(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
(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
(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.
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
(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?