Examples of math hoaxes/interesting jokes published on April Fool's day? What are examples of math hoaxes/interesting jokes published on April Fool's day?
For a start P=NP.
Added 2022-04-01 Anything new in 2022?
 A: I enjoyed the hexasphere by
A. V. Akopyan, J. Crowder, H. Edelsbrunner, R. Guseinov
from last year:
http://pub.ist.ac.at/~edels/hexasphere/

In the link, the sphere is animated, so you can look at it from all sides.
A: I saw Doug Ravenel give a talk that began with him announcing a proof of the Riemann Hypothesis. It was beautifully done, I thought. I didn't even realize what date it was.
http://www.math.wayne.edu/~rrb/MTS/archive/1104.html
A: Here is a counterexample to Fermat's Last Theorem, which is correct according to double precision calculations:

A: The following is output from Maple:
A := 34816783:  
B := 29698715047:  
C := 120979604904878607889:  
D := 103195600023374741883001:

isprime (A);   true    
isprime (B);   true    
isprime (C);   true  
isprime (D);   true 

AxD;  3592938812568633315821457205783  
BxC;  3592938812568633315821457205783  
AxD-BxC; 0 

Thus AxD and BxC are two  prime factorizations of 
3592938812568633315821457205783.
This was widely distributed decades ago by a German mathematician. In the current version of Maple versions this no longer works,but a similar hoax with different numbers can probably be found.   
A: A breathless announcement of a weakness in ubiquitous cryptography based on elliptic curves:

this result will require a major increase in parameter for elliptic curve cryptosystems ... we recommend increasing elliptic curve key sizes from 256 bits to 3072 bits

This 2016 claim seems almost plausible until one considers how sphere packing really relates to faster discrete logarithm computation.  It deserves bonus points for using recent actual papers by Viazovska et al. to construct its argument.


*

*Steven Galbraith, ECDLP can be solved in 24-th root time.  Published 1 April 2016 at ellipticnews.wordpress.com.

A: In 2009, it was discovered that the numerical value of $\pi$ has changed over time. This is a truly interdisciplinary work connecting the study of ancient cultures with string theory, cosmology and bicycle tires. Let me quote from the introduction:

Physicists have long speculated that the fundamental
  constants might not, in fact, be constant, but instead
  might vary with time. Dirac was the first to suggest this
  possibility, and time variation of the fundamental constants has been investigated numerous times since then.
  Among the various possibilities, the fine structure constant and the gravitational constant have received the
  greatest attention, but work has also been done, for example, on constants related to the weak and strong interactions, the electron-proton mass ratio, and several others.
It is well-known that only time variation of dimensionless fundamental constants has any physical meaning.
  Here we consider the time variation of a dimensionless
  constant not previously discussed in the literature: $\pi$. It
  is impossible to overstate the significance of this constant.
  Indeed, nearly every paper in astrophysics makes use of
  it. [..]

A: There is also Daniel Schoch's article in which he give way how to obtain number of Gods in our universe using Euler characteristic.
A: The mathematician philosopher Hilary Putnam otherwise not known for lightheadedness revealed on april 1, 1980 that subtle logical phenomena in the context of the Lowenheim-Skolem theorem imply the impossibility of fixing an intended model of anything, including the natural numbers (!) and the reals. This actually got published the same year: 
Putnam, Hilary. Models and reality. J. Symbolic Logic 45 (1980), no. 3, 464-482. 
A: In 1975 Martin Gardner produced a map with 110 regions which he claimed required five colours:

http://mathworld.wolfram.com/Four-ColorTheorem.html
A: https://arxiv.org/abs/2003.13758, "A non-Euclidean story or: how to persist when your geometry doesn’t", by $\mathbb{R}$ami Luisto.

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally $L$-bilipschitz mapping $f:X \to Y$ between uniformly Ahlfors $q$-regular, complete and locally compact path-metric spaces $X$ and $Y$ is an $L$-bilipschitz map when $Y$ is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set; see e.g. [L17]. 

