It's ironic that Brouwer, one of the fathers of intuitionism (a branch of mathematics and philosophy associated with constructive logic), is best known for his fixed-point theorem, which is explicitly non-constructive.
What will you be remembered for? Not what you think about the most, surely. A 10-second throwaway remark could make a larger impact on those around you than a 10-year project your poured your soul into. What will your legacy be?