This requires more justification than I am currently giving it, but it is easy to find examples of math problems that don’t have even a tenuous connection to reality (I have also noticed that some pure mathematicians nevertheless argue that it does; their arguments are so weak that I can only conclude that they are trying to retroactively justify a decision they already made, and I am saying this as someone who has published papers in the field in question). The source of examples I am most familiar with is (a large portion of) enumerative combinatorics. It is possible that this is the only example, but I suspect that if I was more familiar with algebraic number theory then I could make a similar claim there.
Upon further reflection, I don’t think I can justify my claim that these sorts of problems have no connection to reality at all; perhaps a better claim is that these problems are a very inefficient way of making headway on problems that we care about, even if we extrapolate into the far future. But this would be a much subtler and difficult claim to justify, so for now I’m editing my above post to retract this statement. Since you quoted it in your response, people will still have access to it if they care.
I don’t think I can justify my claim that these sorts of problems have no connection to reality at all; perhaps a better claim is that these problems are a very inefficient way of making headway on problems that we care about, even if we extrapolate into the far future.
Upvoted for correctly understanding the issue (even while taking a position opposite to mine).
For what it’s worth, I was extremely surprised that you listed, of all things, enumerative combinatorics (i.e. counting things) as an example of a branch of mathematics with a “tenuous” connection to “reality”.
For what it is worth, the last time here I tried to give an example of something in algebraic number theory not mattering to reality it turned out that it actually had some sort of practical purpose.
Upon further reflection, I don’t think I can justify my claim that these sorts of problems have no connection to reality at all; perhaps a better claim is that these problems are a very inefficient way of making headway on problems that we care about, even if we extrapolate into the far future. But this would be a much subtler and difficult claim to justify, so for now I’m editing my above post to retract this statement. Since you quoted it in your response, people will still have access to it if they care.
Upvoted for correctly understanding the issue (even while taking a position opposite to mine).
For what it’s worth, I was extremely surprised that you listed, of all things, enumerative combinatorics (i.e. counting things) as an example of a branch of mathematics with a “tenuous” connection to “reality”.