Just create a cat with Fourier series.
I feel like understanding concept by visualization really helps!

I have nearly finished my Masters in Maths, I don't have great marks but I passed. I also have ajoint undergrad in Maths and Physics with hons. I don't want to stop studying this subject but I also don't think I have the grades to be accepted on a PhD or research program, let alone the money! How can I continue developing and use what I've learned?

scoring 100% on it is so much easier than scoring an A*/9 on GCSE Additional Mathematics, to the extent where this gap in level of difficulty is equivalent to the difference in difficulty between:

- scoring an A*/9 on GCSE Additional Mathematics

and

- scoring a perfect 42/42 score (not just a gold medal) on the International Mathematical Olympiad exam

I.e. the jump in mathematical ability from scoring 100% on a hypothetical math exam 'X' to scoring an A*/9 on GCSE Additional Mathematics is equally as profound as the jump in mathematical ability from scoring an A*/9 in GCSE Additional Mathematics to scoring a 42/42 (not just gold medal) on the IMO exam.

How easy would 'X' have to be for this to hold true?

Formalized in Lean: an unconditional lower bound on the proportion of simple zeros of ζ(s) on the critical line, at 0.673401159168. Not a proof of RH — just a density/simplicity bound built on the zeta23 package. Repo + build instructions: https://github.com/VisionToSolution/zeta673401159168

I am a fresher in tech, although, my career goals lie in Cybersecurity, I am very fond of Mathematics, like really (have become fond of it recently), I want to learn more about calculus, tackle Real and Complex Analysis, Topology, and Number theory,.... When I get bored, sometimes I just trying to find any patterns appearing in prime numbers, I fail every time but sometimes one hour goes by and I don't notice, I like integration a lot, more than differentiation or differential equations, I'm in love with Calculus and Number theory part of maths, And, I do want to Learn Quantum Physics and Astrophysics, and i want to research in either mathematics or physics alone(not in a uni), and treat it as a side hobby or a relief work

This video is a beautiful example of a particular facet of geometry. He isn’t the first to use them but M. C. Escher’s work is fun inspiration for tilings and tessellations.

Im curently second year in my pure math program, i have already passed classes such as : Real Analysis 1,2,3, Linear algebra 1,2, Number theory, Analytic geoemtry, Disrcete math, Math logic and peano axioms, Topology.

I liked number theory mostly because of problem solving and i was practicing with my friend who has won medals at imo, so it was fun.

But now i have subject like complex analysis (oral exam every week with professor for 13 weeks ) , set theory(failed it first time i was bored to atudy it), probabikity theory, diferential equations, euclidean geometry and when i take a look at them, honestly i couldnt care less about any of them i dont care what is differntial equation or some proofs of theorem every subject is proof based, in complex analysis for example we do stifd like sequenxes like i just dont care anymore for epsilon >0 and other things. I mean i can learn ir for exam with heuristics algorithklms and pattern recognition but thats not the point, i can passed those classes its just i dont care anymore. I passed basic and aevanced linear algebra i dont know nothing, myb notbnothing but i forgot so many trivial things. I dont know am i burned out or should i leave math, some professors and teaching assistant heard about that (small university) and told me that i shouldnt but i just cant anymore. They say i am good for example in topology i was attending lecturew i was bored, j took the exam , on one part proofs i got 97 /100 on theort part from lectures( we got 3 theorems from lectures, i knrw only one, first two theorems i saw for the first time in my life on exam because i didnt attend lexturew but i ewrote out of despair i didnt think i was gonna get more than 10 points but i got on those 2 theorems 40 out of 60 points. I just think it was huge luck, nothinf special. I dont know should i leave math or am i just burned out

Im in pure math

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To begin with, let me remind you that mathematics is not a science fortunately and that it is perhaps one of the largest organized, consistent symbolic formal systems for developing something: maybe intellect, maybe a certain form of thinking, maybe someone understands more clearly what exactly mathematics develops and can tell us about it.

And whatever it develops in us, there may immediately be a temptation to say functionally: well, then mathematics is needed precisely for developing this, Robert Wide.

The difficulty is that although there are interesting things in it, such as topology, or interesting theorems and models, and especially what seems important is the economic, technological, and research contribution of mathematics,

And yet it seems that this formal system stalls a person and makes it harder for him to think outside this formal system. Of course, one can say this about logic too, and about their similarity, and in general about any old systems of thought or let us call them closed or “controlling” ones. To some, dialectics may also seem like this, though to a lesser degree, and it is precisely dialectics that sets the task of sublating contradiction and arriving at generalization and understanding, that is, in an ethical sense it is a more encompassing system of cognition in the sense of its capacity — though often in verbal form to include something else and incomprehensible in its understanding. And if we abstract from formal dialectics, if you have ever heard these expositions, then the ethical idea and, as it were, real dialectics in full non-contradictoriness and some communication, for example as metamodernism, is the same dialectics or synthesis between sincerity and so-called postmodernity or irony.

