Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.

When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.

Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.

Programming is much much harder than doing mathematics.

Conventional wisdom, fooled by our misleading "physical intuition", is that the real world is "continuous", and that discrete models are necessary evils for approximating the "real" world, due to the innate discreteness of the digital computer.

No Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.

Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.