He is one of Britain's leading science writers, a former Cern physicist, a bestselling author, and he holds a PhD from Cambridge in particle physics. Yet Simon Singh prepared for his latest book by watching numerous episodes of The Simpsons back-to-back, all day long, on his sofa.

Singh is part of a new wave of populist scientists, whose primary goal is to reach as many people as possible. He is evangelical in the way he approaches science. He has toured the country – with Brian Cox, the TV presenter and physicist; Robin Ince, the comedian; and Ben Goldacre, the writer – celebrating science. And he loves Big Brother just as much as questioning the nature of matter.

The 49-year-old's trick is to find a hook, tell an interesting story, and then ensure that science is slipped into it – a little bit like hiding the sprouts at the bottom of a child's favourite dinner. He turned the search for a proof of one of the world's greatest mathematical problems into a bestselling book (Fermat's Last Theorem) and now he wants to use The Simpsons to teach his readers more about mathematics.

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"I don't want to write books that are intellectually staggering if nobody's going to read them," he says, sitting at his kitchen table in south-west London. "These books are about getting people interested in science – in large numbers." He is adamant that his new book, The Simpsons and their Mathematical Secrets, is "obviously a great idea. It's the world's most popular TV series and nobody knows that there's this band of mathematicians at the heart of its writing team. People don't know that they smuggle maths into the series."

So as well as interviewing some of the writers, Singh watched certain episodes over and over again in the hope of spotting mathematical allusions that he could then dissect for his readers. Whether it is Homer referencing Fermat's last theorem or Apu reciting pi to its 40,000th decimal place, readers can learn about both, as well as narcissistic numbers and unsolved maths riddles. David X Cohen, a writer for The Simpsons and Futurama, said Singh "blows the lid off a decades-long conspiracy to secretly educate cartoon viewers".

But should a science writer really be watching episodes of The Simpsons on repeat or could he be doing something more productive? He laughs. He says his wife, Anita Anand, a journalist and radio presenter who is writing a book on Sophia Duleep Singh, the Indian princess and suffragette, spends all day at the British Library, transcribing personal diaries. "She comes back and I'm just lying on the sofa watching The Simpsons. I think she has a huge amount of fun doing that, but rather her than me. I'm happy watching The Simpsons at home."

But there is more to Singh than Simpsons-surfing. His passion for code-breaking led him to write The Code Book and also helped him to woo Anand when they met at a literary festival nine years ago. Preparing for a talk, he bought his Enigma machine into the green room. "I thought I'd kind of try to get her attention, he says. "I thought if a few people gathered around the table, she'd maybe come over as well – and she did."

He insists he has no other hobbies (he hates cooking, doesn't garden) and says that even his parents, who moved to Somerset from India in the 1950s, did not really understand his zeal for physics as a youngster. They were from a farming family and tried to instil a business ethic in their children; his older brother Tom is the founder of retailer New Look.

But Singh is a well-known sceptic – questioning, among other things the validity of alternative medicine. He was dubbed a "superhero" when he successfully took on the British Chiropractic Association and fought for libel reform. The ordeal began when Singh wrote in a commentary that the association "promotes bogus treatments". It sued for libel. Although Singh won the case, he spent £300,000 on his defence. He describes the saga as "incredibly stressful" and the sort of thing that "has destroyed marriages". But his fight was influential in the framing of the Defamation Act which was passed in April, which, he says, "kind of made it worthwhile".

He is adamant that the experience has not blunted his scepticism."I think it makes other people more cautious of me," he adds wryly. He insists he is more committed than ever to tackling "pseudo-science". Top of his list are alternative medicines and the "dodgy and sometimes dangerous" claims made for them. He is looking forward to targeting traditional Chinese herbal medicine, which he thinks is particularly harmful. "Nobody knows if this thing actually works. It's just ludicrous."

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Talking about the education system, and science teaching in particular, he says matter-of-factly that "every single party has screwed it up for the past 25 years. We need genetic engineers and computer scientists, yet the number of people doing physics A-level compared with when I did it 25 years ago, has fallen by half. Are we going get British- born Nobel laureates in physics in the future? Yeah, but they will have gone to a private school. It's not a great situation."

His enthusiasm for science is contagious. He asks if I know why biscuits get soft but bread gets hard if not in an airtight container. When I shake my head, he says he started questioning everything from a young age. "Where do the stars come from? Where does light come from? There were all these questions …"

And it seems his son, three-year-old Hari, has inherited his inquisitive nature. "He could tell you the names of the moons of Mars," he says proudly, and lists the experiments the two of them do together: they put soap in the microwave; they sprinkle different substances on the gas oven to see what colours they make.

It sounds a little like something that Bart would do.

Curriculum vitae

1950 Singh's parents leave Punjab in India for Taunton, Somerset.

1964 Simon Lehna Singh is born in Wellington, Somerset.

1981 Studies maths, physics and chemistry A-levels at Wellington School. Applies to the University of Cambridge but is rejected.

1983 Studies physics at Imperial College, London.

1987 Begins a PhD in experimental particle physics at Cambridge, but spends most of the three years working at the European Centre for Particle Physics (Cern) in Geneva.

1990 Joins the BBC as a producer and director for programmes such as Tomorrow's World and Horizon.

1996 Directs Fermat's Last Theorem, a Bafta award-winning documentary about one of the world's most notorious mathematical problems.

1999 Publishes The Code Book, on the science of codes and the impact of code-breaking on history.

2000 Presents The Science of Secrecy, a Channel 4 series on the use of encryption for internet privacy.

2003 Created MBE for services to science, technology and engineering.

2008 Sued for libel by the British Chiropractic Association. After a two-year battle, he eventually wins.

2013 Publishes The Simpsons and Their Mathematical Secrets.

Zander Swinburne