Support The Right Advanced Mathematics Education, Don't Cut It Off
The UK government has announced cuts to the Advanced Mathematics Support Programme that provides support for promising mathematicians to make them excel. Many in the UK maths and education community are up in arms, arguing that that this will cut off the very AI innovation Prime Minister Keir Starmer says we most need. Is it an ideological "anti-elitist" cut, or a failure to understand the connection between maths and AI? Or are they planning to switch the funding to back a modern, advanced, computer-based maths alternative? Or do they simply have no idea what they’re doing?
AI Leadership Needs Elite Mathematical Thinking, Not Pre-computer A-level maths
I am in total agreement that we need aggressive programmes to take our promising mathematical thinkers, and make them the world's best. We need a highly educated mathematical elite—the country's future prosperity depends on it—however unfair it might seem to some. But that doesn't mean I back A-level Maths and Further Maths, except purely as a temporary measure while they're urgently replaced with the right subject as the default.
If you're backing advanced maths education, be clear what outcomes you're trying to achieve.
The most important is an ability to think mathematically or computationally—to reason using the system of mathematics. Part of that is knowing what tools are available to use to get answers: both today's useful algorithms, and the technology to compute with them. They are linked. Algorithms that produced the best results before computers are rarely the most useful now (with our vastly greater, different applications), because the constraints have been turned on their head. Calculating is now very cheap with a computer; it was stupendously expensive with humans.
Therein lies the problem with A-level Maths and Further Maths. The subject-matter is from a pre-computer era. Wrong algorithms, wrong capabilities being emphasised, wrong style of mathematical thinking—related, but almost completely distinct from what you'd actually need to do now, or know. A little like being trained to drive a horse and carriage so you can drive a Tesla. They're both for getting from A to B but almost everything else in the training is different; and inappropriate; and inadequate.
Where’s Machine Learning in A-level Maths?
Take machine learning, the algorithm on which much of the current AI is based. The idea of it has been around for decades but in practice it's a useless algorithm by hand; for any useful results, you need powerful computing machinery because of the massive number of calculations required for real results. Where is it in A-level maths? Nowhere. Too new. Needs a computer, which isn't in the exams. Instead, lots of emphasis on hand-calculating simplistic integrals.
The trouble is not just learning the wrong algorithms, it's that the needed mathematical thinking, and required experience, shifts dramatically when you have cheap calculations. As one of my maths teachers said when I was doing my A-levels, "maths is the art of avoiding calculation". That was true for centuries; since computers, it isn't. The required fix isn't an adjustment to part of the curriculum, it's a complete redrawing—a fundamental shift, the very shift that's enabled maths to be elevated to its current societal importance in the real world.
AI is powered by computer-based maths, not hand-calculating. Advances in AI itself and its applications are powered by mathematical or more generally computational thinking.
We need an elite set of pioneering computational thinkers if everyone in the UK is to prosper, just like we needed elite engineers for the 19th century industrial revolution. Funding for identifying, encouraging and extra attention is required.
Pre-computer A-level Maths Still The Only Game in Town
Frustratingly, at the moment, Maths/Further Maths A-level are the only options at school for learning mathematical thinking, getting to university. They shouldn't be. I've long campaigned for and drawn up a computer-based maths alternative that could truly represent modern mathematical or computational thinking with a modern toolset. A more conceptual, intellectually demanding—harder—subject that would optimise high-level, modern computational thinking (as well as get everyone to a higher standard of computational literacy).
It is an error simply to cut the funding for the only game in town. An even bigger error is not to fund the new game we need to play. The government should commit today to offer a modernised core computational/computer-based maths curriculum for our advanced students (and indeed for everyone else).
Will Britain Lead, or Throw Away Its Advantage?
The maths community must back a fully justifiable subject, or maths will be sidelined. The government need to get A graders to A**, not just D graders to Cs. Nowhere is this more critical than for mathematical or computational thinking. Or Britain will fail in the AI age. Everything to play for in the next year. It is within Britain's grasp to lead education transformation for the AI age, starting this September ( for the 2025-26 school year).