Dialectics is still an example, not a proposed answer. Although it could perhaps be one of those considered.

Returning to mathematics. Despite its outstanding economic, technological, research possibilities and achievements, and as a result also social and political ones… it still remains rather abstract. One can say that it is the most complex, or one of the most complex, games of the mind, or games within the mind, or separate games within the mind. But for the mind itself this seems like something akin to sophistry or magic, though a very useful one. Or one can say that it is a magical system, or one of the magical systems of this world. But it is almost always something very abstract: it seems to me that this is often said about philosophers too, by those who do not delve deeply into philosophy; but those who do delve in, on the other hand, can understand that we often reflect on the most important questions or phenomena that we can feel or think. As far as I understand and it is not known how much the answers may still differ mathematics is a system of ultimate formal complexity, or of ultimate complexity for thought in general, since in one way or another what we formulate as philosophers often, though perhaps difficult, has a clearer representation of reality, even if it is Lacan’s Borromean rings. In the sense that philosophy, apart from again sophistry, usually does not strive to become complicated simply for the sake of complication because why? It seems that a person, after this stage of formal logic, can also learn other possibilities of thinking. But in mathematics, complexity and possibly even not necessarily, but possibly the degree of abstraction seems literally the quintessence of content. On the other hand, of course, this may also be good. In the sense of ultimate complexity, ultimate constructiveness, ultimate abstraction, in the sense that we as a culture have some content, some achievements that we may still have to comprehend, if some of them can be so complex that there are literally 400 pages of formulas of explanation.

But, like, why?

And returning to what we were talking about, this seems like ultimate sophistry or thinking in idle, in the sense for thought itself and for man, although culturally it brings enormous social results: both economics and technology and research and efficiency.

And even if we assume that mathematics is integral thinking rather than specific thinking, then although it is clear why mathematics should be developed: so that there can be a further possibility of development…

What for, and what from mathematics, and should it and it or they even be present in education?

Because even if we may have grounds to think so but even if mathematics is connected with integral, that is, general thinking, that is, as it were, some generalized function of it, the mathematicality of education then creates a situation in which a person tries to wipe the sofa with a processor without imagining what a sofa is.

And if not, and mathematics is more specific thinking, that is, in the sense that it also remains there and in a constant submetacognitive state: in the sense that it fundamentally cannot leave the box and its language and its formality or formalization… then such thinking is good for producing human-computers useful for working with ordinary computers, for example in a bank or somewhere else. As a result, man has, as it were, given his brain to mathematics, and how is he supposed to live further? Well, that is, then perhaps also the market, where this mathematized brain may be valued higher than the self-esteem or self-understanding of such a person, and so the puzzle comes together: successful recruiting into a successful company.

I will say right away that simply “progressive studies,” which may even be not thinking but to some extent dogmatic propaganda or propaganda at the expense of education hours, trying to lean on Marxism or performatism according to Butler, are, as it were… Well, people can learn something valuable, but on the whole it seems that this is simply the disintegration of education, or rather almost its absence, or its replacement by propaganda so that in an economic-political sense these people could be ever more perfect agents of this very propaganda, possibly even without fully understanding it. And how lucky we are that we can look at this from the outside, unlike the people and economies that this “progressive” propaganda may further repress. And the main complaint against it is probably economic, because a society simply without technical specialties loses economic opportunities; only oligarchs remain, and they would most quickly move to a new place. And in a universal human sense, this is potentially the next target and problem for the next intellectual stratum that will try to do something about this repressiveness. If, in general, there will be anyone left to do anything there.

In general, why was this clarification about “progressive” or agenda-driven education? So that this question is not in support of that very agenda, and, as it were, we understand in advance some of the existing difficulties there and have described them.

And still, the question: is mathematics needed? And such mathematized, formalized thinking — and then we are surprised by further formalizations and the resulting difficulties, such as bureaucracy and media simplification and corruption in many senses.

Additionally:

Maybe the form of my question is a bit of Soviet thinking or a way of thinking about something, and if you understand another or other better ways of asking or thinking about this, you can say so.

IM A POSTGRADUATE STUDENT IN MATHEMATICS AND IM STRUGGLING WITH A PROBLEM I CAN REMEMBER THINGS FAST BUT I ALSO FORGET IT FAST. ALSO I KNOW RHE THINGS BUT IM NOT ABLE TO APPLY IT IN TIME AFTER SOMEONE TELLS ME YOU CAN USE THIS THAT TIME IT CLICKS ON MY MIND . HELP ME WITH THAT PLEASE