Proof Of The Validity Of ‘Fermat’s Last Theorem’ Viewed Through Systemic Functional Linguistics

Penrose (2004: 13-4):

Let me illustrate this issue by considering one famous example of a mathematical truth, and relate it to the question of ‘objectivity’. In 1637, Pierre de Fermat made his famous assertion now known as ‘Fermat’s Last Theorem’ (that no positive nth power of an integer, i.e. of a whole number, can be the sum of two other positive nth powers if n is an integer greater than 2), which he wrote down in the margin of his copy of the Arithmetica, a book written by the 3rd-century Greek mathematician Diophantos. In this margin, Fermat also noted: ‘I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.’

Fermat’s mathematical assertion remained unconfirmed for over 350 years, despite concerted efforts by numerous outstanding mathematicians. A proof was finally published in 1995 by Andrew Wiles (depending on the earlier work of various other mathematicians), and this proof has now been accepted as a valid argument by the mathematical community. 

Now, do we take the view that Fermat’s assertion was always true, long before Fermat actually made it, or is its validity a purely cultural matter, dependent upon whatever might be the subjective standards of the community of human mathematicians?

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From the perspective of Systemic Functional Linguistic Theory, the proof of the validity of Fermat's Last Theorem was mathematical potential only until it was finally instantiated by Andrew Wiles in 1995.