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.
Self-Avoiding Walks, the language of science, and Fibonacci numbers. J. Stat. Inference and Planning, 54(1996), 135-138.
Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.Doron Zeilberger
Programming is much much harder than doing mathematics.Doron Zeilberger
Regardless of whether or not God exists, God has no place in mathematics, at least in my book.Doron Zeilberger
Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion.Doron Zeilberger
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.Doron Zeilberger
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.Doron Zeilberger