There is the famous hoax of Martin Gardner in the mathematical games of April 1975 , april fool, when he claimed that exp(Pi*sqrt(163)) = 262537412640744 exactly. Simon Plouffe Le dim. 2 juin 2019 à 06:41, Mike Stay <metaweta@gmail.com> a écrit :
The first two feature in the 1989 SciAm April fool's edition: https://www.jstor.org/stable/24987222?seq=1
On Sat, Jun 1, 2019 at 7:08 PM Dan Asimov <dasimov@earthlink.net> wrote:
1. There is a lovely dissection proof of the fact that a rectangle of area 65 can be dissected into one of area 64. Hence 1 = 0.
2. Also, Banach-Tarski showed that a unit ball B = {p in R^3 | ||p|| <= 1} can be dissected into 5 pieces that can be reassembled to comprise a partition of *two* unit balls. A likely story!
Hence 1 = 0.
3. Furthermore, the vector field on the complex plane given by
V(z) = i(z^3 - z)
is holomorphic, so the fact that the flow {phi_t} of V satisfies that the times t for which
phi_t(z) = z
for all z form a discrete subgroup G_z of the reals.
Also note that phi_t(z) is jointly holomorphic in both z and t.
But it's not the same subgroup for all z (!) Which clearly contradicts the principle of permanence for holomorphic functions.=
—Dan
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