A small selection:

Urist had been recently promoted to the position of the royal mapmaker... Urist's task is far from easy. Ever since their clash with the local necromancer a century ago, the standard three dimensions no longer limit the geometry of the world as a terrible curse shattered the shape of space. The extent of the distortion is so far unknown... Not that the concept of "dimension" makes much easy sense anymore; it took the scholars years to figure out that while the concept of "direction" was no longer present, distances and volumes still exist and the volume of any given ball of radius $r$ seemed to be equal to $r^q$, up to some global multiplicative constants at least. The technical term for this is that the fortress $(X,d,\mu)$ is a uniformly locally Ahlfors $q$-regular metric measure space, i.e. there exists constants $C \geq 1$ and $r_0 > 0$ such that
$$ C^{−1} r^q \leq  \mu (B(x, r)) \leq C r^q $$
for all $x \in X$, $0 < r < r_0$. This fact had immediate applications to the crucial brewing and storing industries, and the scholars were heralded as the saviors of ale and thus of dwarves.

A: Someone (widely believed to be Henri Darmon) circulated the following email on April Fools' Day, 1994:

There has been a really amazing development today on Fermat's Last Theorem.
Noam Elkies has announced a counterexample, so that FLT is not true
after all!  His spoke about this at the Institute today. The solution to
Fermat that he constructs involves an incredibly large prime exponent
(larger that 10^20), but it is constructive. The main idea seems to be
a kind of Heegner point construction, combined with an really ingenious
descent for passing from the modular curves to the Fermat curve.
The really difficult part of the argument seems to be to show that the
field of definition of the solution (which, a priori, is some ring class
field of an imgainary quadratic field) actually descends to Q.
I wasn't able to get all the details, which were quite intricate...



So it seems that the Shimura Taniyama conjecture is not true after
all. The experts  think that it can still be salvaged, by
extending the concept of automorphic representation, and introducing a
notion of ``anomalous curves" that would still give rise to a
``quasi-automorphic representation".

The email reached Gian-Carlo Rota at MIT, who took it at face value and circulated it more widely.  Eventually David Feldman posted it to the Usenet group sci.math.  The thread is here.
A: I think this short note by D. Zeilberger counts, I am not sure though if it was intended for an April 1st joke.
Note: Zeilberger's conjecture is equivalent with the Collatz conjecture.
A: A genuinely natural information measure [arXiv:2103.16662]

The theoretical measuring of information was famously initiated by
Shannon in his mathematical theory of communication, in which he
proposed a now widely used quantity, the entropy, measured in bits.
Yet, in the same paper, Shannon also chose to measure the information
in continuous systems in nats, which differ from bits by the use of
the natural rather than the binary logarithm.      We point out that
there is nothing natural about the choice of logarithm basis, rather
it is arbitrary. We remedy this problematic state of affairs by
proposing a genuinely natural measure of information, which we dub
gnats. We show that gnats have many advantages in information theory,
and propose to adopt the underlying methodology throughout science,
arts and everyday life.

A: This one is my favorite (especially a mixture of anyons and morons with opposite spins):
> From: Enrico Bombieri <eb@IAS.EDU> Tue, 1 Apr 1997 12:35:12 -0500
> Date: Tue, 1 Apr 1997 12:35:12 -0500 To: eb@IAS.EDU,
> zeilberg@euclid.math.temple.edu
> 
> Dear Doron,
> 
> There are fantastic developments to Alain Connes's lecture at IAS last
> Wednesday. Connes gave an account of how to obtain a trace formula
> involving zeroes of L-functions only on the critical line, and the
> hope was that one could obtain also Weil's explicit formula in the
> same context; this would solve the Riemann hypothesis for all
> L-functions at one stroke. Thus there cannot be even a single zeroe(1)
> off the critical line!
> 
> Well, a young physicist at the lecture saw in a flash that one could
> set the whole thing in a combinatorial setting using supersymmetric
> fermionic-bosonic systems (the physics corresponds to a near absolute
> zero ensemble of a mixture of anyons and morons with opposite spins)
> and, using the C-based meta-language MISPAR, after six days of
> uninterrupted work, computed the logdet of the resolvent Laplacian,
> removed the infinities using renormalization, and, lo and behold, he
> got the required positivity of Weil's explicit formula! Wow!
> 
> Regards also from Paula Cohen. Please give this the highest diffusion.
> Best,
> 
> Enrico
> 
> 
> (1) This is the correct spelling, according to vicepresident Dan
> Quayle.
> --------------------------------------------------------------

