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Dick Lipton wrote a great post over at Gödel’s Lost Letter and P=NP. In his Sept 27th post he talked about surprises in mathematics. In one of his sections he gives three examples of where mathematicians “accepted” a false proof. Sometimes this happens and it might be dozens of years until someone realizes a mistake has been made.
One interesting example of this is the Four Colour Theorem (that’s right ya bunch of monkeys, I spelled colour with a U!!!)…
Lipton says…
“The
Four-Color Theorem (4CT) dates back to 1852, when it was first proposed
as a conjecture. Francis Guthrie was trying to color the map of
counties in England and observed that four colors were enough.
Consequently, he proposed the 4CT. In 1879, Alfred Kempe provided a
“proof” for the 4CT. A year later, Peter Tait proposed another proof
for 4CT. Interestingly both proofs stood for 11 years before they were
proved wrong. Percy Heawood disproved Kempe’s proof in 1890, and Julius
Petersen showed that Tait’s proof was wrong a year later.However, Kempe’s and Tait’s proofs, or attempts at a proof, were not
fully futile. For instance, Heawood noticed that Kempe’s proof can be
adapted into a correct proof of a “Five-Color Theorem”. There were
several attempts at proving the 4CT before it was eventually proved in
1976. See this article by Robin Thomas for a historical perspective of
the problem.“
Go check out the rest of his post NOW.