Better living through geometry

Whatever you wish to keep, you better grab it fast

The UK Chancellor of the Exchequer gave a big speech on Wednesday about how to achieve economic growth. But cynics on Twitter weren’t convinced, because an earlier story on Wednesday coming from the same Government seemed to directly contradict it.

Forgive me for a bit of a rant, but I’m going to agree with Veronica Humble’s tweet:

We were talking about this because earlier that morning, the Financial Times had reported that:

The UK government is to cut back a hugely successful programme designed to encourage teenagers to take up higher-level maths courses, causing dismay among charities and campaign groups. The Advanced Mathematics Support Programme, which has been running since 2018, helps state schools in England teach A-level maths, further maths and a core maths programme that provides “maths for life” skills, such as statistics and finance.

As the head of one of the UK’s leading university mathematics departments, I don’t mind admitting that my head was in my hands at this news, because maths is one of this country’s great strengths and a huge driver of economic growth. I firmly believe that giving young people a mathematical education in some form or another is essential to prepare them for 21st Century skills.

Worse, the sum saved by scrapping this programme was insultingly low by Government standards: £17m over two years. To put that in context, it wouldn’t cover three hours worth of the UK’s debt interest payments. To do it on the day that we announced we were going for growth was particularly ironic. Not everyone is going to be a research mathematician, but the science and engineering degrees that will equip people for the jobs of the future overwhelmingly require A Level maths, so it’s hard to think of a more counterproductive place to make a cut. It’s like burning banknotes to stay warm.

People may disagree about the value of maths. The terminally wrong may sneer about why anyone needs to know about prime numbers for example, and really there are two answers to that. The first is to ask why does anyone need to know about Shakespeare, Mozart or Picasso, because the answer is the same: maths is beautiful, maths is profound, maths helps us see the universe. These pinnacles of human achievement and understanding, building on a chain of knowledge which goes back to Greek, Arabic, Chinese and Indian mathematicians centuries ago, are the things that mark us out as having achieved civilisation. And that’s true.

But also, maths is useful. As viewers of Apple TV’s Prime Target will know, the internet is held together by prime numbers. Every time you put your credit card details into a website, the little padlock on your browser tells you that the transaction is encrypted. Many of you might know that the encryption is based on the pure mathematical fact that splitting a big number into its prime factors appears to be extremely hard. It’s perhaps less well known that this kind of encryption was developed in the UK, by two former members of the UK’s International Mathematical Olympiad team.

And if this kind of encryption fails in the end, it might happen because a lone mathematics genius has a revolutionary idea, or it might happen because of quantum computers. Guess which country has lots of quantum computing companies, and guess what background many of their employees have?

Of course, there can be a bit of a disconnect between mathematicians and the real world. A lot of us set out to solve problems because we like challenges and puzzles, not because we want to change the world and build prosperity. Understandably, research councils and the governments who give them money aren’t always happy with that attitude.

In fact, the last Government set out to understand how to build bridges between academic maths and real world industrial applications, by commissioning 2018’s Bond Report. It’s well worth taking a look, because it sets out more of the ways that maths is valuable to the economy. Some of the estimates of the existing value of mathematics to the economy in there are already astronomical. But the report recommended that we should go further in this direction. Its very first recommendation was that to harness the power of maths for prosperity:

An Academy for the Mathematical Sciences should be established in order to facilitate links between academia, government and industry

We were going ahead and doing that, many of the plans for the Academy were under way. And yet, in September 2024, the incoming Labour Government pulled the plug, for the sake of an even tinier sum of money: £6m over three years. It’s honestly hard to understand what the growth strategy is meant to be, particularly when the Bond Report itself (P6) estimated that investment in mathematics was multiplied by 588 in “a rate of return on investment as benefit-to-cost ratio”.

To go back to Reeves’ speech and the original tweet, there was a particular irony in the Government announcing cuts in maths support and then giving a growth speech standing next to an MRI scanner. There’s a great Substack post from

Ed Conway

about these remarkable machines, and how they are made. As you’d expect from his fantastic book, Ed focuses on the materials side of things, talking about the helium and the magnets.

But there’s actually another angle: and once again it is maths. Medical scanners work by calculating a mathematical function called the Radon transform, and with some clever tricks we can turn that back into a picture. So already maths was built into MRI scanners, before something even more revolutionary happened.

Although these Radon transform methods are clever, they can also be slow. Patients need to lie still in an MRI machine for a long time to take a lot of measurements, which is particularly tough if you are trying to scan children. Once again, mathematicians came to the rescue: people like Terry Tao, Emmanuel Candès, David Donoho and Justin Romberg developed the idea of compressed sensing.

The main result from Donoho’s paper (sorry, paywalled). It may well not be obvious what any of this means, but this is maths that changed the world.

The maths can again be a bit bewildering, but there’s a nice and not too technical explanation in this 2007 blogpost from Tao himself. However, the interesting thing is what happened as a result. By needing fewer measurements, MRI scanners could work faster. Patients needed to lie still for less time, the machines could be used more efficiently. Less than 20 years after Tao’s blogpost, this is now well established technology. Philips will sell you an MRI machine with it built in, and hospitals can tell you that:

We went from hour time slots to 30 minutes. We went from having 13 patients to 26 to 28 every single day

This is a huge deal! If you start thinking about the amount of money this must save each year around the world, it’s a vast contribution. And that’s just one piece of maths, one set of ideas.

Perhaps it’s our fault as a community. We don’t always do a good sales job. But hopefully this newsletter will convince you that maths is a key ingredient for growth, and that it’s the last place any serious Government should be making cuts. If it did, please do share it and pass on the message.

This week, as well as sending lots of emails I have been listening to Cat Power’s reconstruction of Bob Dylan’s 1966 Royal Albert Hall (sic) Concert, watching Brian and Maggie on All4, and reading Knife by Salman Rushdie. All come recommended.