A: There is an "April Fools" issue of the Math Horizons, published in 2007:
http://www.maa.org/sites/default/files/pdf/horizonsarchive/Horizons-Apr07lores.pdf 
A: [only borderline mathematical]
Today Ali Frolop and Douglas Scott published a paper (http://arxiv.org/abs/1603.09703) in which they found:

... there is a remarkable correspondence between each type of peculiarity in the digits of π and the anomalies in the CMB.


A: https://en.wikipedia.org/wiki/Heegner_number#Almost_integers_and_Ramanujan.27s_constant

This concerns the number $e^{\pi\sqrt{163}}$, and says "In a 1975
  April Fool article in Scientific American magazine,[7] "Mathematical
  Games" columnist Martin Gardner made the (hoax) claim that the number
  was in fact an integer, and that the Indian mathematical genius
  Srinivasa Ramanujan had predicted it—hence its name."

The punchline is tied into complex multiplication, though I don't know the details.
A: Well, there's the April 1, 1997 paper by Doron Zeilberger, The Transcendence of E plus Pi and E times Pi (the following quote is snipped a bit; full text available at the link).

The purpose of this note is to announce that Hermite's[H] celebrated
  result that $e$ is transcendental, combined with an amazing
  (but apparently overlooked) statement of Goodwin[G], imply
  the transcendence of both $e + \pi$ and $e \pi$.
But even more interesting than the above implication is the
  way by which it was arrived, via computer-generated deduction.
We first developed a
  C-based meta-language, MISPAR, that has built-in number-theoretical
  deduction capabilities, that inputs suitably formatted statements
  about numbers (especially targeted to handle transcendence theory),
  and outputs new statements. Then, using 
  ten diligent graduate students,
  many results that appeared in papers on the subject were entered
  in the appropriate format. Then we used a genetic algorithm to
  deduce million of new results, most of them either trivial or
  uninteresting (or both!).
Then we made a long list of open problems.
  Whenever the computer made a new deduction, it was compared against
  the statements in the list, looking for possible matches.
While we sure hoped to obtain new interesting 
  results, even in our wildest
  dreams we did not anticipate such a spectacular deduction.
We are sure that MISPAR would make many more interesting
  deductions in the future. The package itself, and implementation 
  details, will be eventually published at the author's website
  (http://www.math.temple.edu/~zeilberg).
References
[G] E. J. Goodwin, Amer. Math. Monthly, 1 (1894),
  246-247.
[H] C. Hermite, Comptes Rend. Acad. Sci. Paris, 77 (1873),
  18-24, 74-79, 285-293.

