I have lectured to secondary school students at least 200 times over the past decade, and I have covered meaty topics such Fermat’s last theorem, statistics, probability, cosmology, cryptography and evidence-based medicine. But my favourite topic at the moment is The Simpsons.

Believe it or not, The Simpsons contains a mountain of maths, from pi to perfect numbers, Pythagorean theorem and infinity. So I use the world’s most successful television show to explore all sorts of mathematical ideas.

The reason why Homer Simpson makes references to numbers and why Lisa Simpson makes jokes about theorems is that many writers of The Simpsons have backgrounds in maths, having studied the subject at universities such as Harvard and Yale.

But you may not have spotted the mathematical themes in The Simpsons because they are often embedded as “freeze-frame” gags, designed to appear briefly to avoid getting in the way of the plot or scaring away non-nerds. For example, in the episode MoneyBart, Lisa is depicted with a book that has an equation on its spine. It is Euler’s identity, arguably the most elegant equation in the history of maths. Similarly, in Treehouse of Horror VI, the equation P=NP flies behind Homer; a reference to an unsolved problem so notorious that the Clay Mathematics Institute in the US is offering a $1 million (pound;610,000) reward for whoever can tackle it successfully.

My book The Simpsons and Their Mathematical Secrets documents dozens of examples of maths in The Simpsons and similar references in its sister show Futurama, which was penned by some of the same mathematically gifted writers.

Although there are straightforward sums in The Simpsons and Futurama, I tend to focus on the more sophisticated ideas when I visit schools, perhaps because my main concern is with stretching more able students. It is obviously important to interest, inspire and educate all students across the range of abilities. But too much focus has been placed on helping students to overcome a fear of numbers, leaving the most able as an afterthought.

This may seem harsh, but it is hard for an unbiased outsider to come to any other conclusion. My initial concerns arose after visiting schools and talking to teachers. Such evidence could be dismissed as merely anecdotal. However, a more concrete survey of the problem was presented in a report, Educating the Highly Able, authored by Alan Smithers and Pamela Robinson at the University of Buckingham and commissioned by social mobility charity the Sutton Trust.

The report’s most damning paragraph contrasts the performance of English 15-year-olds with their overseas rivals: “In the 2009 Pisa [Programme for International Student Assessment] tests, only just over half as many achieved the highest level in maths as the average of 3.1 per cent for OECD [Organisation for Economic Cooperation and Development] countries. England’s 1.7 per cent has to be seen against the 8.7 per cent in Flemish Belgium and 7.8 per cent in Switzerland. On a world scale, the picture is even more concerning - 26.6 per cent achieved the highest level in Shanghai, 15.6 per cent in Singapore and 10.8 per cent in Hong Kong.The few top performers in England are in independent and grammar schools and almost no pupils in the general run of maintained [schools] reach the highest levels.”

This might raise concerns that countries such as Singapore and Switzerland focus on the highly able and neglect the average students, but the top 10 countries that excel in teaching the highly able also trump England when it comes to average achievements in maths.

Physics is in a spin

The problem also extends to physics. When I completed my A-level in 1982, I sat it alongside 55,728 others in the country. In 2006, only 27,368 took the exam. Given the lack of mathematical ability on these islands, I should point out that this is less than half the previous number. This year that figure has increased to 36,701, but that is still only two-thirds of the 1982 level.

Some argue that quality is more important than quantity, but it is generally accepted that today’s A-level physicists cover less than their predecessors in a less rigorous fashion, largely because the maths that is integral to physics was removed to tempt those who might be fearful. This ultimately means that we now have fewer physicists knowing less physics.

It baffles and saddens me in equal measure that today we have more money, resources and online tools to develop maths and physics potential than ever before, yet we have taken big steps backwards compared with a generation ago.

There are some ongoing initiatives aimed at improving maths and science education in England, but at best they tinker around the edges and prop up a failing model. Instead, the Department for Education needs to implement a radical policy that rescues our future inventors and cosmologists from oblivion. We could do worse than follow the New York City model, which relies on nine selective, publicly funded high schools to nurture the highest flyers. Most focus on maths, science and engineering; the Bronx High School of Science, for example, can count seven Nobel laureates in physics among its alumni.

We desperately need a similar network of schools, or something even more radical, here in the UK to realise the potential of ambitious young mathematicians and physicists. They deserve to be stretched. Michael Faraday and Sir Isaac Newton must be gathering angular momentum in their graves over the sorry state of A-level maths and physics.

Simon Singh is an author, journalist and television producer specialising in science and maths. His book The Simpsons and Their Mathematical Secrets is published by Bloomsbury

Learning by Bart

Simon Singh has created a classroom resource for A-level students that explores the maths and physics featured in The Simpsons. Find it at www.tesconnect.comsimpsonsmaths