I saw an animation whose title is "A couple of science human, fell in love, so they try to prove the existence of love."

If I were to write a script for this anime (Of couse it will not), the title may be

"A couple of science human, fell in love, so they try to calculate the existence of love."

This is the difference between mathematicians and engineers.

Mathematician proof is a method of pursuing truth (mainly using mathematics) that is absolutely universal in time and space, however,

Engineer's "calculation" is a method that checks whether it is useful in a limited space-time.

Neither is superior, and the purpose is different primarily.

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This is a tactless question, however, as an engineer, I'd like to dig into the messages of the main characters at the beginning of Episode 1.

"Polynomial time return"

In this story, it is good to understand that "an algorithm program using a personal computer, that can complete the calculation by returning home"

The opposite is "an algorithm programming that does not finish in 100 million years."

"Hamilton Pass"

A path that passes through all of a plurality of cities only once, or an algorithm that calculates such a path.

Googling for "NP problem" or "NP proof", the above words come out.

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By the way, as a general rule, proof of mathematics cannot be obtained by computer.

Computer calculations can only try a finite number of patterns in a finite amount of time.

Because it's just looking for a small part of the solution space.

However, as far as anime is concerned, they seem to be asking for "something" using a personal computer.

I think "what they are doing".

(Continuation from yesterday)