Saturday mornings are perhaps not the times at which we associate that the brain is most awake. It is more time for slumber, than the gathering of thoughts. Unable to come up with anything remotely useful to say on an early Saturday morning, I tweeted the following:

*trying to think of something truly inspirational to say on a Saturday morning, I think I have it, but it's too long to fit in 140 chars*

It is perhaps somewhat facetious to compare myself to the great French mathematician (in retrospect, that sentence sounds more accurate without the word "somewhat"). However, the tweet alluded to something Fermat wrote in the 17th century and well done, to @ewankirk for recognising the Fermat reference in my tweet too. To quote that fountain of all knowledge, Wikipedia, with some help from Google, Fermat claimed that he discovered a proof to the following, Fermat's Last Theorem, which states that:

*no three positive integers a, b, and c satisfy the equation a*

^{n}+ b^{n}= c^{n}for any integer value of n greater than two. The cases n = 1 and n = 2 were known to have infinitely many solutions.
However, Fermat wrote that the proof was too small to fit in the margin of the notebook he was working on. Alas, he never thought to buy another notepad to write it down... either that, or he didn't really have a proof. The theorem remained unsolved till the mid-1990s, when Andrew Wiles solved it. He was subsequently knighted recognising this great achievement. His proof amounted to around 150 pages. So Fermat was right in some respects, the proof was indeed far too big to fit into his notepad's margin.

Mathematics is often about the proof, not so much purely the statement of fact. There are many ideas which are very easy to understand in mathematics (and might seem intuitively true), but their proof is so much more difficult to articulate. Indeed, if we consider Fermat's Last Theorem, it isn't that difficult to understand what it says.

Unlike in mathematics, in markets, there is very little that we can actually "prove". We can have theories about how markets behave, we can use historical data to illustrate them. I can use statistics to show a trading strategy would have made money. We can use our intuition to judge that the conditions necessary for the strategy to make money, are likely to be there in the future (or indeed that they won't be there). But can I "prove" that you will definitely make money in the future. No.

In a sense, trading and in particular, quantitative trading (or least successful variants of it) requires a modicum of skills from many different areas. The first one is common sense. Sorry, no amount of mathematics can erase the necessity for common sense when it comes to trading.

Instead mathematics and statistics, needs common sense to guide its correct usage when trading. You may have found the best ever strategy in the world (ever, ever, really!), but a bit of common sense, might tell you that it's impossible to execute in practice or that transaction costs you've assumed are totally unreasonable. As well as common sense and a good knowledge of statistics, an ability to code is important for systmatic trading, after all, the more data you have to play with, the less likely it is that Excel will be sufficient to crunch it. Oh, and a bit of luck can help too! We might live by our median result (which we hope is above zero), but a good start is always a bit of a luck.

I can't prove any of this obviously. But if we could prove everything easily, wouldn't everything suddenly become very boring? With that, I wish you a very merry Christmas!

**Like my writing? Have a look at my book Trading Thalesians - What the ancient world can teach us about trading today is on Palgrave Macmillan. You can order the book on Amazon. Drop me a message if you're interested in me writing something for you or creating a systematic trading strategy for you! Please also come to our regular finance talks in London, New York, Budapest, Prague, Frankfurt, Zurich & San Francisco - join our Meetup.com group for more details here (Thalesians calendar below)**

20 Jan - London - Nick Firoozye - Managing Uncertainty, Mitigating Risk

29 Jan - Budapest - Robin Hanson - The Age of Em

08 Feb - London - Saeed Amen/Delaney Granizo-Mackenzie - CTA/Pairs trading (joint Thalesians/Quantopian event)

29 Jan - Budapest - Robin Hanson - The Age of Em

08 Feb - London - Saeed Amen/Delaney Granizo-Mackenzie - CTA/Pairs trading (joint Thalesians/Quantopian event)

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