> mean something beyond basic calculus and linear algebra.
"Fluency" in mathematics, in my experience, isn't about being able to perform more complex computation, that's what computers are for. The key to fluency in mathematics is increased efficiency at equational reasoning.
Granted, I work in data science, but I've personally seen that more and more problems I have are solved writing out a few equations and reasoning about the problem than writing code. It's not about knowing, for example, what SVD is, but seeing how a variety of common problems trivially map to it. Or figuring out how to transform a business problem into a probability problem so you can quickly estimate your success. Many times now I have spent a few afternoons writing equations that simplified what would have been very large and unnecessarily complex programs.
The mistake programmers make is thinking that math is just fancy computation, but mathematical reasoning is an entirely distinct way of reasoning about problems and computation is usually the least important part.
I used to also think that there was no reason for programmers to learn any math outside of enough calculus and linear algebra to compute basic things. But really understanding these areas and reasoning about them fluently (as well as other areas of mathematics) opens up many possibilities of problem solving that code it self does not.
"Fluency" in mathematics, in my experience, isn't about being able to perform more complex computation, that's what computers are for. The key to fluency in mathematics is increased efficiency at equational reasoning.
Granted, I work in data science, but I've personally seen that more and more problems I have are solved writing out a few equations and reasoning about the problem than writing code. It's not about knowing, for example, what SVD is, but seeing how a variety of common problems trivially map to it. Or figuring out how to transform a business problem into a probability problem so you can quickly estimate your success. Many times now I have spent a few afternoons writing equations that simplified what would have been very large and unnecessarily complex programs.
The mistake programmers make is thinking that math is just fancy computation, but mathematical reasoning is an entirely distinct way of reasoning about problems and computation is usually the least important part.
I used to also think that there was no reason for programmers to learn any math outside of enough calculus and linear algebra to compute basic things. But really understanding these areas and reasoning about them fluently (as well as other areas of mathematics) opens up many possibilities of problem solving that code it self does not.