The importance of <i>calculus</i> is most easily demonstrated by applying it to physics problems. For example, if I tell you how a ball moves in time, and then ask you how fast it's moving after a certain number of seconds, then calculus will help you find the answer (take the derivative of the equation of motion and plug in the time).<p>What is the equivalent computer science problem that lambda calculus can help you solve? Challenge: pretend like you're Richard Feynman and avoid jargon, if at all possible.<p>EDIT: I find it quite curious that I got so badly down-voted (-3 and counting!) for simply asking for concrete examples of applicability to actual, concrete problems. I've always found that tools are best understood in the context of their use. Even an abstract concept is useful to speak about in this way - for example, complexity/Big O analysis helps us with capacity planning, comparing algorithms, and so on. It may be that lambda calculus helps us with, oh, decomposition of computation or something like that. But for all the digital ink I've read about it, it's always seemed like an academic form of name-dropping. Even the name is intimidating, right? Reminds me of terms like "schroedinger's equation" or "canonical ensemble" from the good old days in physics class. But behind the intimidating names is just a tool for solving problems - and I have yet to see anyone demonstrate this for lambda calculus. Granted I haven't looked very hard!<p>It takes self-awareness to realize that you are enthralled with something without understanding it. The litmus test for this is the umbrage taken by someone who's asked simple question about what their high-status concept is really used for. That's why I mentioned Feynman in particular, because of his wonderful reputation as having knowledge that was totally grounded in reality.