THE CARELESS STEPS OF A GULL
Pierre de Fermat (1601-65), the early investigator into the nature of probability, was of the habit of scribbling bits and oddments of ideas in the margins of the treatises he would consume.
While studying the Arithmetica of Diophantos the Alexandrian, he encountered the notion that certain squares are the sum of two other squares .
Catalyzed into thought he noted,
“On the contrary, it is impossible to separate a cube into two cubes, a fourth power into two fourth powers, or, generally, any powers above the second into powers of the same degree.
I have come upon a truly marvelous demonstration which this margin is too narrow to contain.”
The proof was never published, nor was it found among his papers.
To this day it is lost.
That this was so had little impact upon the intellectual development of
mankind, the proposition being little more than a mathematical curio.
However, consider the possibility that a similar fate befell a theorem integral to the foundation upon which later number theory would be based.
For example if Pythagoras, that half'-mythical high priest of pre-Socratic Ionia, had never tread the verdant valley of the Nile, he might never have set his eyes upon that ancient rule of thumb which the Aegyptians utilized in measuring their fields, the Golden Triangle. It is this which he later generalized into the theorem which bears his name:
In a right triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.
If he unsecreted this, let us say, upon his native isle, Samos, while factoring with a stick upon the sands and it was erased by the mindless breath of Aeolis or the careless steps of a gull (as it is what proof he used is unknown), the theorem might have never been recorded. (When he stumbled upon it, it is said, he sacrificed an ox to the gods. ) If that was the case, then a man yet unborn for some two thousand years and known to his contemporaries as Renatus Cartesius might never have developed his analytical geometry being that he utilized the forty-seventh theorem of Euclid, as it later came to be known, as the basis for his Methode (in which it became possible to describe the properties of whole families of curves by means of simple equations).
