This week saw an esteemed Oxford University professor, Sir Andrew Wiles, awarded the Abel Prize – the richest, most prestigious mathematics prize in the world – for his tour-de-force proof to Fermat’s Last Theorem, a mathematical conundrum that has stumped the world’s brainiest maths geniuses for more than 300 years.

Fermat’s theorem – in case you didn’t know (we didn’t) – states that you cannot find three positive integers that can satisfy the equation a^{n} + b^{n} = c^{n} , where n is a number greater than 2. It was posited by the 17^{th} century French mathematician Pierre de Fermat in 1637. Fermat, a brilliant mathematician but also something of a tease, was fond of conjuring up brain-stretching puzzles and challenges for his students. In Fermat’s Last Theorem he created the granddaddy of them all. None of the great maths minds of the past three centuries was able to crack it – that is until Wiles worked out a proof in 1994.

Indeed, for many years it was listed in the Guinness Book of World Records as the world’s toughest mathematical problem. For his work in solving it, the Norwegian Academy of Science and Letters this week awarded Wiles the Abel Prize – a sort of Nobel Prize for maths – and the £500,000 stipend that comes with it. Nice.

So what does this have to do with tall boots and bootmaking? Well, not a lot, really, but it does put us in mind of another delightful little mathematical formula, one that was worked out by physicists at Britain’s University of Surrey a few years ago. It reads as follows:

h = Q*(12+3s/8)

Now this is one that makes sense to us, Far less taxing than Fermat’s Last Theorem, and frankly a lot more fun and practical, it’s an equation you can use to determine the optimum heel height for your boots (or shoes, if you must).

In this High Heel Theorem, the ‘h’ represents heel height in centimetres, the Q in the equation is the so-called sociological factor (of which more in just a moment) and the ‘s’ is your shoe size (in UK sizes). Unlike Fermat’s Theorem, the High Heel Theorem is susceptible of many viable solutions – yours among them.

The trickiest part, of course, is establishing your own correct value for Q, which requires plugging a series of values into a rather formidable looking equation. This contains all those niggling hard-to-quantify variables – the overall sexiness of your boots, how experienced you are in wearing high heels, fashion trends, how much you spent on your boots, and how many units of alcohol you are likely to be consuming while wearing them. As you can imagine, solutions vary. Calculating optimum heel height is an exercise in situational mathematics.

The equation for establishing Q is:

Q = P*(9+y)*L /(t+1)*(a+1)*(y+10)*(L+£20)

Happily solving for Q is not as intimidating as it looks. (How could it be? Einstein’s Theory of Relativity is expressed as a simple e=mc^{2})

So let’s break it down.

The ‘p’ in the equation concerns the style of boots you are swearing and the probability that they will catch the eye of the opposite sex. Values range from 1 (sizzling hot!) to 0 (might-as-well-be-wearing-galoshes).

Y is the number of years you have been wearing heels.

L is the cost of the boots in pounds (remember, this formula was a British effort) The theory here is that the more expensive the boot, the more likely you are to be to put up with a bit of discomfort. After all, you bought these for a reason.

T equals the time, in months, since your particular boots were at the cutting edge of fashion. Zero is red hot, the *dernier cri*. Again, the University of Surry physicists reckon that if your boots are all the rage, the glow of being at the forefront of fashion will dull any discomfort. It’s what they call suffering for your art.

Lastly, ‘a’ is the number of alcohol units consumed, as this will reduce your coordination and ability to balance. For example, when the physicists tested out their formula, they plugged in estimated numbers for Carrie Bradshaw, the actress famed for her killer heels in Sex and the City. Crediting her with being an accomplished heel wearer with at least five years’ experience, and almost certain to be wearing the latest fashions and drop-dead gorgeous heels, they calculated that if she hasn’t had anything to drink she can easily cope with killer heels of 125 millimetres, or 5 inches. Add six units of alcohol to the mix, however, and her best heel height drops to a considerably less killer one-inch.

The University of Surrey’s High Heel Theorem, of course, was designed primarily as a bit of fun, although it is based in sound mathematics and geometry and comes up with what appears to be pretty reasonable results. When you crunch your own sets of numbers you should get a decent guide to your optimum heel height. So give it a try. See what you come up with. There’s no £500,000 jackpot prize and free trip to Oslo at the end of it, but it’ll add to the fun of dreaming up your next pair of boots. Oh, and by the way, if your optimum heel height turns out not to be on the menu for the particular style of boot you fancy, send us a note or give us a ring. We are custom bootmakers after all and many of our styles can be made with different heel heights.

Variables. We like to think that Fermat – who was a Frenchman after all – would have approved.

(P.S. If the boots you are dreaming of resembles the elegant thigh boot in the photo above, you read more about it, and order it, here)