<P> The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken . It was the first major theorem to be proved using a computer . Appel and Haken 's approach started by showing that there is a particular set of 1,936 maps , each of which can not be part of a smallest - sized counterexample to the four color theorem . ( If they did appear , there would be a smaller counterexample . ) Appel and Haken used a special - purpose computer program to confirm that each of these maps had this property . Additionally , any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps . Showing this required hundreds of pages of hand analysis . Appel and Haken concluded that no smallest counterexamples exist because any must contain , yet do not contain , one of these 1,936 maps . This contradiction means there are no counterexamples at all and that the theorem is therefore true . Initially , their proof was not accepted by all mathematicians because the computer - assisted proof was infeasible for a human to check by hand ( Swart 1980 ) . Since then the proof has gained wider acceptance , although doubts remain ( Wilson 2014 , 216 -- 222 ) . Stephen Wolfram , for example , stated that in general , proofs can be arbitrarily long , and can be quite devoid of what might be considered meaningful structure and thus are often considered controversial - listing the Four - Color Theorem as just one example of such case . </P>
<P> The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken . It was the first major theorem to be proved using a computer . Appel and Haken 's approach started by showing that there is a particular set of 1,936 maps , each of which can not be part of a smallest - sized counterexample to the four color theorem . ( If they did appear , there would be a smaller counterexample . ) Appel and Haken used a special - purpose computer program to confirm that each of these maps had this property . Additionally , any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps . Showing this required hundreds of pages of hand analysis . Appel and Haken concluded that no smallest counterexamples exist because any must contain , yet do not contain , one of these 1,936 maps . This contradiction means there are no counterexamples at all and that the theorem is therefore true . Initially , their proof was not accepted by all mathematicians because the computer - assisted proof was infeasible for a human to check by hand ( Swart 1980 ) . Since then the proof has gained wider acceptance , although doubts remain ( Wilson 2014 , 216 -- 222 ) . Stephen Wolfram , for example , stated that in general , proofs can be arbitrarily long , and can be quite devoid of what might be considered meaningful structure and thus are often considered controversial - listing the Four - Color Theorem as just one example of such case . </P>
when was the four color map problem solved
when was the four color map problem solved
1976
1976