Date: Mar 14, 2002 1:24 PM
Author: Gottfried Helms
Subject: [JSH/HSJ] Another document of P.d.Fermat discovered

Hi -

just discovered a document which is obviously left from P. de Fermat.

The size of the paper was astonishing; in the cryptic words of the

header line he recurred to his sproblem of too small margins in

contemporary scientific books.

On this note he left us a formula, which ontains y and x in implicite

form. He annotated this formula as one of his greatest proceedings to

match human mind and maths. He seems to have stated that even after

his "last theorem"; but he didn't retrieve a theorem of this equivalence,

so his second great contribution to maths would not be devaluated.

I was not able to write it down in explicite form for y; but

possibly someone with a CAS is able to do that.

In the meantime I searched with brute force for solutions

in x and y for the term to be zero. The plotted result was an astonishing

example of math-of-objects (an early OOM?).

0= 8100*x^14

+81*x^12*y^4-972*x^12*y^3+20574*x^12*y^2-73548*x^12*y-212139*x^12

+162*x^10*y^6-2592*x^10*y^5+680662*x^10*y^4+2508656*x^10*y^3

+3849558*x^10*y^2+3755408*x^10*y+1436778*x^10

+6643*x^8*y^8-54124*x^8*y^7+1405820*x^8*y^6+183004*x^8*y^5

-31256044*x^8*y^4-96872636*x^8*y^3-130469224*x^8*y^2-64062468*x^8*y-26572131*x^8

+13124*x^6*y^10-157504*x^6*y^9+1228888*x^6*y^8-2627232*x^6*y^7

-33434620*x^6*y^6+14917728*x^6*y^5+352452172*x^6*y^4

+767822016*x^6*y^3+742831896*x^6*y^2+346005760*x^6*y+63102240*x^6

+6643*x^4*y^12-105972*x^4*y^11+715982*x^4*y^10-2380932*x^4*y^9

-13653099*x^4*y^8+69892632*x^4*y^7-83172764*x^4*y^6-315776456*x^4*y^5

+455109326*x^4*y^4+421270032*x^4*y^3-1662578068*x^4*y^2

-2265900800*x^4*y-768080880*x^4

+162*x^2*y^14-2592*x^2*y^13+23814*x^2*y^12-104976*x^2*y^11-184682*x^2*y^10

+1579216*x^2*y^9+1269962*x^2*y^8-5172096*x^2*y^7-3372752*x^2*y^6

+7054656*x^2*y^5+802984*x^2*y^4-14167808*x^2*y^3-12415968*x^2*y^2

-3116160*x^2*y

+81*y^16-1620*y^15+14256*y^14-70956*y^13+5750*y^12+1313844*y^11-5350316*y^10

+6066108*y^9+11577797*y^8-36654752*y^7+8262684*y^6+62578288*y^5

-41418748*y^4-47850112*y^3+55066256*y^2+37929920*y

Gottfried Helms.