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Sorry if this question is not too fit into the website. I want to know if there're some methods that we can actually do mathematical deduction with formulae just on the computer instead of with pen and paper? I think latex is not a what you see is what you get type of way, so it might not be a good choice to do the mathematical deduction, so is there some other ways?

Sherlock
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    There are WYSIWYG equation editors, although there are also folks that will take notes in LaTeX anyway. – Ian Apr 06 '22 at 12:49
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    I suggest staying with Latex. After a while, you will become so accustomed to reading/writing the Latex that you won't care that it is not WYSIWYG. Your mind will learn to naturally think in Latex similar to a pianist learning to get the feel of a piano. – user2661923 Apr 06 '22 at 13:02
  • It isn't too hard for a computer to spit out a series of true statements in mathematics. The trouble is to identify which ones are useful. – MasB Apr 06 '22 at 13:13
  • @user2661923 I'm afraid not... After reading your comment, I look at the long equation in my latex(transferred from MathType directly), I can spot the meaning of it, but it's just too indirect for long terms... – Sherlock Apr 06 '22 at 13:26
  • @lan Thank you very much for comment. I temporarily use MathType style equation editors with a lot of customized shortcuts for formulae typing and using LaTeX for notes taking. Wonder how others doing. – Sherlock Apr 06 '22 at 13:28

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I can come up with several ways to do so:

  • Using an electronic pen, so that ones writings are directly processed digitally.
  • Using a markup language of ones choice to type math with a keyboard or other input device (including speech or maybe thought recognition)
  • Use what you see is what you get editors, for instance some peoples beloved Word processor

But all what I listed is just obvious I guess. If you mean also to have computer aided mathematical arguments, sure there are many tools: Mathematica, Maple, Matlab,... or languages like Prolog, Haskell or all others like C++, Python, Fortran, Java,... with the desired libraries.

But if you mean to have some software which is doing the proofs for us, or which finds new mathematical results, then the big question would be: is it still mathematics and how does it help us? Since mathematics seems to me, at least in our world, mostly about humans understanding some mathematical idea/principle/law and not about a machine telling us some results which we cannot comprehend, no matter if true or not.

Edit: I would like to add IPE, extensible drawing editor, which can render Latex and is very nice for doing presentations, which is an essential part of teaching or communicating mathematics and also a way of deduction

Numa
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  • I use MathType with customized shortcuts temporarily. – Sherlock Apr 06 '22 at 13:24
  • Thank you for mentioning IPE, which was new to me. – awkward Apr 07 '22 at 14:32
  • @awkward I also discovered it only very recently, after a colleague recommended it to me. One can use it in a way similar to an I python notebook for lectures. But one of the best things is, after installing ipe2tikz, one can generate readable tikz Latex code from ones drawings and paste it to ones papers written in Latex, hence no picture files needed and all fonts can be matched. – Numa Apr 07 '22 at 16:14