Penrose (2004: 10):
In the long run, the influence of the Pythagoreans on the progress of human thought has been enormous. For the first time, with mathematical proof, it was possible to make significant assertions of an unassailable nature, so that they would hold just as true even today as at the time that they were made, no matter how our knowledge of the world has progressed since then. The truly timeless nature of mathematics was beginning to be revealed.
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From the perspective of Systemic Functional Linguistic Theory, the validity of propositions ('significant assertions of an unassailable nature') is a matter of interpersonal meaning. Mathematics does not exclude interpersonal meaning, but it does provide a means of determining validity, given an agreed set of assumptions.
From this theoretical perspective, one reason why the validity of mathematical assertions does not change with changing 'knowledge of the world' is that mathematical assertions are concerned only with intrinsic logical relations between quantifying Numeratives, whereas changing 'knowledge of the world' is more broadly concerned with the changing construal of experience as Things, and their participations in processes.
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