Friday 13 April 2012

My First Published Maths Article - Maths V Science

The secondary school I attended was a specialist science college, and so we had an in-house science magazine that came out every term. When I was in year 13, I submitted an article for it. This was a little bit weird because I wasn't taking any science A-levels, so I wasn't part of the science "crew". What was weirder was that the article was anti-science. It is about how maths is so much better than science.

It was the first time I'd written about maths and I loved it. I've always loved writing. I've kept a journal since I was 12 (when I first read the Princess Diaries) and I always did well in creative writing in English. Aged 17, my passion for maths was really starting to show itself. I'd been reading books by Simon Singh and Marcus du Sautoy and Ian Stewart on the bus to school and I was spending roughly 30 hours a week studying maths. Writing this piece made me realise that this was what I wanted to do: try to get people excited about maths through words. Which is what teaching is about, and also what this blog is about.

Anyway, here is the article.


A not-at-all-biased look at the strengths and weaknesses of two essential subjects*

Round One: Proof

It is an indisputable fact that mathematical proof is far more powerful and more rigorous than scientific “proof” (please note the use of ironic quote marks). This is because when a mathematician proves something to be true, we know that it will always be true and that there is not even a small, slight, snowball-in-hell chance that it will ever be false. Mathematical proof’s spotty younger brother, scientific proof, relies on evidence backing up a hypothesis. So if an enormous amount of evidence supports their claim, a scientist will say they have proved that it is right. However, consider this: we know that if you flip a coin 100 times you would expect 50 heads and 50 tails, but we know that it is possible to get all heads and no tails, or vice versa. Now if a scientist flipped a coin fifty million times and got all heads, they might well conclude that this coin will always produce heads. But how do they know that on the 50 000 001st time they flip it it won’t be a tails?
Maths: 1 Science: 0

Round Two: Problem Solving

Amongst other things, mathematicians and scientists have to solve many problems. The main difference between the problems that mathematicians solve and those that scientists solve is that, most of the time, scientific problems are of great importance, whereas maths problems are usually as useless and unnecessary as sleeping pills in a geography lesson. One of the greatest mathematicians ever, GH Hardy once said “no discovery of mine has ever made or is likely to make…the least difference to the amenity of the world”. (in actual fact, Hardy’s discoveries have been of great use, but lots of the maths that number theorists do is really comparable to thermal-underpants-in-hell in terms of usefulness). Despite this, it is clear that mathematicians are better at problem solving than scientists are. Consider the following example: you have a normal 8x8 chessboard, and you cut the top left and bottom right corner squares off. What you are left with looks like this:

So there are now 62 squares remaining. You have been given 31 dominoes, the same size as a pair of squares. Can you put all 31 dominoes on the board so that every square is covered? A scientist would solve this problem by experimenting, by trying out different arrangements. (Have a go yourself- you can make a board and dominoes out of paper. It’s a fun alternative to listening to Mr Clargo in your maths lesson). After trying out a few different arrangements with no success, a scientist would conclude that it can’t be done. However, the scientist would never be sure whether they are right or not (unless they tried every one of the millions of arrangements-which would be a very pitiful existance). Now, a mathematician would tackle this problem logically : the corners that were cut off were both black. So there are now 30 black squares and 32 white. Each domino covers two adjacent (neighbouring) squares. Adjacent squares are always the opposite colour. That means that for every white square that is covered, a black square is also covered. So to cover all 32 white squares, 32 dominoes would be needed, and we only have 31. therefore, it can’t be done. Pure genius! The mathematical way of solving problems is often quicker than the scientific way, and you can always be sure that you are right.
Maths : 2 Science: 0

Round Three: Fame and Fortune

Most of you will probably find it hard to name a famous mathematician or scientist who is alive today (and no, the guys from Braniac do not count). However, if you look way back in time, the only people from that period who are remembered are the mathematicians. So whereas most of you don’t know who Andrew Wiles** is, in a thousand years time, he will be remembered and Jade Goody will not. Again I am going to refer to the great GH Hardy: “Immortality may be a silly word, but probably a mathematician has the best chance of achieving whatever it may mean”. To be fair, a few scientists will also be remembered. I suppose. Now as for fortune, you should know that there is a lot of money up for grabs for talented mathematicians (or someone with a calculator and way too much time on their hands). If you find a prime number with loads and loads of digits, the FBI will give you $1 million. However this is easier said than done (I have wasted many a Sunday afternoon number crunching to no avail).
Maths: 3 Science: 0

There we have it; maths wins hands down. So if you think maths is boring, hard, or pointless, think again!

*please note: maths is more essential than science.
 ** English mathematician famous for solving a 358 year old problem: Fermat’s Last Theorem

By the Way...

Several things in this article were edited without my permission for the magazine. The above is the unedited version. The bit about Mr Clargo was edited out. Also, the asterisked bit "*please note: maths is more essential than science" was changeed to: "*please note: maths is more essential than science, in my opinion" which completely ruins the joke. It was obviously written in a tongue-in-cheek way, I really don't know why they had to change it and make me look like a dork.

What do you think, not bad for a 17 year old?

Emma x x x 

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