> Mathematicians do not concern themselves with the physical universe - if
> they did they would be something else. The results which they prove are
> meaningful within their own realm. The exact nature of this "meaning" is
> complicated, but it essentially relates to "procedures" (how arguments
> are conducted) than any physical reality. A great deal of mathematics
> (for example, almost all of probability theory) is concerned with
> "infinity", which arguably has no physical meaning at all.
Except that in many cases, it has been physical scientists who *introduced*mathematicians to various uses of infinity (differentials, Fourier analysis, delta functions, ...). But that's history.
It is also clear from history that mathematics developed from very concrete foundations in things like counting and measurement. It is incomprehensibl e to me that many mathematicians wish to deny this, preferring to believe in Platonic fairy tales. A nasty consequence of this denial was the 1960's "New Math" curriculum for American schoolchildren. Supposed to strengthen math comprehension, it did exactly the opposite.
I cringe when I hear a mathematician talk about Fourier analysis as being about functions in L2. That notion ignores out a large part of the application space: "carrier waves", "flicker noise", delta functions, ... Here we see mathematicians willfully avoiding *meaningful* infinity.
Let me just point out that the origin of this interesting and passionate discussion was the question of what should be the content and tools of the mathematical education for students in non-mathematical specialities at present, observing that since long computers have become the reality of our world.