Love Maths

Maths… the only place where people buy 64 watermelons and no one wonders why!

However comical, there is truth in this heading… examiners and teachers can be guilty of shoe-horning real life into the Maths problems we set our students. Combining this with the historically heavy emphasis on procedure means that Maths gets a pretty bad rep. I will go about dispelling this over the coming article.

Maths is lovable

I have always loved Maths. This most probably stems from my strength in the subject from an early age – there is no denying the correlation between ability and enjoyment of something. Credit must also go to my teacher Mr Hunter who, like all great teachers (and football managers for that matter), struck the perfect balance between warmth and authority. But objectively, I feel there are four reasons that elevate the subject proudly above the others.?

1.????It is astoundingly beautiful, from Euler’s jaw-dropping identity, to Escher’s tessellating art, the occurrence of Fibonacci’s sequence throughout nature and of course its link to the Golden Ratio – the very ratio that holds the key to aesthetic beauty in humans, art and architecture… more on that later.

2.????It is the subject that offers the most spectacularly satisfying penny-drop moments, from the exclamations of “ahh” as links are made between concepts, to the shrieks of “yes” that accompany a tick.

3.????The subject transcends cultural boundaries and its importance is universally recognised. The only other two things I can think of that seem to speak so universally are football and Mr Bean.

4.????The development of the subject through the ages is truly fascinating, which leads us nicely into my favourite mathematicians of all time.

My top 10 mathematicians, in no particular order

1.????Gauss, for his childhood solution to the problem 1+2+3…+99+100 = ? Rumour has it, Gauss’ Maths teacher set him this puzzle at the tender age of 9 to shut him up for a bit. Within 60 seconds, Gauss had paired up the 100 numbers into 50 pairs of 101, creating a total of 5050. Remarkable!

2.????Newton, for being humble in attributing his success to Copernicus, Brahe, Galileo, Kepler, Descartes and Archimedes with the famous quote “if I have seen further, it is by standing on the shoulders of giants”. His contributions to the subject are of course hugely significant, but it is his humility that endears him to me. Oasis borrowed the quote for the title of their third album (misspelled I might add), although Liam and Noel’s giants were presumably a little different, perhaps Lennon, Jagger, Rotten, Curtis, Marr and Brown – who are indeed all giants in their own right.

?3.????Euler, for helping me find my wife. This needs some explaining but in short it relates to the optimal stopping theory. Euler advises that you should date 1/e (=37%) of the sample, then pick the first one who betters those first 37%. I wanted to find my wife between the ages of 20 and 40. 37% of 20 years is roughly 7 years. I met my wife at 27; she bettered the girls from the previous 7 years; so, to quote Beyoncé, I put a ring on it.

?4.????Turing, for defeating fascism. Turing’s bombe machine (affectionately referred to as Christopher in the blockbuster hit The Imitation Game) cracked Hitler’s Enigma code, shortening the war in Europe by more than two years, saving over 14 million lives… talk about a legacy! Subsequently, this national hero was treated quite atrociously: he was tried for acts of homosexuality at the courthouse of my hometown of Knutsford. He was convicted, underwent chemical castration and was later found dead from cyanide poisoning, a half-eaten apple by his bedside. The story goes, Apple’s logo pays homage to Turing’s significant contribution to the field of modern computing.

5.????Wald, for his astute and quite genius observation during World War II to “put the armour where the bullet holes aren’t”. This is in reference to armour reinforcement of American planes: too little and the planes are vulnerable to Nazi bullets; too much and manoeuvrability is compromised. There is an optimal amount of armour, and positioning is key. Wald’s starting point was that bullets scatter a plane randomly, but bullet holes on returning aircraft were not scattered randomly. Wald’s logic, which contradicted previous practice, was that if the plane comes back with bullet holes, it clearly flies fine being hit in these places. However, areas that time and again contain no bullet holes must be the vulnerable areas, as when they are hit, the plane goes down. Hence, his recommendation: “don’t put the armour where the bullet holes are, put the armour where the bullet holes aren’t “.

6.????Fibonacci, for creating a sequence that links so mesmerizingly to nature (examples include flower petals, the family tree of bees, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern, the arrangement of a pine cone and spirals in a sunflower, amongst many others) as well as its link to music (e.g. piano keys) and the Golden Ratio. Studies by psychologists such as Fechner in 1876 have found that this ratio, formed by dividing consecutive numbers of Fibonacci’s sequence, plays a significant role in human perception of beauty. Indeed, Steve Jobs attributes the success of the iPod to this ratio: its dimensions were closer to the ratio than any of its competitors, as seen below.

7.????Pascal, for his triangle and its uses within binomial distribution. For example, if you have four children, the probability of outcome relates to the 5th row of the triangle: i.e. the chance of four boys is 1/16, the chance of three boys and one girl is 4/16, the chance of two boys and two girls is 6/16, the chance of one boy and three girls is 4/16 and the chance of four girls is 1/16.

8.????Pythagoras, for his work with triangles, even if he did steal the theorem from the Egyptians! Oh, and for his contribution to music (octaves, scales and harmonies), for discovering the first two perfect numbers, his distaste for irrational numbers and for being a bit of a maverick – his placement of women on equal terms with men is particularly commendable, considering this was so unusual in Ancient Greece.

9.????Borel, for his infinite monkey theorem. He pithily explained infinity using the concept, “an infinite number of monkeys, hitting keys on a typewriter for an infinite amount of time, will type the complete works of Shakespeare”.

10.?Wiles, for proving Fermat’s Last Theorem. In 1637 Pierre de Fermat proposed a conjecture in the margin of a copy of Arithmetica, adding that he had a proof that was too large to fit (in all likelihood, he had no proof – he was merely toying with us). This note was only discovered after his death – a wily move indeed, ensuring one’s name lives on – I must give this a try. Its magic is in its simplicity, easily understood by any year 9 student studying Pythagoras’ Theorem. Essentially, a2+b2=c2 can have whole number solutions such as 3,4,5 or 5,12,13. But when the indices are changed to a number bigger than 2 (e.g. a3+b3=c3), Fermat proposed that there are no whole number solutions. It did however appear that Homer found a solution in an episode of the Simpsons, but while at first glance it looked legitimate, it was in fact what we call a near miss. In contrast to Homer, Wiles solved this 300-year-old problem, proving definitively why there can be no whole number solutions – a marvellous feat!

I must concede I have left some corkers off my list, so a worthy shout out to Galton (Wisdom of Crowds), Hardy & Ramanujan (Taxicab Number), Van Berkel (Munchausen numbers), Kasner (Googol), Lucas (Towers of Hanoi) and Euclid (for his ground-breaking book elements. In fact, one Eton headmaster of the mid-nineteenth century divided the books of the world into three classes… class I: The Bible; class II: Euclid; class III: all the rest. Praise indeed, and it must be said that Euclid’s proof by contradiction that there are an infinite number of primes in book VIII is nothing short of glorious).

?Maths is important

Its importance is extensive, and therefore requires its own article (to follow).

Maths… the only subject that counts ;-)

Whilst I may not have convinced you that Maths is ‘the best’, I hope I’ve shown you that “Mathematics, rightly viewed, possesses not only truth, but supreme beauty” (Bertrand Russell). Or, put a little stronger, “La matematica è l'alfabeto nel quale Dio ha scritto l’universo” (Galileo Galilei).

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