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It is generally accepted that this was done by Kenneth Appel and Wolfgang Haken in 1974. In 1976, they published a paper with a proof.

But it wasn't perfect.

First, most of it was done on a computer. Second, the article itself was huge. To understand the proof, the reader had to master 50 pages of text +85 pages with an additional 2500 diagrams+400 pages with proofs of lemmas from the main text.

In such a huge volume, typos and errors are inevitable. It takes a long time for a large team to check all the work and correct errors and shortcomings. This was never done.

But later, other evidence was found that also relied on computer calculations – this was done, in particular, by Paul Seymour in 1995 and Gontier in 2004. Therefore, it is generally accepted that Appel and Haken proved the four-color hypothesis.

Although ideally we all think of a chain of logical conclusions that follow from one another as proof, in practice everything is more complicated. Proof in mathematics is social. The history of science tells us that ideas about what can be considered proof and what can not, are constantly gradually changing.