A programmer once told me that as you get more and more complicated with what your code is trying to do, programming and mathematics converge.
A big part of it is that for a lot of things, making a rudimentary algorithm to solve a problem is pretty easy. But this rudimentary algorithm will require a lot of steps and computations. And each step costs money in hardware (computer parts don’t last forever), energy (electricity ain’t cheap, and time (you actually need a solution).
Mathematics can be used to improve algorithms and make things faster, easier, and cheaper. And depending on time constraints, usable.
The Alan Turing film about code breaking shows all of this. In the film Turing makes a machine and has a rudimentary calculation for breaking the enigma cod le relatively early in the story. But the algorithm is rudimentary and after computing for a week it’s still not done; and since the code changes every day this is useless. So they spend all day every day improving the algorithm to the point where the computer can perform all the calculations in minutes.
Lots of real world problems are like this. Logistics systems change in scope and what products and locations are involved constantly, so you also want your calculations done ASAP.
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