How much math you need for programming (2014)

Asking the converse. Are there any fields in programming that require like measure theory or topology or whatever?

I agree this is a common sentiment among mathematicians, but this is a very modern perspective. If you look back 100 years ago to Hilbert, there was less distinction between physicists and mathematicians, much less the pure/applied rift that now exists. Arnol'd (who is referenced above) was one of the mathematicians who tried to keep this unity alive.

Agreed!

> Computer Programming is not Math. Let me say it again, computer programming is not Math and will never be. You want to learn computer programming, then learn computer programming.

Programming is far more aligned with writing than math. If you want to be a better programmer be a better writer. Math will not make you a better programmer.

Conversely, programming will not make you a better writer, but it will make you better at math. This is complicated, but provable with testing.

The term math is extremely misunderstood. Math is not a practical exercise, it is a philosophy, a way of thinking. Lay people believe the word math is interchangeable with arithmetic, which it isn't. Arithmetic is the expression of immediate computation. Math is more than that.

Writing algorithms and instructions is algebra. Algorithms are always algebra. Always. Algebra is the conveyance of instructions, which is inclusive of arithmetic, but is more expansive and accounts for variability. The word algorithm literally comes from the Latinized name for the father of Algebra, Algorithmi. https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi

Planning is calculus. Calculus is the expression of continuous change. Calculus accounts for states in fluctuation and differentiation. Calculus allows for thinking in terms of various potentials and collections of decisions.

The reason why writing makes you a stronger programmer but math doesn't is because math doesn't force critical examination like writing does, at least not until you get to Calculus. The reason programming does make you better at math is because it teaches you to solve tough math problems without ever having to do math, because Math is a philosophy, a way of thinking.

This is provable with numbers. Simply test people, compare the testers, and then compare those differences against programming capability. This is provable objectively with numbers. If you want to hire better programmers test for writing performance. The best filter of a group of candidates, for programming potential, is a tough essay to write under time pressure.

When I took the military aptitude test, the ASVAB, the first time I was 17. My scores indicated that I was smarter than 79% of the people who took the test that year, but the only score that really mattered is the GT score. It is an examination of solving complex mathematical word problems under time pressure and is graded on a scale of 0-130. I scored I 107. Smarter than average but not smart enough to become a military officer. 17 years later when I wanted to be a military officer I needed to retake that test at which point I was smarter than 98% of the population who took the test that year and I scored a GT score of 129 (out of 130). I had been programming for 6 years at that point.

When you do design you need to know about typography, when you do finance, you need to know about accounting, when you are making a game, you need to know about game design, when you are doing weather forecasting, you need to know about meteorology.

None of them are skills that a programmer needs unless he works in the field. Maths is the same. You need very little maths to code unless your field requires it.

And even then, sometimes you don't even need to. I worked on a software that computed material fatigue with absolutely no idea about the maths involved, the mechanical engineers just told me the formulas and constants to use as well as the expected results and I implemented them. (not entirely true, but it was just personal curiosity, absolutely not required for the job).

I agree. Counting might not have any intrinsic relationship to the physics of the universe, but it's a strange universe where thinking beings can exist, yet are incapable of constructing the mathematical rules that would allow them to count.