As someone who has done research in the area, I'd argue that a lot of work on temporal logics is at about the same level of difficulty as a better-than-average undergraduate linear algebra course. Certainly none of the standard results about various temporal logics even come close to approaching the difficulty of a first or second year graduate mathematics course.

No, not completely unaware. I'm glad I've reminded you of something you find entertaining. I hope you discourage more people from learning something awesome.

Hes just being real. Ive been self learning group theory, and cardinality/ordinals, surreal numbers, VN universe, shit is hard. Foundation is key. In order to be profound one needs tools. Unlike programming, dedication to tightening ones toolbelt first, helps immensely later. Order in math progression is way more significant than programming by trial and error.

It'd be interesting to know what the optimal order of progression would be.

It'd be simple to grab a curriculum and start from point A (as in, the method is simple - not the content), taking that as the order.

More thoughts and discussion on this would be extremely interesting.

I'd say it really depends on what one wants to specialize in. You could do a ton of calculus and it wouldn't help all that much in some other areas of math. Yet, calculus is a pillar for some things. Ramanujan used integrals everywhere in his work on infinite series. I don't think there's a very straight forward path. Math is a very diverse subject.

I was intrigued because there is some indication of a rough but important ordering to the topics in formal maybe antics education. I was interested in seeing what that order was.

I've seen others say that linear algebra is a prerequisite of any kind of maths maturity goal.

I think, personally, maths is an incredibly important field and there's a feeling that some degree of comfort with it will help me in more ways than I can imagine. That is, however, an opinion formulate after some self study based on a great interest in the field.

It fascinates me that even things we take for granted, such as addition and multiplication, has entire subfields that have generalised the structure of those operations over those types of sets (in what's taken for granted: addition and multiplication over the set of integers). What's even more fascinating is that this work has had an impact on other areas of deep interest e.g category theory and Haskell.

Right, in fact the interaction between multiplication and addition is one of the most fundamental forms of chaos due to combining recursive operations. One could say, addition is repeated counting. Multiplication is repeated addition. And the interaction between the two points a finger at the relationship between space and time.

And yes I agree. It is glorious that the binary operations that seemed so natural to us formed the basis for groups, rings, and fields. Associativity, commutativity, distributivity of two related operations are quite the pearls :-) Its also interesting as a programmer and from a "properties of functions" perspective to study magmas and semigroups and groupoids..etc..

Knowing more about abstract algebra in terms of special properties of functions has led me to believe that most programmers are missing out on some of the beauty of functions by merely implementing them and not so much understanding the common properties and classifications of them.

Does anyone have like, a map or presentation or article or something that will give me an intuition of how vast maths is?

just go to the local university library and look at the math section. :P

to give a personal anecdote, i often commented with my fellow graduate students that our first two years in graduate school were spent merely getting to the 1950s in terms of mathematical technology. most people who graduate with a bachelor's in math only know math up until the late 1800s and early 1900s at best.

mathematics is the hardest intellectual activity i have done, and it has made my job as an engineer and software developer much, much easier. the ability to abstract yet get down and diry with details is something math beats out of you.