It would be nice to take a common gadget, say an iPhone or an Android phone, and split it up into small bits and pieces (including software) and then list all the pieces which are based upon a theory or research which decades ago was considered irrelevant and useless. I.e. all the findings which make up an iPhone, but where decades ago people would have said 'what does this add to our life'. What I can think of, right now, is

- Cryptography (iCloud, iMessage, Online Banking): Is all based on prime numbers. For hundreds of years, prime number theory in math was considered a purely academic exercise, something with no real world usage at all. And suddenly it is the basis of many things we consider granted. [1]

[1] http://www.claymath.org/posters/primes/