Are there any famous disproved conjectures?

[Peter]

It turns out that the most famous mathematical conjectures are either
proved (Fermat's last theorem, Poincare conjecture) or still neither
proved nor disproved (Riemann's hypothesis, Goldbach's conjecture, P!
=NP), but I've never heard of a widely known hypothesis which turned
out to be false though many believed otherwise. The only major one(s)
I read about is one or two of Hilbert's problems to which a
counterexample was found. Could you give me a few more examples of
"great disappointments" in mathematics or maybe there aren't any
significant ones?

[Pubkeybreaker]

Mertens' Conjecture regarding the (order of) the Mobius Function.

[hagman]

Euler's sum of powers conjecture:
"a_1^n + ... + a_{n-1}^n = a_n^n has no solutions if n>=3."
COunterexample found 1966

Fermat (1637):
"2^2^n + 1 is prime."
Counterexample n=5 found in 1732.
(Today, it is widley believed that *all* n>4 are counterexmples;
maybe you can disprove *this* conjecture)

And people had believed for about 2000 years that the parallel
postulate
might be a consequence of the other axioms of geometry.

One instructive example for people taking enourmous numerical
evidence as proof:
"The number of primes < n is less than \int_{2}^{n} dt/ln(t)"
It is known that conterexamples exist and are not small.

hagman

[Robert Israel]

Peter <pil...@poczta.onet.pl> writes:

See <http://en.wikipedia.org/wiki/List_of_disproved_mathematical_ideas>
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

[Gerry Myerson]

In article
<23c9e830-7fe2-4e78...@v17g2000vbo.googlegroups.com>,
Peter <pil...@poczta.onet.pl> wrote:

There are two plausible conjectures in Number Theory which have been
proved to be inconsistent with each other, that is, they can't both be
true. One is the prime k-tuples conjecture, which says (roughly) that
if 0 < a_1 < ... < a_k are integers, and if there's no trivial reason
why there can't be any n such that n + a_1, ..., n + a_k are all prime,
then there are infinitley many such n. The other says that there are at
least as many primes between 2 and n, inclusive, as there are in any
other interval of that length.

--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)

[Butch Malahide]

Euler conjectured that orthogonal Latin squares of order 4n + 2 don't
exist.