I recently struck up a conversation with a woman in my local takeaway. The banter began to run out of steam, so I switched the subject to maths. This uncharted chat-up territory. I asked her to doodle on a napkin. Without taking the pen off the paper, she drew a pattern of consecutive loops, then joined the line back to where she started. Then she criss-crossed the squiggle with an open grid of parallel lines. I asked her the minimum number of colours she would need to fill in the doodle completely, so that no two areas with the same colour were adjacent to each other.

She hesitated. “Four?”

The answer, in fact, is only two. She stared at the napkin in disbelief, then started to shade it in. Her eyes lit up as she realised that it was true.

My experiment was a success. Yes, I got her number. But, more importantly, it reinforced my belief that maths can be fascinating to people who would usually claim to have no interest in it. You don't need to understand the proof of the two-colour doodle theorem to appreciate the “wow” of seeing such an inky mess reduced to a simple black and white mosaic.

At school, those who shine at maths are seen as socially retarded, more comfortable around numbers than around people. I'm a card-carrying mathmo: I studied maths at university and am writing a book on it. On balance, however, I prefer people to numbers. In fact, the general perception that maths is just numbers is part of the problem with the prejudice against us. My mental arithmetic is bad (and I'm not proud of it) but this does not restrict my love of the subject.

Maths, for me, is about seeing the world in terms of patterns and symbols and marvelling at how they interrelate. Recursive language and a self-reflecting consciousness are uniquely human; so is the ability to think mathematically. I'd argue that the most impressive, and creative, expressions of pure thought in human history have been mathematical. That's pretty cool.

OK, as an opening gambit the line is not exactly dynamite. Yet maths has definitely helped me conversationally. For a start, mathematicians have a refined sense of humour. It is no coincidence that many writers on The Simpsons are maths and computer science graduates. One of the most basic forms of proof is proof by contradiction. This is when you prove the truth of statement A by assuming that A is false, and then show that the falsity of A leads to an impossibility. This is precisely the structure of many jokes - start with a premise that is a slight modification of reality, and bring out the absurdity of the consequences. Doh!

Mathematicians are good at bashing ideas around - negating them, turning them inside out, pulverising them and rearranging the pieces. Sometimes the result is meaningful, sometimes it isn't. And even then it has its rewards. Lewis Carroll, the father of nonsense verse, was a mathematician. Actually, he was a logician - they are even more hilarious.

Mathematicians are playful. I don't mean by this the cliché of the wacky boffin with his Van de Graaff generator hair (nothing reinforces maths as boring so much as someone shouting “fun!”). French mathematicians in the 17th century analysed their gambling habits and ended up inventing the science of probability, a basic understanding of which is as crucial in the modern world as the ability to remember one's times tables.

For me, maths becomes most exciting when it touches on deep philosophical issues. We are taught that maths is a rigid and consistent system. Well, sorry to break the news, but it isn't. Many weirdnesses lie within it. An example: there are two types of infinity, one bigger than the other. Actually, there are an infinite number of infinities, all of different size. That's fascinating, and I would probably bring it up on the second date.

One paradox connected with the British disrespect for maths is our veneration of those with musical talent. Many mathematicians are musical and many musicians have good intuitive understanding of maths. Both subjects involve a search for elegance, an improvisational creativity and a familiarity with symmetries and rules. In terms of “cool music”, Britain punches above its weight. Perhaps attitudes to maths would change if just one rock star admitted that he spent his time at the back of the tour bus doing Su Doku puzzles.

It wouldn't make him a pariah. Researching my maths book I have learnt that there is no social skill more guaranteed to charm than the ability to fold two business cards into a tetrahedron. Maths can be a powerful aphrodisiac. I now use it only sparingly in social situations.

Prime example: try this test yourself

Proof by contradiction is one of a mathematician's most powerful tools. Its most famous use is in proving that there are infinitely many prime numbers. A prime number is a whole number that can be divided only by itself and 1. So 7 is prime because it cannot be divided by anything else, but 8 is not because it can also be divided by 4 and 2. Also, all numbers can be reduced to their primes. 8 could be 2x2x2, but 7 could only be 7x1.

To prove that there are infinite prime numbers, we first assume that there are finite prime numbers, then try to show that this leads to an impossible situation. So, assume that there are finite prime numbers. There could be seven, or a hundred million. For this example, let's say that there are four. Now, imagine another number which is all existing prime numbers multiplied together, plus 1. As we are mathematicians now, let us call that number “p”. So in our example, p would be 2x3x5x7+1, or 211.

If we divide p by any of these other prime numbers, we are never going to get a whole number. We will always have 1 left over - a remainder. Check for yourself: in our example, divide 211 by 2, and you get 3x5x7+ (or 105 remainder 1). Divide it by 3, or 5, or 7, and that remainder will still be there.

Remember, all numbers can be reduced to their prime factors, without any remainders anywhere. So, either p is prime, or there is another prime that we haven't yet figured out. Either way, our initial assumption is false.

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