csc@watmath.UUCP (Computer Sci Club) (02/08/84)
Recently (Jan 12) the Guardian (London & Manchester) published an
article supporting claims by Arnold Arnold that he has solved Fermat's
Last Theorem, can generate primes of arbitrary size, and can factor
numbers of arbitrary size. Part of his "proof" of Fermat's Last Theorem
was given in the article. Unsurprisingly, it was nonsense. (Arnold
appears to believe that Fermat's Last Theorem states that if
a**2 + b**2 = c**2 then a**n + b**n not equal to c**n for n>2. He then
makes a bad job of proving this trivial proposition. Or maybe he is
doing something else, the presentation was VERY confusing.) A retraction
of the claims was printed two weeks later and Science News had an article
in its Jan 19 issue purporting to disprove Arnold's "proof".
What I find most interesting about this is not the addition of another
flawed proof to the scrap-heap of proofs of Fermat, squarings of the circle
and trisections of the angle, but the incredibly shabby treatment the
mathematics community got from both publications. The Guardian dismisses the
entire body of "conventional" (used by them in a derogatory sense)
mathematicians in a single sentence implying that they are too inflexible to
look at new methods. The authors of the article did not bother to obtain
any comment from an established mathematician, and when (after recieving a
quick education from outraged British academics) they published their retraction
they did not apologise for either insult!
Even worse is the coverage in Science News. They at least point out
that Arnold is wrong. However the mathematics in their refutation is almost
as bad as Arnold's (their presentation is clearer so their blunders are
easier to see). They claim that it is a reasonable assumption that an
integral root of an integer is rational! Then they later state that they
have found a contradiction. This statement would still be incorrect even
if their first idiotic assumption were right.
The most dismaying fact is that both of the above are
reasonably prestigous publications. And what little (very little) coverage
of mathematics I've seen here suggests that the North American publications
are no better. Sigh! Back to the journals.
William Hughes