Mathematics and computer science

Intuitionistic Type Theory

Mathematics, logic, and computer science share a common history. Mathematics and logic are ancient dragons, and not much upheaval is to be expected in their futures. But where lies the future of computer science?

Many philosophers of the 20th century embraced a view going back, at least, to Leibniz, viz., that, by using a formal language where all assumptions are made explicit, most differences in opinion can be solved by tracing the differences back to different (implicit) assumptions. It becomes evident, by reading a newspaper, e.g., that this view, though of great potential, has not had a large impact in the domains of every-day life.

Computer science would seem to be much more fertile soil for such ideas, and this makes it all the more surprising that computer programming is an activity performed by people who, by and large, have little or no knowledge about formal languages and formal methods.

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