After a year of writing this blog, what have I learned about the nature of the relationship between computer programs and mathematics? Here are a few notes that sum up my thoughts, roughly in order of how strongly I agree with them. I’d love to hear your thoughts in the comments.
- Programming is absolutely great for exploring questions and automating tasks. Mathematics is absolutely great for distilling the soul of a problem.
- Programming is fueled by the excitement of what can be done. Mathematics is fueled by the excitement of how things relate, and why they relate.
- Good mathematics makes for short programs.
- Good mathematics can be sloppy. Good programs cannot.
- Useful algorithms can come from any branch of mathematics, so it is best to be familiar with them all (at least a little).
- Most programs written for the real world use no mathematics beyond the level of an average twelve-year-old, but
View original post 103 more words