Dick Lipton wrote a great post over at GÃ¶del’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.