Silver sea.    © PJ Croft 2017

The mystery of the passport is solved. I was nearly going to go back to Clarkson PO today to try again to find my new passport, but put the trip off. Then about 3pm there was a knock at the door and the postie was there with a registered letter. I could tell straight away that it was my passport.

Funny, I could have sworn I said no to registered post because the woman at the post office told me if I wasn’t home, I’d have to go in to the city to retrieve it. Oh well, all’s well that ends well.

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Trigg 2011   © PJ Croft 2017

I wrote in the last post about the book I bought that had that odd bird-shaped illustration. The book is Fermat’s Enigma, one of a series on maths put out by National Geographic. They are being sold for $14.99 in newsagents, stuck onto a large card. Unusual. They are cheaply printed, with no colour, but are an attempt to reach younger readers, I assume. I’ve bought two so far, the other one being on higher dimensions – i.e. above the three we can visualise.

Actually, I’ve never had trouble visualising the fourth dimension, time. I can see in my mind the three, x, y and z simply moving across the visual field with the passage of time. But note: although the three x, y and z axes can be positive or negative, the time axis can only ever be positive and increasing. Otherwise we would be going back in time. Why is it so?

Anyway, Fermat’s Enigma is about a seemingly simple proof – that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.

That is, x² + y² = z²  works (this is Pythagoras’s theorem, 3 squared plus 4 squared equals five squared), but no more, not for 3, 4, or 5 or any other number. How odd!

I find this amazing. It had seemed to be true since ancient times but no-one could prove it. Pierre de Fermat 1607-1665, a French nobleman, claimed in 1637 to have found a proof, but it was lost, and in the following centuries no-one else could come up with a proof.

Until 1995, when a British mathematician at Cambridge, Andrew Wiles, came up with a proof, and won a Nobel Prize for his effort. He worked on his proof for several years and when he thought he’d done it, an error was discovered. He nearly gave up at that point, but kept on it and finally found the definitive proof.

But how odd. x² + y² = z² works, but no higher powers work. Why?