In high school, before having begun with a degree in mathematics, I derived pleasure from studying [mathematics]. At that time, I was naturally looking forward to university, since it meant no more subjects that I found uninteresting, such as languages, and instead complete focus on what interests me. I am now a semester and a half into my degree, and find the passion I have once felt fading. I believe there are several reasons: I underestimated the difficulty and was ill prepared (from a 'study technique' perspective), resulting in having to catch up through only understanding things superficially (for example, skipping proofs). The situation has improved this semester, but nonetheless, I am having trouble gaining a deep understanding due to the workload being very heavy (too many courses, in my opinion), and therefore only having time to gain a broad but shallow understanding overall. I also simply find some courses to be incomprehensible and would much prefer studying the topic from a book, by myself. A major factor contributing to my sentiments is the lack of the freedom I had before, in choosing what I wanted to study and going at my pace, as well as picking the resource I liked the most. I should note that despite feeling this way in the first semester as well, I passed with satisfactory grades (above-average even, perhaps).

One potential solution I am considering is choosing several books to self study the topics covered in the courses (and hence not going to the lectures). Most professors put their lecture notes online, so I would be able to see which theorems, etc. were presented. Despite this, there is still the risk of missing out. In any case, I plan to revisit and review everything during summer holidays.

Did anyone face similar feelings during their studies (not necessarily in mathematics)? What did you do?

Edit: I am located in Central Europe. I should specify that I did not like high school math (lack of rigor). What I liked was the free time (compared to now) that I had, which provided me with the opportunity to study more advanced math on my own.

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    Have you discussed this with any of your professors? Commented Apr 22 at 22:50
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    – cag51
    Commented Apr 23 at 2:35

19 Answers 19


Yours is a surprisingly common experience, so do not think there's something wrong with you.

I submit that what you are in fact disliking is not mathematics itself, but the academic structure that a higher mathematics program imposes on students.

Everything you've described suggests that if you had the option to explore at your own pace and choose the topics you want to study, that you would be far more motivated. So it's not that you are losing your love for mathematics, or disliking particular aspects of mathematics, but rather, you are unhappy with the way it is presented, which perhaps feels rushed, unmotivating, arcane, and fraught with pressure.

My advice to you is that you don't have to become a research mathematician in order to enjoy mathematics. For most students, it takes a certain willingness to tolerate or endure the academic structure of a degree program, irrespective of the area of study. Few, if any, pursuits in life are completely free of struggle, disappointment, or failure. Few allow total flexibility without consequences or sacrifices. As such, pay attention to your tolerance level for discomfort. I'm not saying you should accept your lot and struggle, but I'm also not saying you should do whatever you want, because disappointment is to be found with both routes. The best way to proceed is to avail yourself of as many resources as you can: professors, instructors, and/or research advisors; university counselors; friends and classmates; family. Take stock of yourself. Ask others what they think and if they might be able to help, because maybe they can provide you with tools that you might not have been aware of.

Success often involves knowing when to persist and when to change paths, and forgiving yourself when you don't know.


As someone who did a mathematics degree and can see myself in your comment, I hope I can provide some advice. I felt much like you did for the first two years of my degree: skipping proofs in a vain attempt to "keep up", relying upon old methods of study that simply did not serve higher mathematic study properly, pushing myself altogether too hard in the wrong ways and burning out. It is not a recipe for understanding, let alone mastery.

Here are the hard truths you must understand:

  1. Mathematics is proofs. That is all it is. If you do not take the time to understand proofs, you will not understand mathematics. Skipping proofs in maths is like skipping chapters in literature. Mathematics is also a very "buildable" subject, if you miss blocks at the bottom, you will not be able to learn higher order concepts without going back.

  2. You may currently not be at a stage of learning that's sufficient to cover everything on your courses. I wasn't. It's not that it's not understandable to you (I believe strongly in the maxim that "If someone understood it, it is understandable"); rather, you simply do not have enough time to cover all the material in the necessary depth for an exam.

So, what can you do?

