Questions about aesthetics are of course inherently subjective. In your third point you seem to be expressing a strong aesthetic preference for mathematics which starts from a smallish set of axioms and builds a large, unified theory, constructed with maximal generality. I can think of other areas of mathematics than Australian-style category theory that fit this description, like universal algebra, point-set topology and several areas of set theory and logic. I believe a young mathematician in any of those areas could have posted a similar complaint bemoaning the general drift away from the kind of mathematics they care about.

By contrast let me try to articulate how I perceive the dominant aesthetic preference of the mathematical community, without necessarily endorsing it myself. One imagines that there is a "core" of mathematics, consisting perhaps of geometry, arithmetic and analysis. Questions in these areas are inherently interesting and deserve to be studied. Other parts of mathematics deserve to be studied only inasmuch that they can be applied to those core areas. From this perspective HTT is "superior" to Australian style category theory only because it has been more useful in algebraic geometry, K-theory and topology, which are all close to that "core".

A more blunt take is that this is memetic evolution in action. In a toy model, all mathematicians start out being interested only in the specific problem assigned to them by their advisor. During their career they'll become interested in more things, determined by randomness, personal preferences, but above all self-interest: "oh, it seems I can maybe prove something about X (which I care about) if I only learn a bit of Y (which I have only heard of)"... Rightly or wrongly, such a process will "reward" areas exclusively on the basis of whether they are useful to other areas, and "punish" those which aren't.

So what can you do if you work in an area which is out of vogue? Of course you can advertise your work and your point of view, but you can't force people to care about the theorems you prove. So you have two extreme options: (a) Keep working on what you care about, no matter what others think. This is not easy, but it can be done - you'll just have fewer job opportunities, fewer funding options, etc. Or (b): Switch fields. This is not easy either, but it can also be done. This is of course easier if you know someone you can collaborate with and learn from, and if you can switch to something reasonably close to your own interests. Most people will maybe do something inbetween - try to nudge their own interests in the direction of things that can be applied to what other people are working on. Good luck.

Questions about aesthetics are of course inherently subjective. In your third point you seem to be expressing a strong aesthetic preference for mathematics which starts from a smallish set of axioms and builds a large, unified theory, constructed with maximal generality. I can think of other areas of mathematics than Australian-style category theory that fit this description, like universal algebra, point-set topology, finite group theory, and several areas of set theory and logic. I believe a young mathematician in any of those areas could have posted a similar complaint bemoaning the general drift away from the kind of mathematics they care about.

By contrast let me try to articulate how I perceive the dominant aesthetic preference of the mathematical community, without necessarily endorsing it myself. One imagines that there is a "core" of mathematics, consisting perhaps of geometry, arithmetic and analysis. Questions in these areas are inherently interesting and deserve to be studied. Other parts of mathematics deserve to be studied only inasmuch that they can be applied to those core areas. From this perspective HTT is "superior" to Australian style category theory only because it has been more useful in algebraic geometry, K-theory and topology, which are all close to that "core".

A more blunt take is that this is memetic evolution in action. In a toy model, all mathematicians start out being interested only in the specific problem assigned to them by their advisor. During their career they'll become interested in more things, determined by randomness, personal preferences, but above all self-interest: "oh, it seems I can maybe prove something about X (which I care about) if I only learn a bit of Y (which I have only heard of)"... Rightly or wrongly, such a process will "reward" areas exclusively on the basis of whether they are useful to other areas, and "punish" those which aren't.

So what can you do if you work in an area which is out of vogue? Of course you can advertise your work and your point of view, but you can't force people to care about the theorems you prove. So you have two extreme options: (a) Keep working on what you care about, no matter what others think. This is not easy, but it can be done - you'll just have fewer job opportunities, fewer funding options, etc. Or: (b) Switch fields. This is not easy either, but it can also be done. This is of course easier if you know someone you can collaborate with and learn from, and if you can switch to something reasonably close to your own interests. Most people will maybe do something inbetween - try to nudge their own interests in the direction of things that can be applied to what other people are working on. Good luck.