Thursday, April 2, 2015

More Mathematical Cranks

(Crossposted from my Facebook page)

I am now 200 pages into Mathematical Cranks. Neat book. I have a few more comments:

(1) So far, only one woman has been mentioned. The author doesn't use the people's real names, but she was a teacher with a PhD in Mathematics who tried and failed to give a short, simple proof of Fermat's Last Theorem.

(2) Speaking of Fermat's Last Theorem: One interesting fact is that this book was published in 1992, before Andrew Wiles came up with an actual proof.

Other fun fact: Fermat's Last Theorem was, until 1993, neither a theorem nor Fermat's last anything. He wrote it early on in his career, famously saying that he had a marvelous proof that wouldn't fit in the margins of the book he was writing in. But there's good reason to believe that, whatever Fermat's proof was, it was wrong and Fermat himself knew it, because apparently there is evidence that he worked on proving the theorem for n = 4 and 5 later in life life (which would be redundant if he already had a proof for the general case).

(3) You might have heard about the Indiana Pi Bill, and how legislators allegedly tried to legally change the value of Pi. This is a misrepresentation of the story. It wasn't a story about a scientifically ignorant government trying to change reality to their liking: it was the story of one crazy guy who claimed that he had found a set of exact algebraic solutions for Pi (I think this was known to be impossible even at the time) and convinced his representative (no doubt desperate for votes) to bring a bill to the senate proposing that these solutions be made freely available to public schools.

Although, it is still pretty absurd that the bill managed to get to the senate before the other senators laughed it out of existence. It's come up again and again in the book: apparently, it's surprisingly easy to get your bad ideas noticed if you can find a politician desperate enough for your votes.

(4) Most of the stories of these cranks start with, "Person X wrote up their theory, and sent it to over 100 universities across the continent." Apparently, if you just mail your dumb theory to a random university's math department, you'll sometimes get a response.

Don't believe anyone who tells you that scientists are in an elitist conspiracy to keep out people with unconventional ideas: the responses from the mathematicians who deal with these cranks are surprisingly polite for the most part, often more polite than warranted (the cranks themselves usually take criticism personally and immediately start hurling insults at anyone who points out their errors). One guy, who claimed to have come up with a short proof of the Four Colour Theorem, got offended when a professional mathematician said that there would be room for other mathematicians to "build on" what he had done -- as if his work wasn't perfect already!

(5) One more thing: A lot of people have tried to "disprove" non-Euclidean geometry, claiming that Euclid was divinely inspired and anyone who dares question his wisdom is engaging in blasphemy.

But then they try to show that non-Euclidean geometry is invalid by trying to derive Euclid's fifth postulate from the first four. (This is known to be impossible. Euclidean Geometry starts with 5 postulates, and non-Euclidean geometry looks at what happens when you change the fifth postulate.) But if they think Euclid was so perfect, why would they think that Euclid was so stupid as to add a redundant postulate to his system if he only needed the first four?
 
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It Seemed Funny at the Time by Ben Buckley is licensed under a Creative Commons Attribution-Noncommercial 2.5 Canada License.