Firstly: Stop skipping proofs. Your lecturers will be showing you every proof for a reason, and many of your answers will be adapted forms of proofs you have seen. You are assessed on two things: your ability to reproduce proofs you have seen (which you can't do if you skip them) and your ability to adapt proofs to new contexts (which you, repeat after me, can't do if you skip them).

Secondly: If you really don't have the mental capacity to cover everything before the exam/sheet is due, you need to learn to strategise. I took an approach of "Just learn as much as possible". Many of my courses (in my third and fourth years, once I wised up) I studied about 2/3 to 3/4 of before the exam, very few I had a good understanding of 100% of. I would create Personal Learning Checklists using the course spec and the lecture notes, and I would go beginning to end trying to understand as much as possible.

I hope this helps, but please: Don't skip proofs!

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    Thank you for the honest advice. I am very well aware of the importance of proofs, which is why it bothers me so much having skipped some. I plan on rereading all the ones I skipped during summer holidays. I am curious, how many courses did you have/is it typical to have in your educational system per semester?
    – RNX2D2X
    Commented Apr 22 at 17:26
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    I think that "Mathematics is proofs. That is all it is." is an overstatement. I say this as someone who finished undergraduate studies very proficient in reproducing proofs but almost completely unable to calculate examples. Commented Apr 23 at 12:53
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    Mathematics is proofs. That is all it is. - While some people may agree with this, I would say proofs are just one part of mathematics. See math.stackexchange.com/q/1296255/11323 for some discussion.
    – Kimball
    Commented Apr 23 at 14:08
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    I agree with the statement "Mathematics is proofs" in the scope of first few years of math courses, but carefully skipping proofs is also a skill every mathematician has to learn, in my opinion. There are theorems with extremely difficult proofs that run hundreds of pages, and there are theorems with pages upon pages of straightforward, but extremely annoying proofs. Understanding a theorem and being able to reproduce the proof are correlated, but in some cases only a little. Just don't want to OP to burn out even further memorizing every single proof he encounters. Commented Apr 23 at 18:32
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    @SergeyGuminov you don't have to memorize every proof. I don't think it is even possible. Understanding it is often enough. Skipping a proof because it is too long is risky, but sometimes understandable (after all time is a limited resource). Skipping a proof because it is annoying is a straightforward bad advice. Life is annoying. If you keep avoiding annoying things you will end up like OP. You can't do maths, or anything valuable in the long term without discipline, without facing boring and annoying things.
    – freakish
    Commented Apr 26 at 5:56

First, I agree with everything @Victoria-walker said, but I just want to add one more thing to consider.

Sometimes, what we think a subject is about at the high school level isn't what the subject is actually about when you get to the university level.

I suggest taking a step back and identifying what it was about your high school math courses that you most enjoyed, as well as what you enjoyed the least.

For example, if you enjoyed charting and graphing, analyzing data, and making inferences from it, but you hated proofs, then you would likely be happier in what we might call a "math-adjacent" discipline, such as data analytics or statistics, rather than pure mathematics.

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    I disliked high school math (no rigor). What I enjoyed was the free time I had, in which I could study university level math as I saw fit.
    – RNX2D2X
    Commented Apr 23 at 6:39
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    @RNX2D2X But what were you studying at that point that you're calling "university level math"?
    – lfalin
    Commented Apr 23 at 15:41
  • Good question; some set theory, proof writing, and introductory real analysis.
    – RNX2D2X
    Commented Apr 24 at 10:03

Note: This answer was written from a U.S. college perspective, and the OP later clarified that they're in Europe with a predefined all-major courseload sequence. Nevertheless I'll leave it for those in a possibly different context.

[In high school], I was naturally looking forward to university, since it meant no more subjects that I found uninteresting... [Now in university] I am having trouble gaining a deep understanding due to the workload being very heavy (too many courses, in my opinion)...

Is it possibly the case that, in your antipathy for liberal-arts subjects, you have registered for a full load of nothing but pure math courses?