The explanation is here; apparently, due to some careful phrasing, the statement of the paper is actually technically correct (or at least so says Zeilberger).
A: https://arxiv.org/abs/1504.00108
A Farewell to Falsifiability
Douglas Scott, Ali Frolop, Ali Narimani, Andrei Frolov
(Submitted on 1 Apr 2015)
Some of the most obviously correct physical theories - namely string theory and the multiverse - make no testable predictions, leading many to question whether we should accept something as scientific even if it makes no testable predictions and hence is not refutable. However, some far-thinking physicists have proposed instead that we should give up on the notion of Falsifiability itself. We endorse this suggestion but think it does not go nearly far enough. We believe that we should also dispense with other outdated ideas, such as Fidelity, Frugality, Factuality and other "F" words. And we quote a lot of famous people to support this view. 
A: One year maybe about twenty years ago an April 1 story circulated on email, giving the news that TeX had been sold to Microsoft (and would therefore no longer be free). It included a pretty convincing firsthand account, complete with embarrassing technical glitches when Bill Gates took the stage at the grand public announcement.
A: More Physicsy than Maths, but there's Don Schneider's "discovery" of a quasar with redshift 4.1 (NB - the largest quasar red-shift known at that time was 3.7), announced at Institute of Advanced Study, Princeton on 1st April. 
The number 4.1 was chosen to be a subtle hint, that this whole presentation was a prank. Few people got it right away, most others didn't and were particularly curious regarding the finer nuances of the discovery, which Schneider did happen to address convincingly on the course of his "report". It was a well-cooked up prank! 
This is chronicled in Ed Regis - ``Who Got Einstein's Office'', Addition-Wesley (1987):

... But Schneider hands out his charts to the audience, and there's no 
  disbelieving the data. Wavelength plotted against energy flux, the graph 
  looks like a distorted view of lower Manhattan, with sharp peaks and 
  valleys, and one very sharp spike, looking like the World Trade Center. 
  That's the quasar, with its record-breaking redshift. 
  The whole room is abuzz. People are talking to each other a mile a 
  minute, and John Bahcall has the devil of a time moderating the question 
  period. They want to know everything: Where's the object located? What's 
  its coordinates? What's the exact time the observations were taken? But 
  Don answers them all, every last one. . . until it's clear that the thing has 
  gone far enough, and he brings it all to a close. There's another speaker to be heard from, poor fellow. Schneider is going to be one tough act to 
  follow. 
Indeed. Some people are even now getting the drift, an inkling of 
  what's actually been going on here. A redshift of four point one, and today is 
  April first. Can this be? . . . Oh, Jesus! It must be. And in fact, yes, it is! It's 
  all . . . an April Fool's joke! Don Schneider has just pulled off the coup of the 
  decade, getting the combined astrophysical brains of Princeton University, 
  Bell Labs, and the Institute for Advanced Study to believe that in the space 
  of a few hours in the morning, at an Institute with absolutely no observing 
  facilities whatsoever, not even so much as a pair of binoculars, he's discovered the world's farthest object smack in the middle of a gravitational lens. 

A: 
The most recent additions to our Seeley G. Mudd Manuscript Library feature contributions from the estate of Oliver Wendell
Holmes, Jr., which include letters and legal manuscripts of Pierre de Fermat (a lawyer by vocation).  It is in the density of Fermat's
litigation records during the period 1660-1662 that his lost mathematical proof is finally to be found.

It  turns  out  that  Fermat's  proof  employs  what  is  now  known  as  the  Mason-Stothers  theorem  (proved  independently  by
Stothers [2] and Mason [3] in the late 20th century).  In the discovered manuscript, Fermat himself gave an elementary proof of the
Mason-Stothers theorem, but his approach resembles that presented in
An  alternate  proof  of  Mason's  theorem
by Snyder [4].  For
this reason we here omit Fermat's proof of the Mason-Stothers theorem, and only reproduce the subsequent part of his proof of his
last theorem, paraphrased in modern terminology.
https://web.archive.org/web/20150403002852/http://www.princeton.edu/~aloo/fermat
A: This list is missing one of the greatest mathematics April Fools, the Mandelbrot Monk article by Girvan from 1999. It is beautifully done and famous enough to have its own Wikipedia article.
A: This is perhaps only borderline mathematical, but the ChessBase website has historically made a fine art of the April Fool's joke, and arguably its most successful prank was also the most mathematical: A claim that the King's Gambit had been solved.  They were careful not to claim that the opening had been mathematically solved, but that a generous cutoff for the score function had been set (i.e., if the computer thought that one side was "far enough ahead" then the assumption was made that that side really did have a win) and that the game tree was exhausted under this assumption.  It was clever enough that even after knowing that it might have been an April Fool's joke, I was still uncertain for a while.
