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The question of how mathematicians think is closely related to the question “How does a musician compose?” Ali Kayaspor, Math Teacher emphasiz.
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| How to Think Like a Mathematician Photo: Medium |
Similarly, this question is asked to learn how the creative process works. Those who are interested in computer science or especially artificial intelligence can give the correct answer to this question. A real mathematician is not interested in finding the answer to this question. He’s just busy doing math.
Unfortunately, there is no clear way to answer the question of how a mathematician thinks. But we can approach this question as follows; if you watched any chess tournament, the game’s analysis is shared in detail at the end of the match. When you examine the analysis, you will see a breaking point in each game. Similarly, mathematicians also experience a breaking point while working on a problem, just before they find a solution...
Now, we talked about rational mathematical thought and its forms, but there is another layer to it as well. Mathematics is getting more complicated by the day. Some proofs can take hundreds of pages. For example, the classification of finite simple groups has proof that fills thousands of pages. There are even rumors that there was a mistake somewhere that says there should have been a few other groups among the sporadic. That is why some mathematicians are currently working on whether it is possible to make computer programs that can control the proofs or, better, computer programs that can directly make the proofs.
The same goes for music because music and mathematics progress in parallel. Musicians are also dealing with similar things like mathematicians. For example, there are music composers for the computer. There is a specific speed limit for humans, we cannot type eight symbols at the same time, but you can do anything on the computer. So there are people who wonder whether we can find a place for the computer in mathematical thinking. That idea raises the question: Can a computer start doing mathematics on its own? Alan Turing is the first to ask this question. As a closing thought, while we examine how a mathematician thinks, we should also start thinking about what a computer can do if it starts thinking like a mathematician in the future.
Source: Medium
