what are mathematicians trying to do?
That’s apparently not clear even to mathematicians and is a total mystery to the rest of us. For example, I suspect that all physicists believe they are simply discovering existing natural laws, but mathematicians are divided on whether they are discovering or creating mathematical facts. Was Wineland right about the utility of what mathematicians do? Well here’s a quote from G. H. Hardy’s A Mathematician’s Apology. Hardy was one of Britain’s most respected mathematicians in the first half of this century. “I have never done anything ‘useful.’ No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.
