> Can't mathematicians and theorists not agree on what areas of math are most helpful and what areas least helpful in arriving at a Unified Theory?
Not fully, and with good reason (see below).
But actually, my point was that the existence of mathematical constructs that do not correspond to any physical reality means that there will be math to do when (and if) all physics has been done.
> Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money?
Yes and no. There is the branch of applied math, and I'm sure they get funding more easily.
But there are also mathematicians (cited several times in the comments here) who see math as art and want to do it for its own sake.
And it has happened quite often that these "pure" mathematicians came up with enirely new stuff that only afterwards (and without anyone foreseeing it) turned out to be useful in modelling physical processes. Even among mathematicians you sometimes find that you can prove something in one field by using constructs and theorems from an entirely different field that nobody thought was in any way related. I believe Wiles' proof of Fermat's Last Theorem was like that.
Not fully, and with good reason (see below).
But actually, my point was that the existence of mathematical constructs that do not correspond to any physical reality means that there will be math to do when (and if) all physics has been done.
> Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money?
Yes and no. There is the branch of applied math, and I'm sure they get funding more easily.
But there are also mathematicians (cited several times in the comments here) who see math as art and want to do it for its own sake.
And it has happened quite often that these "pure" mathematicians came up with enirely new stuff that only afterwards (and without anyone foreseeing it) turned out to be useful in modelling physical processes. Even among mathematicians you sometimes find that you can prove something in one field by using constructs and theorems from an entirely different field that nobody thought was in any way related. I believe Wiles' proof of Fermat's Last Theorem was like that.