Why are mathematicians a kind of programmers? Besides applied maths, aren't they more researchers that explore and discover, in contrast to the majority of programmers who are more like handymen?
Metamathematics, by Kleene, is programming in maths. Theoretical computer science is maths. A lot of foundations work is programming. Coding itself is like an extended problem set from a maths class. LaTeX itself is programming.
The difference to me is one of directionality - maths research is seeing a far off island and getting there by hook or by crook; bridge, draining the swamp, inventing an airplane or boat, whatever it takes. Software engineering is like covering a plain with tiles - every feature is ultimately filled in and the underlying beauty is obscured by a fractal of complexity required by the ever growing requirements.
> Metamathematics, by Kleene, is programming in maths.
Ookay.
Back in the day i was confused by 'Linear programming', which is optimisation and has nothing to do with coding.
> every feature is ultimately filled in and the underlying beauty is obscured by a fractal of complexity required by the ever growing requirements.
Right. I would say Mathematics tries to unobscure (patterns in) nature. Engineering is creating tools, sometimes leveraging natural patterns.
But yeah, Fourier or Laplace definitely created tools, too.
The * in regular expressions is from that book by Kleene; it used to be called the Kleene star. And the book is all building up the apparatus of functional programs, recursion, implementations of arithmetic and logic, etc. it is a great book for programmers. But it is for basic computability theory, the Gödel incompleteness theorem, results on regular languages and so on.
The difference to me is one of directionality - maths research is seeing a far off island and getting there by hook or by crook; bridge, draining the swamp, inventing an airplane or boat, whatever it takes. Software engineering is like covering a plain with tiles - every feature is ultimately filled in and the underlying beauty is obscured by a fractal of complexity required by the ever growing requirements.