[chongli]

You’re confusing syntax and semantics. Programmers write code for syntax machines (Turing machines). The computers care a lot about syntax and will halt if you make an error. They do not care at all about semantics. A computer is happy to let you multiply a temperature in Fahrenheit times a figure in Australian dollars and subtract the volume of the earth in litres, provided that these numbers are all formatted in a compatible enough way that they can be implicitly converted (this depends on the programming language but many of them are quite liberal at this).

If you want the computer to stop you from doing such nonsense, you’ve got to put in a lot of effort to make types or contracts or write a lot of tests to avoid it. But that’s essentially a scheme for encoding a little bit of your semantics into syntax the computer can understand. Most programmers are not this rigorous!

Mathematicians, on the other hand, write mathematics for other humans to read. They expect their readers to have done their homework long before picking up the paper. They do not have any time to waste in spelling out all the minutiae, much of which is obvious and trivial to their peers. The sort of formal, syntax-level rigour you prefer, which can be checked by computers, is of zero interest to most mathematicians. What matters to them, at the end of the day, is making a solid enough argument to convince the establishment within their subfield of mathematics.

[agos]

But programmers are expected to get the semantics right. Sure, it happens to mismatch temperatures and dollars, but it’s called a bug and you will be expected to fix it

[chongli]

Software in the wild is full of millions of bugs. It’s a gigantic mess! Who is out there fixing it all?

[passion__desire]

Why do mathematicians hide their natural way of thinking ? They provide their finished work and everyone is supposed to clap. Why can't they write long articles like about false starts, dead ends and so on. It's only after magazines like Quanta and YouTube channels that we get to feel the thinking process. Math is not hard. Atleast the mathematics we are expected to know.

[chongli]

Mathematics is extremely hard. The math people are expected to know for high school is not hard, but that is such a minuscule amount of math compared to what we (humans) know, collectively.

Mathematicians do speak and also write books about the thinking process. It’s just very difficult and individualized. It’s a nonlinear process with false starts and dead ends, as you say.

But you can’t really be told what it feels like. You have to experience it for yourself.