How to do Math in programming

How to do Math in programming at TECH

1:デフォルトの名無しさん
24/03/21 09:41:43.97 85WuJ+Bw.net
What is "mathematics in programming?"

Some well-known facts in mathematics are difficult to prove using a computer.
For example, the Leibniz series

1 - 1/3 + 1/5 - 1/7 + ...

is exactly equal to π/4, but calculating this series directly is impossible because it requires infinite computation.
However, from the theorems of analysis, this equality can be shown. Thus, if all these theorems are formulated in terms of logic symbols, the proof is reduced to a finite algorithm.

Some might say that a "proof assistant" or "theorem prover" would make this possible.
However, the language of proof assistants is too complicated to describe proofs of non-fundamental theorems, so proof assistants are used only to check proofs that have already been solved.
This is far from doing mathematics.

My question is where do mathematical ideas come from and whether programming can help yield them?

30:デフォルトの名無しさん
24/04/19 12:06:54.47 0YEF9E1Q.net
まず代数計算は自動化したいよね
ほぼ定義を再掲するだけみたいな証明は自動で演繹できるようにしたい
全部が全部そうできなくてもいいけど、書き方に若干のルールを設ければ自動で証明できる範囲は広がるはず
型駆動でも、OOPでいうとこのデザインパターンを発見して、
>>10や >>19みたいな微妙に命題を変形するようなのは楽に書けるようにしたい

31:デフォルトの名無しさん
24/04/19 12:59:19.99 wsMDWrIu.net
その平凡なアイデア思いついたのお前が初めてだと思うか？

32:デフォルトの名無しさん
24/04/19 13:58:03.23 3z6RQVPy.net
「自分が初めて思いついた」という話題はどこから出てきたの？

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