I happened to debate with a friend during college days whether advanced mathematics is necessary for any veteran programmer. He used to argue fiercely against that. He said that programmers need only basic mathematical knowledge from high school or fresh year college math, no more no less, and that almost all of programming tasks can be achieved without even need for advanced math. He argued, however, that algorithms are fundamental & must-have asset for programmers.
My stance was that all computer science advances depended almost solely on mathematics advances, and therefore a thorough knowledge in mathematics would help programmers greatly when they’re working with real-world challenging problems.
I still cannot settle on which side of the arguments is correct. Could you tell us your stance, from your own experience?
To answer your question as it was posed I would have to say, ‘No, mathematics is not necessary for programming’. However, as other people have suggested in this thread, I believe there is a correlation between understanding mathematics and being able to ‘think algorithmically’. That is, to be able to think abstractly about quantity, processes, relationships and proof.
I started programming when I was about 9 years old and it would be a stretch to say I had learnt much mathematics by that stage. However, with a bit of effort I was able to understand variables, for loops, goto statements (forgive me, I was Vic 20 BASIC and I hadn’t read any Dijkstra yet) and basic co-ordinate geometry to put graphics on the screen.
I eventually went on to complete an honours degree in Pure Mathematics with a minor in Computer Science. Although I focused mainly on analysis, I also studied quite a bit of discrete maths, number theory, logic and computability theory. Apart from being able to apply a few ideas from statistics, probability theory, vector analysis and linear algebra to programming, there was little maths I studied that was directly applicable to my programming during my undergraduate degree and the commercial and research programming I did afterwards.
However, I strongly believe the formal methods of thinking that mathematics demands — careful reasoning, searching for counter-examples, building axiomatic foundations, spotting connections between concepts — has been a tremendous help when I have tackled large and complex programming projects.
Consider the way athletes train for their sport. For example, footballers no doubt spend much of their training time on basic football skills. However, to improve their general fitness they might also spend time at the gym on bicycle or rowing machines, doing weights, etc.
Studying mathematics can be likened to weight-training or cross-training to improve your mental strength and stamina for programming. It is absolutely essential that you practice your basic programming skills but studying mathematics is an incredible mental work-out that improves your core analytic ability.