Conference rusure::math

589.0. "Recent net.math posting about Grurmstipth" by CLT::GILBERT (eager like a child) Sat Sep 27 1986 17:26

Newsgroups: net.math
Path: decwrl!amdcad!amd!intelca!qantel!lll-lcc!lll-crg!seismo!columbia!heathcliff.columbia.edu!zdenek
Subject: Re: Grurmstipth
Posted: 25 Sep 86 15:34:09 GMT
Organization: Columbia University CS Department
 
In article <350@aw.sei.cmu.edu.sei.cmu.edu> firth@sei.cmu.edu (Robert Firth) writes:
>Grurmstipth is also famous for Grurmstipth's Number (G),
>defined as the smallest transcendental number with no
>mathematical symbol.  His 1835 paper gave this number to
>150 decimal places, of which the last 144 are wrong.
 
Looks like you have read one of the reviews of the Grurmstipth's paper
instead of reading the original. Some of the reviews were later shown to be
incorrect and biased against Grurmstipth. There was, indeed some speculation
about correctness of Grurmstipth's number shortly after the paper was
published. But the major disagreement among mathematicians was about the
actual method Grurmstipth used to generate the solution of his equation,
later known as Grurmstipth's number. Nobody seemed to be able to understand
the relation between the Grurmstipth's equation
 
	G - sin(-i*ln(i*G + sqrt(1 - G^2))) = 0
 
and the series he used to enumerate the digits
 
	G = 1/5! + 1/13! + 1/14! + 1/35! + 1/161! + 1/180! + ........
 
The problem was finally resolved in 1841 when Karl Weierstrass published his
famous paper "Power Series in Complex Analysis". Using a brilliant proof
Weierstrass showed that ALL the digits in the original Grurmstipth's paper
were correct!
 
zdenek
 
Zdenek Radouch
457 Computer Science Department
Columbia University
New York, NY  10027
 
ARPANET (or Internet):	zdenek@CS.COLUMBIA.EDU
USENET:			...!seismo!columbia!cs!zdenek

Re: .0

I don't understand the definition of Grurmstipth's Number.  Can someone
elaborate?  It seems to me that the definition chases its own tail.  Once
you find Grurmstipth's Number it has a mathematical symbol, "G", so the
definition no longer holds.

- Don

This Grurmstipth thing seems to be developing into a bit of a running gag. It's
not supposed to make sense.  It started when Colonel Sicherman of SUNY at
Buffalo crediting Grurmstipth with proving the equation x^n - y^n = z^n had no
roots for n>2 in 1833, as a reply to a discussion on Fermat's Last Theorem.  A
few seconds of thought would realize that adding y^n to both sides gives it as
a proof to Fermat's Last Theorem!  You have to know the guy to understand this
(I do), Col. Sicherman has a very dry sense of humor. 

Grurmstipth also proved that it's impossible to color a map in 5 colors with
only 4 crayons in 1845.

-Mike

    Re .2:
    
    A recent net.math posting credits Lewis Caroll with a report of
    Grurmstipth in 1885. 
    
    
    				-- edp