If so, that's likely too many highly technical courses at once (and it's probably not what the recommended sequence for your program suggests). For my own math & computing students in the first two years (at a community college, admittedly) I usually recommend only 2 out of 5 courses in a semester to be critical-path courses in the major; maybe 3 at the most.

The first two years of an undergraduate degree are not generally supposed to be hyper-focused. Normally they're intended as a transition to a specialty, where you get an overview of many other subjects from working research professionals in the various fields. In my own case (as a math & philosophy major), I was delighted to be able to survey as many different subjects as I had time for.

If you're finding that the current load isn't working for you, then consider if you can and should reduce the number of technical courses you're taking at once.

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    I should have specified that I am from Europe. For the first two years, the program is pre-specified. As an example, our first semester consisted of Analysis 1, Linear Algebra 1, Group Theory (included proof writing), Computer Science, and Mechanics.
    – RNX2D2X
    Commented Apr 23 at 6:44
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    I don't think this answer works in Central Europe. We don't have much choice in courses and it is unusual or even impossible to choose courses that don't fit in the core topic of the major (I did a course in graph theory while studying applied physics, and this was questioned; non-scientific courses would not be recognised).
    – gerrit
    Commented Apr 23 at 7:10
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    I do think it works, at least in Germany. Yes, there are courses that you are required to take in the first few semesters, but you could still choose one or two of those and just do them one year later. Actually, that was very normal at my university because the workload was too high otherwise. Commented Apr 23 at 9:26
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    This is an interesting perspective but if pursued - if possible to do so - then it would mean a degree course much longer than usual in order to attain the same degree of familiarity as students of more focussed math courses - of which there are many in UK/IRL/EU. Yes, the student has a richer educational experience and hopefully a better social life - something desirable for usually introverted math students. Then again, math graduate hirers in financial sector and for graduate schools seem to want the elite always.
    – Trunk
    Commented Apr 23 at 10:06
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    In my experience in central europe, the first two years of university are very generic. For instance, students who will major in physics, maths, or computer science, are all mixed together in year 1; then they have to focus mostly on two of these three majors in year 2; and only in year 3 they have to focus on one major.
    – Stef
    Commented Apr 23 at 20:30

While, yes, "math is proofs" is partially correct, it is indeed also about phenomena, and our narrative(s) about them.

And, yes, the compulsion to formalize/administratize education leads to many dubious situations... where interesting subjects turn into formalized gauntlets to be run ... and for realistic success we have to figure out how to cope with this.

Not liking, or feeling oppressed by, much of the high-school or lower-division undergrad math in the U.S., is actually a positive in any test for mathematical sense, in my opinion.

For that matter, in my observation, "proofs" are introduced at a point where the facts in dispute are physically obvious (!), and, thus, the seeming demand for "proofs" is obviously perverse... so, seeing it as perverse is sane. Accepting it is, I think, at best a willingness to take on some crazy game, because it might be an adventure.

I do think there are many ways to feel sympathetic/interested in mathematics. The pretended pure/applied distinction is pretty dumb, but lots of people self-identify by one of those two labels, so they'll not be gone any time soon.

While you are young, you should study what you want, and not worry (yet) about what other people will think. For one thing, much of the internet-"information" is significantly flawed... AND, more seriously, your own understanding of the meaning(s) of what is said is seriously limited.

So, really, follow_your_interests, and don't try to second-guess yourself. Try to avoid squandering energy on worrying about "how to succeed". In the current U.S., you have plenty of room to try things that do not really succeed, and, then, try again, ...

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    So, really, follow_your_interests, and don't try to second-guess yourself. So are you saying here - in answer to the OP's question of how to sustain their love of math in a system where they haven't the time to cover all the content in depth - that they ought to pick out certain course topics and study them in depth ?
    – Trunk
    Commented Apr 23 at 9:57
  • @Trunk, yes, partly that: don't "force yourself" to study... Forced study is like "forced feeding"... Commented Apr 23 at 15:38

I absolutely loved math in high school. I did all the math competitions, took multivariable calculus and differential equations from a local college since I'd finished all the math courses my high school offered.

