Math is just a language for describing consistent, non-contradictory structures.
Our universe is very likely one such structure and will obviously obey some geometry and logic.
What this particular troll appears to be claiming is that real numbers and infinity (whatever he means by that, infinities need to be defined to mean anything) cannot exist in reality. I tend to prefer the finite digital world view myself, as it avoids all kinds of weird stuff that would be possible otherwise, and QM and GR does hint at reality possibly being like that, however I'm always ready to be surprised by nature.
Since it's possible to construct limited forms of turing machines in this world, general branches of math also apply.
What the troll refuses to do is consider sets like the natural numbers which have infinite values. Such sets are of theoretical value and can help simplify a lot of things without actually breaking anything, instead the troll prefers to only think of limited sets of numbers, as required in practice. This will prevent him from creating more advanced abstractions and overall limit him.
For all the ad-hominem attacks, he should instead try to do some constructive criticism if he so hates math, such as defining his own systems and publishing them so we can look at them and compare them with modern math.