I am a scientist/engineer/mathematician who studied the hell out of abstract mathematics at an extremely rigorous undergrad program. In the 20 years since, not once has that knowledge been useful in my academic or industrial work, not even remotely. I am all for studying theory for its own sake, for the career theoretician and the interested hobbyist, but as an investment I regret those four years of my life as a colossal waste of time.
so, in real world application, what's the most useful/valuable topic in mathematics?
Although I wonder for 90% people of this world that math is just a tool to pass the exam at school, not any real application (or they just can't sense it).
It depends on what your relative judgements are for what is deemed 'valuable' or 'useful'. Are the number theory foundations that allow digital transactions to occur more valuable than the subtraction done to figure out how many minutes until the next hour?
