtake us. The truth is that intelligence is a multi-dimensional, multi-faceted concept. And this is why in some directions machine intelligence will easily outstrip us, but in others, humans will have the upper hand. The message of my book The Creativity Code (2019) is that it is a combined intelligence, human and machine, that will always be better than either individually.

Where does AI stumble?

Empathy is something that AI will probably always have difficulty with, since this requires understanding the mind of the other. To do this, requires two minds that are built in a similar fashion. We already find it difficult to understand the thought process of an AI because it is so different from our own. At the moment, our ability to integrate many different strands of intelligence is something that AI struggles with. Human General Intelligence is something that AI aspires to, but is still some way off achieving.

If we have written the code for AI, why can’t we understand its ‘thought’ process?

In the past, code was written in a top-down manner. Humans wrote the code, which machines implemented at speed and depth. But ultimately, humans knew what the machines were doing. The last few years have seen a phase change in the way we write code. It is now being written from the bottom up. It is allowed to change, mutate and update itself as it encounters new data. This means that the final code is so complex and opaque that we don’t really understand how it makes decisions. Looking at lines of code isn’t very helpful. It’s like trying to understand human thought by looking at the firing of individual neurons. That is why we need to find ways to probe the code to understand its thought process. As this technology takes hold, this is the challenge for us.

My favourite example is of Deep Dream. Google used machine learning to produce a very powerful vision recognition algorithm, but they wanted to probe what the AI was actually ‘seeing.’ So they reversed the process, giving the AI pictures with unclear images asking the AI to accentuate anything it saw in the image. It’s a bit like the way we look at the clouds in the sky and see a dragon or a dog. The images that the algorithm produced revealed a lot about the way that the AI had learned to see, and in particular showed up strange, bad learning that had occurred. For example, when the AI reproduced images of dumbbells, the pictures always showed arms attached to them, revealing that the AI had never seen a dumbbell that wasn’t held by a human. It thought dumbbells were an extension of human anatomy.

What is the point of AI art and should artists fear losing their jobs?

In The Creativity Code I conjecture that human creativity emerged at the same time as human consciousness. Our art became a fantastic tool to probe and understand this mysterious inner world that was emerging in the human species. We are seeing a new mind emerging in the guise of AI and we don’t really understand its inner world. It is certainly not conscious yet, but the code is so complex that we need tools to probe how it is making its decisions. Asking it to create art is a clever way to investigate the thought process of complex code.

The message of my book is that these tools are not going to replace human creativity but enhance it. As creative artists, we get stuck in old ways of doing things, repeating behaviours that were successful in the past. We end up behaving like machines. The exciting thing about emerging AI creativity tools is that they are suggesting new ways of thinking.

What is the largest roadblock to public understanding of science?

One of our biggest challenges is countering the wave of scientific disinformation and false news stories that social media spreads so easily. We have become very tribal in our approach to knowledge. Adopting the same view as a strong member of your group is a powerful way to identify with, and bond with that group. One of the toughest things that scientists must learn is to adopt a rather unscientific approach to this challenge. Often, one story of a child who has had an adverse effect to a vaccine will fuel a whole anti-vax movement. No amount of counter data seems to overturn that story. The only way to undo a story, is to tell another story, such as the story of a child who died of measles because they weren’t vaccinated.

More scientists need to step up to the plate and share the stories that science has to offer. Part of the key is to not polarise the debate, and to engage with understanding where contrary opinion is coming from. Alas, this engagement requires nuance and debate, something that social media is not good at.

Can science and religion ever intersect?

My previous book What We Cannot Know (2016) explores this interesting intersection between science and religion. They are inevitably going to collide given that both are trying to answer the big existential questions about our origins. But what I argue in my book is that perhaps religion is about the realm of the great unknown; knowledge that will always be unknowable. I wonder whether there are any questions that science will never be able to answer.

If I have 14 varieties of crisps, 25 varieties of drinks, and 10 varieties of sandwiches, can 'shortcut thinking' lead me to the best combination?

Interestingly you have cooked up an equation in three variables that you are trying to maximise so mathematics is perfect territory for finding the best combination, without trying all (14 x 25 x 10 = 3,500) different possibilities. Of course, learning the maths might take some time, but the point is that soon, someone will implement that mathematical shortcut into an app which can then lead to the best meal deal.

Marcus du Sautoy’s book ‘Thinking Better: The Art of the Shortcut (2021)’ is published by 4th Estate. The author will be speaking at the Emirates Festival of Literature 2023.