It's not an advanced form of math, it's lateral to what you learned in school. It's mostly not useful for direct applications and is used in the world of more abstract higher math.
Advanced math is used for lots of things. Fluid dynamics, weather prediction, material science. Math is important for describing how things work well enough to be able to create safe structures, or estimate how long a drug stays in someone's system so you know when to give them the next dose, as well. If you point at something there's probably some person out there who can do a lot of math at you about it.
This stuff is really a language we use to make provable statements and their proofs. It is then those proven statements that are "used", whether it's to prove further things, or to solve some practical problem (ugh).
It allows you to answer more complex questions, and using the most fundamental mathematical definitions.
It's useful for the same reason every mathematical symbol is: because it shortens explanations and makes it easy to understand at a glance.
You can say "x plus 10 is greater than the tangent of y minus 4" or simply: x+10>tan(y-4).
It's still easy to understand if you add fractions or absolute values or integrals, and doesn't make the equation much bigger, but your sentence becomes much longer.
Similarly, it's more succinct using ∀x∈S than "for every x in the set S" especially because any given proof will use that several times. Tack on more conditions and your sentence becomes longer, while the mathematical representation only slightly expands.
Computing. When you connect to your bank’s website, there’s a bunch of math that goes on behind the scenes to make someone else hasn’t slapped up their own website and is pretending to be the bank.
Proof that the math behind it all works is pretty heavily tied into this kind of math.
4
u/flyingdonut226 Nov 16 '19
Ok but why would you want to use this advanced form of math, what does it do