Four color theorem
English mathematician Arthur Cayley presented the problem to the mathematical society in London, in 1878. Within a year, Alfred Kempe found what looked like a proof  of the problem. Eleven years later, in 1890, Percy Heawood showed that Alfred's proof was wrong. Peter Guthrie Tait presented another attempt at a proof in 1880. It took eleven years to show that Tait's proof did not work either. In 1891, Julius Petersen could show this. When he falsified Cayley's proof, Kempe also showed a proof for a problem he called Five color theorem. The theorem says that any such map can be colored with no more than five colors. There are two restrictions: First, any country is contiguous, there are no exclaves. The second restriction is that countries need to have a common border; if they only touch in a point, they can be colored with the same color. Even though Kempe's proof was wrong, he used some of the ideas which would later permit a correct proof.