Then I got to college and took a course called "Math from a mathematicians perspective." It was all about proofs, and I thought it was the most useless thing in the world. I dropped my math major and switched to engineering.

While I don't really regret my choice, as I ended up loving engineering, I have come to love proofs and think that if I'd stuck with the program I would have been fine after understanding the beauty and usefulness of proofs. For me, my love of math came from being able to discover new and useful things and really get an intuitive understanding of how things fit together. Proofs just seemed like some rules you could follow if you didn't really understand something to still end up with the right answer.

Well, now I've come to understand that being able to be sure of your answer even without an intuition about it is extremely powerful. It can even help shape and improve your intuition, allowing you to really understand concepts that might formerly have been beyond your capabilities.

In terms of what you can do about struggling with following lectures an understanding everything fast enough, there's a few things I'd suggest. First as others have recommended, you need to find a resource that helps you get proofs and hopefully get a really good grasp on them over the summer.

Second, you already mentioned that it seems like the course load is too heavy. It might be worth it to see if you can lighten it, maybe plan to take an extra semester or two. If you can build a solid base of these new topics now, it'll really help with your speed of understanding things later. If it's solid enough you might be able to catch up.

Lastly, I'd try to evaluate what study techniques really help you get it the quickest. I know the way I learn best is by trying to explain the topic to somebody else, it helps me break it down into simple digestible chunks and helps me identify the areas that I don't really know that well because I can't explain them. That might not be your jam, but it's worth trying out some different things to see what might help.


You say that your experience is killing your passion for mathematics, but the fact that you long for the time to study mathematics on your own makes me suspect that something else is happening instead. Some theories that you can ponder:

  • Maybe your university experience is killing your passion for school (which is different from killing your passion for learning).
  • Maybe the legitimately higher workload, expectations, and stress of university are dampening your feelings of enjoyment in general (rather than specifically for mathematics).
  • Maybe you, like so many strong students, were able to coast a fair bit in high school and enjoy the win-win experience of academic success without having to try too hard or structure your time too consciously. Like most students, you're not experiencing that in university (you yourself mention a lack of study technique for example). Maybe part of your high-school passion was in fact an enjoyment of the ease and freedom of learning (and if so, it's perfectly natural to not be experiencing that in the current situation). But if so, it doesn't necessarily mean that your enjoyment of mathematics itself is any less—it's just that it's no longer augmented by the satisfying feeling of stress-free progress.

No matter what, definitely keep experimenting with ways to optimize your learning and your subjective appreciation of your chosen subjects!


This is natural and can happen to anyone. It also happened to me in my undergraduate courses. And even after that, when my major was geometry and I was studying logic something like a minor at the same time.

I think if one loves maths, one can fight the difficult situation and change the situation to some extent. Also, pay attention to one point, you have to go through the defined path of the system to get the documents and grades, While trying to improve the situation at the same time. (If you think that this compulsion to endure educational systems is a part of your mathematical path, the difficulty will be easier for you)

What do I mean by improving conditions? It is to follow the topics you are interested in. Choose the sources, textbooks and papers you like and immerse yourself in them. Search for lectures and seminars related to your favorite topics and participate in them. Study the papers and think about their concepts for hours or even days. You can send an email and ask the authors your questions. In short, study maths and enjoy.

  • I think OP is trying hard to do that but the extent of the content is overwhelming him. Please clarify your answer so OP had a feasible way forward in his situation. Remember he has to pass exams in math topics he dislikes as well as in those he does like.
    – Trunk
    Commented Apr 23 at 10:14

I also simply find some courses to be incomprehensible and would much prefer studying the topic from a book, by myself.

To me, this is possibly the most important part of your story.

For whatever reason, in academic settings on both sides of the Atlantic the belief has settled in that the best way to learn math is by listening to lectures. This is true at both the university level, and at the elementary and secondary level - you learn math by listening to a teacher or professor and watching them write on a board. Other subjects, like history, you might learn by reading a book - but math you learn by listening.

