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\bf
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{
Amanda Folsom and Ken Ono's Error Could Have (and Should Have!) 
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{
been Discovered by Their Computers (in Less than Three Seconds!)
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\centerline{ {\it Shalosh B. EKHAD }\footnote{$^1$}
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c/o {\eighttt zeilberg  at math dot rutgers dot edu}.
\hfill \break
Exclusively published in: {\eighttt http://www.math.rutgers.edu/\~{}zeilberg/pj.html} .
Nov. 22, 2011.
}
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Experimental Mathematics giants, David Bailey and
Jonathan Borwein, describe ([BB]) how  the use of computers is revolutionizing
doing mathematics. The
most {\it obvious} and {\it trivial} use, that {\it even} ``pure'' mathematicians
(like Amanda Folsom and Ken Ono) should be able to do,  is the {\it empirical} checking of formulas and statements.
Unfortunately, they don't. 
Frank Garvan (see [AGL]) discovered that the statement of Theorem 1.2 in
[FO] is false as stated. You can't trust humans, they are such screw-ups! This prompted me to find out for myself.

Once the short Maple code (written in a few minutes by D. Zeilberger):

{\eighttt http://www.math.rutgers.edu/\~{}zeilberg/tokhniot/KenAmandaError} ,

is downloaded and read (or copied-and-pasted) into a  Maple session, typing:

{\tt CheckKenAmanda(507);} \quad ,

returns (in less than three seconds!): 

\quad {\tt false} \quad .

(Note that $24 \cdot 507-1=23\cdot(23)^2$, but $spt(507)$ is even).

The fascinating paper [AGL] contains a corrected statement of this theorm, and {\it much nicer} proofs
({\bf not} using Maass forms, but rather elegant combinatorial arguments). It also describes
how to fix the original proof of [F0].

{\bf References}

[AGL]  G.E. Andrews, F. G. Garvan, and J. Liang, {\it Self-conjugate vector partitions and the parity of
the spt-function},
{\eighttt http://www.math.ufl.edu/\~{}fgarvan/papers/spt-parity.pdf} \quad .

[BB] David H. Bailey and Jonathan M. Borwein, {\it Exploratory Experimentation and Computation},
Notices of the Amer. Math. Soc. {\bf 58} (2011), 1410-1419.

[FO] A. Folsom and K. Ono, {\it The spt-function of Andrews}, Proc. Natl. Acad. Sci. USA {\bf 105} (2008), 20152-20156.






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