I thought modern physics was strange, but then I decided to learn a bit about what mathematicians are doing nowadays and I am completely baffled. I have a pretty good understanding up to vector calculus and linear algebra, but this stuff is beyond so many layers of abstraction it might as well be gibberish to me. What is this shit even used for
>>16830345
>>16830345>What is this shit even used forIt's an academic pursuit, you autist. There is more to life than putting shekels in Mr Steinberg's pocket.
>>16830350coolwe can cut the grants then
>>16830350OP here, I'm not even talking about money or solving concrete problens, I mean what is the purpose on a level of "what does this do"
>>16830355>what does this doIf your question isn't in bad faith, you're gonna have to be more specific.>>16830351>weQuit LARPing like you have any say in the matter.
>>16830359I mean like what does this stuff allow mathematicians to do? What is there goal?
>>16830364I'm not sure what stuff specifically you're referring to, but a lot of math goes as follows.Some concrete problem will provide examples of some kind of object which has nice properties. Looking at these properties allows the object to be generalized in some way and this then leads mathematicians to a definition of some sort of object which is considered to be natural in a certain sense. A common question is how to classify these kinds of objects. Typically, a strict classification up to equality is absurd, so weaker notions of equivalence are used, and mathematicians try to classify objects up to equivalence. The task then is to figure out ways to show that two things are equivalent (usually easier), and to show that two things are not equivalent (often very difficult). This difficulty leads mathematicians to look for invariants; these are simpler objects - for instance numbers - associated to the more complicated objects, such that objects with different invariants cannot be equivalent. In other words, the task of distinguishing objects can be reframed (somewhat, but maybe not entirely) in terms of invariants, hence simplifying the problem. Another strategy employed, which philosophically follows the same lines, is to compare the objects in question to some other type of objects which are better understood, or easier to handle in some sense. This is usually done by this second-order abstraction which comes under the name of category theory and functoriality. If one can prove that two categories of objects are "essentially the same", then the classification of one category of objects will immediately give the classification for the other.
Okay let me unpack this for you in a polite and not meant to be mean-spirited way OP,All of mathematics is based on the fundamental axioms of number theory. The most fundamental axioms of all are called the Peano axioms, which themselves rely on primitive first-order logical induction to invoke a hypothetical "successor" function to any identifiable "object". Doing that lets us then further postulate a recursive sequence of "successors" which sums to equal what is called the set of natural or "counting" numbers. And then, if you have the counting numbers, you can use the same first-order logical induction method along with the same successorship function you used to do that to postulate the operations of addition and multiplication, recursively as well.So, that's just how to generate the most basic set of numbers, the "natural" or "whole" or "counting" numbers that are used to denote cardinality (size: one unit, two units, three units, etc) and ordinality (first, second, third, fourth, etc). From there you can derive subtraction and division as the inverse operations of addition and multiplication, since you can already derive those from just deriving the whole numbers at the start. That's the strength of what's being done here, it's an unbroken chain of validity starting from the beginning and being extended further and further to allow for the organization of more and more complexity.From the basic axioms of numbers, out of abstract void or pure randomness, you can still use induction to derive the natural number and then by extension, a scalar that can define the magnitude of a vector in any n-th dimensional measurable spacetime reality. Thus, you see where this is going? Exploring vector spaces and number fields and these sorts of mathematical conceptual territories is it's own exploration and process of discovery, and it is just inccidental that some of it is useful in most areas of science, because yeah, no shit, it's the objective definition of nature.
>>16830345>up to vector calculus and linear algebraKind of funny how I used to see that stuff as "high level math" until relatively recently
>>16830345>Modern Mathematics
>>16831055Charles dodgson was a great champion against the wonky gay math
>>16831055>you don't exist when i can't see youAnon, please. The roots exist.
>btfoed by complex numbersmany such cases
>>16831128In which dimension? If it is above or below the two circles, then they aren't circles anymore, they're a torus or a surface of some kind.
>>16831149>i sliced my loaf of bread>now it's not a loafStill bread.
>>16831055whats even the logic behind this , I feel like a very stupid crazy person could absolutly do something very dumb with this . stupid crazy person.
>>16831055>>16831149>>16831154literally this bros, don't overthink it!two slices of bread touching each other in the middle of the loafrearrange the slicesit's still the same loaf lolShip of what? Theseus, more like... deez nuts lmao. Eat shit nerds. Why don't you just shut up and calculate? Lesser mortals should not trouble themselves with the mysteries of the Gods.
Complex numbers aren't what I'm talking about. That shit is from the 1700s. I'm talking about the crazy stuff they have done in the past century, that has so much jargon and weird notation that it is impossible to even attempt to understand as a layman
>>16831173can you explain the logic behind that charles fella.- stupid crazy person
>>16831055Le quantum entanglement electron math