But in my experience, lectures are a terrible way to learn math, because the best lecturer will not be as precise or as clear as a textbook covering the same topic. And math has to be learned precisely, or it will either be incredibly difficult to learn, or won't be learned at all. I found math much easier to learn once I decided to essentially ignore the teacher or professor and learn directly from the associated text. Instead of "listen to me in class, and then open your book and do the problems on page 19" I decided to read pages 1-18 and then do the problems on page 19. Once I did that, concepts that seemed difficult or obscure became almost easy.

Text is a vastly better educational tool than speech. Find books that will teach you what you aren't learning in class, and work independently from those texts.

  • This approach certainly worked at school for me via Teach Yourself Calculus when I had a "teacher" who tended to the abler students only.
    – Trunk
    Commented Apr 24 at 12:29
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    This approach got me through an undergraduate program in math very successfully, but then pretty much crashed and burned in a graduate program. I was in kind of bad shape not having the tools to get help from professors and other grad students at that point. And the texts were arguably not as carefully written (with key insights "hidden" in parts of the problem sets, etc.) Commented Apr 24 at 16:46
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    Keep in mind that for some classes there is no "associated text" available, or the text does not cover all the relevant material. This was the case for over 90% of math classes that I took. Commented Apr 24 at 18:18
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    For whatever reason, in academic settings on both sides of the Atlantic the belief has settled in that the best way to learn math is by listening to lectures. --- For what it's worth, my recollection is that once reaching upper undergraduate level and definitely graduate level (U.S. perspective), lectures tended to be an overview of what you needed to carefully go back over on your own and/or with classmates (class notes, the textbook, related books from the library or elsewhere, etc.), with various guidance, tips, judgements, etc. thrown in, and maybe some missing steps in a text's proof. Commented Apr 24 at 20:55
  • Wish I could accept multiple answers.
    – RNX2D2X
    Commented Apr 29 at 19:18

There are subjectt student and professor combinations that make it just a better option to self-study

I am not in mathematics but computer science but there is a reason why reasonable universities to not require attendance for non-seminar courses.

Because nobody cares how you learn (and as opposed to high school you're likely old enough to learn by yourself).

So - if you have the discipline - absolutely do stay home and self study. Mathematics is especially well suited for this because - as opposed to soft sciences for example - there is far less ambiguity so it matters less "from whom" you learn.

I'd recommend going to all classes in the opening week to check out if there is a professor-class combination which style you like (and to keep somewhat in touch with uni life and to socialize) and stick to visiting one or two of the better ones, but don't force yourself to sit in classes where you know you'd be more efficient while self-teaching from books.

There is a reason why most professors present recommended literature in their opening lecture. It is to encourage self-study.

  • I plan on doing exactly this the next semester.
    – RNX2D2X
    Commented Apr 29 at 19:24

I'm not a math grad (I did eng/sci with a good level of math in it but nothing on a par with single honours/major-major math) so I can't advise you as specifically as some of the many other math professors on this forum could. That is, if they may be minded to share some of their own condensed wisdom on math study with you !

When we are studying anything, we are also learning to study more effectively and efficiently. Ideally we'd like our professors to focus on the core concepts that run through the vast majority of topics in our course and hammer them home as a foundation to our thoughts about any question arising on any topic. But they rarely do this. So it might be worthwhile now and again to take stock for yourself of what approaches you have been using in getting proofs, what patterns of development emerge from different math courses, what limitations apply to various math objects and so on. Whatever the core concepts are, they are likely to emerge again and again through your entire degree program.

I don't advocate study groups (even informal ones) to split up the workload as math people are necessarily individualistic and you'll have to derive your own proofs so as to satisfy yourself anyhow.


I had a somewhat similar experience, though almost inverted. I started at university planning to study computer science, found it was not what I wanted and ended up switching to pure/theoretical mathematics, after passing through a stint in philosophy and another stint in physics.

