Why Physics is Better than Maths (a More-Than-Slightly-Biased View from a Physics Graduate)

Image courtesy of https://xkcd.com/435/

I'm writing this post for my Mother who for years has pondered this question: "You were so good at maths at school, why didn't you become an accountant?"

There is nothing wrong with accountants. Let's get that statement out of the way now. Without my wonderful accountant my books would balance like a one legged kangaroo on a wine cruise.

But a Maths degree was not for me. A career in accountancy was not for me (and I'd like to point out here - as much for my Mum's benefit as anyone else's - that accountancy is not the only career you can get out of a Maths degree).

I always struggled to explain why Physics holds a place in my heart that Mathematics never did.

Then, I started reading a wonderful book "Fermat's Last Theorem" by Simon Singh, which is a fascinating account of an equation whose proof stumped mathematicians for the best part of 300 years. (I've put a few more details on Fermat's Last Theorem at the end of this post.)

It tells the tale of finding a proof to an equation that originates from Pythagoras' Theorem. You know, that much-taught equation you probably came across at school: the sum of the square of the longest side of a right-angled triangle equals the square of the sum of the other two sides.

With a little mathematical jiggery-pokery it's easy to prove why this equation is true for every right-angled triangle you could throw at it.

This is known as a mathematical proof. It is true everywhere and for all eternity.

​Now, a mathematical proof is a thing of beauty. To unequivocally prove a concept and sit back in the knowledge that no one will ever disprove your work is something that eludes physicists. I think that's what makes physics so much fun - and why I chose it over mathematics.

Let me explain why with a tale of neutrinos.

The story of science's renegade particle

A neutrino is a tiny particle that's caused a massive amount of upset within the scientific community. Don't blame the neutrino though - it's actually our tiny human minds that are at fault.

First, the neutrino has a very small mass (electrons are about 500,000 times more massive). But the neutrino shouldn't have any mass at all.

Why? Because this mass doesn't fit with our best explanation of all the particles in the universe: the Standard Model. (There are actually a couple of other problems with the Standard Model - it doesn't include gravity or dark matter, for example. But I digress.)

Second, scientists found evidence that neutrinos may travel faster than light.

Why would this matter? Because if something were to travel faster than light it would pretty much break everything we know about physics.

​This excellent post describes the implications and states: "When you assume that it's possible to travel faster than the speed of light, you're taking the laws of physics and punching them in the stomach and throwing them down the stairs."

​Yikes.

Naturally, this result caused quite a stir in the science community. Particle physicist and TV presenter Professor Brian Cox claimed it would be "most profound discovery in physics for more than a century." 

Fellow physicist and TV presenter Professor Jim Al-Khalili was a little more bullish in his response and claimed that if the findings were proved to be correct, "I will eat my boxer shorts on live TV".

In the end, Jim didn't have to ingest any underwear. The findings were eventually debunked by a range of other experiments that attempted to verify the results and the cause of the anomalous results was discovered to be a loose fibre optic wire.

But what a shame - and not just because two of the scientific team's elected leaders lost a vote of no confidence and tendered their resignations (click here for a brilliant piece where one of the leaders, Antonio Ereditato, is interviewed about the case).

It's a shame because the result wasn't verified.

Can you imagine if it had been? If we had unwittingly proven that matter could travel faster than light?

What a wonderful world physics is where we don't just disregard a result because it doesn't fit. Teams of physicists swooped in and immediately tried to recreate the result. They tested it until there could be no doubt that there was an anomaly.

It is this lack of perfection and need to endlessly test and question everything that makes physics so very appealing to me.

​Maths is too tidy.

A non-mathematical proof that your Mother is always right

As I reach the end of the Singh's beautifully written tale of Fermat's Last Theorem, I suddenly realise that I'm wrong about maths.

You see, mathematical proofs are a thing of perfection. But they are also the pursuit of a few dedicated souls who won't rest until that perfection is found.

​​Andrew Wiles, who eventually cracked the Fermat's Last Theorem nut, announced his findings in June 1993. The proof took decades to devise - and in August 1993 it was found to contain an error.

After a breakthrough in September 1994, Wiles published the corrected proof in 1995.

So, I am wrong. Maths is not tidy. It's just as messy and open to criticism, verification and debate as physics.

​The ability of scientists of any discipline to work relentlessly, debate, discuss and open their minds to the seemingly impossible is what makes every discipline so wonderful.

Maybe it's finally time to apply for a degree in mathematics.

Appendix: What is Fermat's Last Theorem?

If you take Pythagoras' Theorem and replace the square by any number greater than two, then you will never get a solution. In other words:

It's a devilishly simple equation that anyone can understand - but finding a proof for this equation taunted mathematicians for centuries.

What didn't help was that French "amateur" mathematician Pierre de Fermat tantalisingly claimed to have found the mathematical proof to this equation but never wrote it down - an irritating quirk which he was notorious for.