The Four Color Theorem

The four color theorem is familiar to many mapmakers since it began to create maps to display various regions (states, countries etc) 100 years ago. Because the map creator can make a plan, only four colors are required for coloring the map created. The basic rule for coloring a map is that if two regions are adjacent, the map maker will need to use two different colors to color the adjacent region. The reason is that if the two areas share a boundary, they will never be the same color.

I am looking forward to fear because the rigorous demands of mathematicians are only those who do new research and are not a good sign for humanity. Calculation of the four-color theorem proved to be a watershed of mathematics when first seeing the acquisition of intuition of human intuition and intense computing. In mathematics, the promise of artificial intelligence (and propaganda) takes the form of proof of the automatization theorem, and one day may make a human being redundant in pursuit of mathematical discovery. Mathematics is more complicated and abstract than ever, but everyone alienates everyone except that few people can draw little insight through hundreds of pages of tedium . Mathematics research may become a field someday witnessed by humans for a long time, do not dare to never enter the front line with little understanding.

An important milestone in artificial intelligence in the 1970s was the automatic discovery of the mathematical proof of "four color theorem". In this case, artificial intelligence is not particularly complicated, and human mathematicians will still simplify the proof of the general theorem to a simpler assumption for each of the hundreds of cases. Artificial intelligence is very detailed, you can complete all cases and prove every time. Still, it shows that the computer can lead research mathematics to an unexpected direction.

As with the most complicated mathematical proofs, proof of optimization may be difficult to build. The interactive theorem has achieved great success in accomplishing tasks such as proof of the four color theorem and proof of the validity of the seL4 microkernel. However, since the proposer needs to build proofs for possible thousands of lines of code, the theorem proves that it should be a joint effort to maximize efficiency. Collaborative interactive theorem prove is a relatively new field of research aimed at designing a system in which the task of constructing proof is distributed among thousands to millions of users (ProofPeer). In addition, there are several studies on the proof of the first theorem as a simple game interface (Sundar & Bringsjord) that people who are not trained in formal mathematics can learn to play immediately.