Everyone is different, and my experiences were in the USA, I'm not sure how different your country is. But I would suggest there were a couple of things that worked for me and might work for you:

Be open to exploring other topics. I wound up in pure mathematics as an undergrad, but I formally changed my major three times as an undergrad before graduating with pure mathematics. I then started a masters in theoretical math and wound up transferring to law school. You do need to eventually pick something to focus on, but at least in the USA the first year or two of university are often viewed as being for exploration of topics with specialization coming later.

Consider seeking tutoring or even remedial classes if needed Many subjects build on prior knowledge and coming into some subjects without the right background knowledge can be hard. While this applies in varying degrees to most subjects, it probably applies more to math than most other subjects. A tutor or even remedial classes can be very helpful if you feel you are behind. If those aren't available, then study groups can be very helpful. I wouldn't have passed Abstract Algebra without my study group.

Remember that it is hard for (almost) everyone. College is not meant to be easy. It is not at all uncommon to find the transition difficult. This applies to all subjects, though I would submit it may be more true in math and math intensive fields like physics than most fields. Don't be discouraged by the fact that adjustment may be necessary or that it feels much harder than high school. (Almost) everyone goes through that to varying degrees.


University math is not for everybody -- to make an analogy, as much as I enjoy cooking, I would rather progress as a home cook at my own pace than enroll in cooking school and start getting tested on French technique. One path is naturally self-motivating, the other, you have to generate your own motivation (other than "it'll all be worth it after four years!") lest you burn out. Both are valid options depending on what you want from your life and how fast you want it.

But given that you've chosen the latter path, maybe the following may help:

  • Behind all the proofs and exercises and tests, the professors are trying to teach you something profound about mathematics, but this doesn't always work so well. For example, group theory arose out of a long history of motivated and interesting problems, so by starting with modern group theory we are teaching it "backwards", giving undergrads all the machinery without any of the motivation. What may make it more interesting is by taking a more curious approach to it, asking questions of the text and theory, actively seeking intuition behind concepts. A Terry Tao article on this
  • However, this isn't always advisable with your limited time and substantial course load. Many times you'll have to make do with "understanding things superficially" and memorizing things, and do what you can to pass the class, and the intuition and understanding will follow as you develop mathematical maturity. You should not feel guilty or discouraged about this. For example, linear algebra didn't really "click" for me until two years after I took it, although I did well in the class. By remembering more from the class two years prior, even superficially, I had more to draw from and understand down the line.

Lastly, I would recommend How to Study as a Mathematics Major by Lara Alcock to add to your reading list...

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    "For example, linear algebra didn't really "click" for me until two years after I took it, although I did well in the class." Very reassuring.
    – RNX2D2X
    Commented Apr 29 at 19:28
  • Yep! To get on my soapbox a little bit: and as a general principle very few things (since high school) have made perfect sense and step-by-step clarity to me, not like working through your set theory and analysis books might suggest. Sure, there are the rare times when the teaching style/material/background knowledge align (or when it's too easy) such that the learning feels lucid and predictable. But I strongly believe long-term success comes from learning to deal with confusion and uncertainty and forging ahead anyways. Arguably, you are learning more in these states...
    – luk
    Commented Apr 30 at 20:25

This is my story, except I studied physics and I was more frustrated and disappointed. The only thing the kept me going was my insane amount of passion and love for Physics. I had issue with the pedagogical methods, altogether. What you need right now is a little bit more patience. After two or maybe three year, you'll see things will start to change.


Sincerely, that's the most common story when you talk with students of any engineering and technology school. Unfortunately... I was even a fierce competitor of those math/physics events back on school days, but as soon as I got into university, I practically developed a trauma of math for several reasons...

I also noticed that typical in-campus life made me kind of dislike being in front of a computer for long hours, since I worked/studied on it - and that's a serious thing for someone who left medical school for tech/eng for loving so much computers/technology. It was a completely different experience when I started my postgrad fully online. I felt I was really getting useful information and learning the right way, on my own pace, without having to rush to write down my notes and follow up with a human teacher who didn't even care who was attending or understanding the classes at all. Since you're in Europe, I recommend you looking for universities (specially German ones) that have an interactive & asynchronous online program and that matches your interests, and check if it's worth switching to it.

