Apple, the iPhone 7, and assuming Taniyama-Shimura

There’s an Apple event next week, but anyone who follows tech news online knows that already. They have also read what Apple is announcing, even though Apple has confirmed absolutely nothing about the event. And the great thing about the tech reporting industry is that everyone is cool with that.

I find it curious that this attitude follows one of the great ‘I hope this is right’ moments of 20th century mathematics. In 1955, a presentation by Yutaka Taniyama and Goro Shimura proposed that every elliptic curve had a modular form. Every mathematician was confident that the Taniyama-Shimura conjecture was correct, even though nobody could prove it. Acres of mathematical theory were built on a foundation that started with the words ‘Assuming Taniyama-Shimura…’, and every accepted that they were trusting a hunch.

For the record, it was eventually proved and is now known as the Modularity theorem.

If everyone believes something, then (a) of course it is true and (b) if it turns out to be wrong then everyone is wrong and nobody suffers any disadvantage. Taniyama-Shimura was a get out of jail card to speculate on something that you don’t have confirmation of is probably true and you want to go ahead and do it anyway.

The same issue crops up when I write about the smartphone industry in general, and Apple in particular. We all know what’s coming, it’s not confirmed, and if we’re wrong, we’re all wrong together and it doesn’t matter.

And that, ladies and gentlemen, is why my iPhone 7 coverage over the last few months is littered with phrase ‘assuming Taniyama-Shimura’.

Originally published at www.ewanspence.co.uk on September 2, 2016.