Apart from relational algebra, two big ones are regular expressions and diff (longest common subsequence). However, you're saying vice versa: Almost all math w

Apart from relational algebra, two big ones are regular expressions and diff (longest common subsequence). However, you're saying vice versa: Almost all math we use has a clear and direct lineage from a popular tool or technique. There's something to this - many of the well-known theorems and algorithms for regular expressions started with Ken Thompson, though of course he used Kleene algebra. And for relational algebra in this submission, there's almost no mathematics, just a set of tuples... and make an algebra around it. That's why Codd's paper has hardly any references, he pretty much made it all up, to solve a practical problems he saw (unnecessary rewriting of code). Though he was a mathematician, so... The limits of knowledge, of what can be proven, is to do with "computability" - sure sounds like a prpgrammer thing! So maybe you have something there...