Step back and look at your situation from a wider angle. Just think about all the bad professionals (including teachers) you have encountered on life... do you want to become one of them? Forcing yourself to keep up with a bad situation just because others make you believe you have no choice.. it's just postponing the inevitable...

Do yourself a favor: take a deep breathe and think about the future you that's gonna make you proud of yourself and happier in your life.


I'll tell you my own tale. Loved math in high school. Did fantastically well, top of my class, great grades on AP tests, etc. Everyone thought I'd end up as a professor. Got to college for an engineering degree and skipped some of the early math classes due to my AP scores. That was a huge mistake. I got dropped into courses that I just never totally understood. I spent the semester floundering, never really understanding the math, just memorizing how to apply it. I got good grades, but I dreaded every test. Then I got to the next semester, and my lack of foundation caused me to again flounder. That continued throughout my education as math is pretty fundamental to an engineering education. I took to the practical aspects of engineering, and finally graduated, but I look back thinking I likely should have been more theoretical except for what happened that first semester in math. 30 years later I still regret it.

I'd suggest talking to your professors ASAP. I don't think this is unusual either. Maybe taking a semester off where you can just go back and audit the early courses, and read on your own. It may feel like giving up a year or a semester is an abject failure, but it's not. Good luck...


I suppose people enroll in universities for various reasons, but if one of them is the expectation that it would enable them to learn something they want to, then in the event that someone does not find universities productive or amenable to learning, a natural conclusion would be to focus on more effective learning strategies (for them).

Therefore, one suggestion would be exiting university, if you don’t find it useful.


This sounds similar to my experience studying Biochemistry and it mirrors most STEM fields, although mathematics is a special case.

When the material seems perplexing, baffling and frustrating, that is when most learning can happen. I would say don't give up. It is true the workload in university is a lot more than at school and it always rely of self study. It is so by design, you have to discover how to organise your time to achieve what you want to achieve there. Also mathematics is a subject that is painful until you reach the higher levels when you master particular techniques. Until you learn those techniques it seems difficult but once you learn them you open up a method for solving a new array of problems.

Finally, I don't think that many academic mathematicians make novel contributions to all fields of mathematics. You will in time specialise and focus on what seems interesting to you.


My personal experience with university, is that you have a choice between learning a subject, and getting good grades, but you can't do both. If you want to learn, you study all the proofs, and try to carefully understand all the axioms and main theorems. If you want to get a good grade, you look up solved previous year tests and assignments, and memorize the way problems are solved. If you have an average university workload, you're unlikely to have time for both, and even if you did, the two would be fighting for space in your head as well.

Another thing that may just be my personal opinion, is the sense that math is "taught backwards". You first learn practical models like natural numbers, arithmetic operations, real numbers, etc, and then gradually generalize up to groups and fields. It initially seems to make sense to not start with concepts too abstract. But somewhere in between, you go through things like path integrals over complex functions, where it no longer makes any sense without having the concept of groups and fields to even understand why complex numbers need to exist.

As a specific example, I personally found topology, with just a handful of axioms/definitions, a lot easier to learn and understand than calculus. Building up from axioms also makes it easier to make (and interpret) formal proofs with a lot less handwaving, and potentially with no natural-language text at all. I feel like most of the so-called "introductory" academic courses horribly underestimate how much of modern math is built on top of Bertrand Russell et al's creation of formal logic.

If you're interested in keeping your love for mathematics, and keep expanding your knowledge in it, the only solution for it that I'm aware of, is to turn to non-academic resources. You can often get a much clearer view of mathematical topics, their implications, and relevant proof, from resources like Wikipedia, Wolfram MathWorld, or Brilliant.

If I had to point out a difference, is that such resources are designed to teach you, while academics are designed to grade/filter you. Academics can gain prestige (sense of exclusivity) and money (stay and pay for another year) by failing you. Learning resources do not. Even with paid resources, if you're not enjoying yourself, or feel like you're not learning anything new, you'd simply unsubscribe.

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