Name: Anonymous 2010-12-09 11:18
Andrew Wiles had a proof of Fermat's Last Theorem that had a hole, but then he corrected the hole and got a legitimate proof. This would mean, according to Popper's "falsifiability" theory, that mathematics is a pseudo-science.
The scientific community is deeply committed to a view of its own destiny which is well articulated by theoretical physicists. Historically, science is a series of commitments to mathematical apparatuses which, once they are established, are endlessly elaborated, but never discarded. One builds on Newton, Maxwell, etc., by recycling them; one never repudiates them.
In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics. These tenets are held to be valid by the latest, "Left-wing" standards--and to be the source and guiding light for all that followed them in mathematical history. The profession does not want the Greeks--who adopted the elementary theorems on the basis of elementary proofs--to have taken any other course.
The scientific community is deeply committed to a view of its own destiny which is well articulated by theoretical physicists. Historically, science is a series of commitments to mathematical apparatuses which, once they are established, are endlessly elaborated, but never discarded. One builds on Newton, Maxwell, etc., by recycling them; one never repudiates them.
In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics. These tenets are held to be valid by the latest, "Left-wing" standards--and to be the source and guiding light for all that followed them in mathematical history. The profession does not want the Greeks--who adopted the elementary theorems on the basis of elementary proofs--to have taken any other course.