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I struggle at proofs but can do statistical inference or actuarial probability problems like Hogg/Mckean/Casella/ODEs/Calculus because I find that the exercises are similar to the examples.

In a proofs based class, I can't see how the problem I'm doing is similar to any classroom or textbook example.

If I work hard, I can memorize a proof, and some basic set theory proofs about deMorgan or powersets or induction proofs or cantor snake or the infinite many primes, injective, andsurjective proofs make sense. When I first learned doing proofs, I spent 3months asking about how to prove deMorgan's laws and figured how to prove deMorgan's laws by the 4th month.

However, proving that things are cauchy or converge, or doing abstract algebra with lagrange's theorem I'm lost. I trust the well-ordering principle, but to prove something is an injective subsequence is beyond my ability. I tried number theory and take class made no sense. I didn't understand CRT, euler phi function...

Memorization alone won't let me pass proofs beyond an introductory course because I won't be able to do the homework or take home exams and because other's can't always give me the answer on every problem.

At this point, I realize that I can't find a white collar job unless I figure out how to do proofs to become a machine learning expert, so I'm wondering what I need to do. I could resort to learning a blue collar trade.

Some graduate programs require proofs based classes even for statistical programs. While the biostatisticians may disagree about how much math is needed, I'm sure the cutting edge of machine learning is all done by math phDs who require proofs knowledge in their programs.

I think I would have been better off studying Biology or Psychology or Geology and maybe dabble in medical organic chemistry/biochemistry because those are purely memorization but it's too late to change degrees. Even Physics might be possible because it's manipulating examples in the textbook to solve the problem.

Some person expert in math told me they think I can do proofs but it wouldn't be worthwhile to learn anymore and said I should study financial Accounting instead. Were they just telling me that I can do proofs to make me feel better?

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    At this point, I realize that I can't even find a white collar job unless I figure out how to do proofs to become a machine learning expert, so I'm wondering what I need to do.

    This is false. While being able to do proofs is really important in math, it's not so important in trying to obtain a lucrative job.

     – MathematicsStudent1122 Oct 03 '19 at 14:50
  • I don't have the skills to obtain a lucrative job. –  Oct 03 '19 at 14:51
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    I think you over estimate the math required for white collar jobs. Most of the job that requires a quantitative master degree wont require you to go any further than a linear regression. You will most likely never have to come up with or prove a new mathematic result throughout a while collar carrer – Frostic Oct 03 '19 at 14:56
  • Anybody can learn to write proofs, it just takes practice. Note too that memorizing a proof is not the same as learning how to produce a proof. Memorizing a proof doesn't teach you the concepts you need to exercise and strengthen. You should look at the structure of the proof, to try to internalize what the techniques are. Stick with it, you will learn. – MPW Oct 03 '19 at 14:57
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    There are books that are meant to teach you how to prove things. Have you had a look at them? – Theoretical Economist Oct 03 '19 at 14:59
  • I've take an 2 semester long course on this. Didn't come out knowing how to prove it. Doesn't the fact that I remember cantor snake or injective sequence show you anything? –  Oct 03 '19 at 15:00
  • if I could program computers, I'd be fine Max FT, but I don't. –  Oct 03 '19 at 15:03
  • I've practiced and thought about it and got nowhere useful. –  Oct 03 '19 at 15:08
  • @Germania the most lucrative job I ever had I stumbled into as a programmer. I worked for one of the wealthiest guys in NYC and the dude had a cult of followers in his office that did his bidding every day. I produced a high frequency market making trading program and was fired because they pressured me so much i got into a car accident and nearly killed. I can produce proofs. Trust me when I say no one cares. I can code too, but now even the "machine learning" jobs are just some idiots wanting you to click on predefined programs rather than create anything. I'm doing blue collar work now – crow Oct 03 '19 at 15:24
  • @crow what about joining academia instead? –  Oct 03 '19 at 15:49
  • @Germania I only have about 15 hours of college credit to my name, I'm self taught. I dont know how I would pay for it I'm already in debt. I wrote this paper http://vixra.org/abs/1702.0273 but cant get any constructive feedback from anybody so far and the mathematical editorial boards have always treated me with arrogance and hostility because my paper wasnt formatted precisely how they expected it to be. I would like to, be working in neuroscience or something like that as well, but i have no idea how to get there. – crow Oct 03 '19 at 17:16
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    @crow Put your bibliography and appendix on a separate page. –  Oct 03 '19 at 18:08
  • Given that the original asker has opted to delete their account, it's fine with me if we want to close this now (as I have voted to do). It's also fine if we want to leave it up, of course. – Aaron Montgomery Oct 04 '19 at 18:50
  • That's what I'm talking about. Nitpicking about bibliography rather than addressing the contents and statements of the paper. This world sucks – crow Nov 30 '19 at 00:44

1 Answers1

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I don't think this is really a question about math, but I hope that we can leave your question up. I sense from your post that you're feeling lost and hurt, and I'd like to (try to) help.

I want to be both kind and blunt. It seems like the crux of your problem might be a problem of maturity. Reading into your post a bit, it seems possible that up to this point in your mathematical career, you have succeeded in your math classes by doing a process like this:

  1. See problem
  2. Find similar problem
  3. Copy similar problem's solution (to the extent that you can), adapt it where you must

If that is indeed what you've done, two things are unsurprising: (1) this used to work, and (2) it doesn't anymore. The unfortunate fact about this process is that whatever it is, it isn't math.

If you've been trained so far to believe that the process above was appropriate, and that doing that is what constitutes success in math, then that conviction is the essential problem here. What it means to do math is decidedly not to do a process like the above. Instead, mathematics involves something much harder to grasp; it's careful thought, exploration, experimentation, finding patterns, constructing arguments, and things like that.

Imagine a person who believes very early in their schooling that they are very good at math because they know all their multiplication tables. If you give them a pair of two-digit numbers, they can multiply those numbers quickly and efficiently, and they can give you a correct answer. And yet, somehow when algebra is introduced into the discussion, they are lost. They cannot conceptualize what it means to have an unknown $x$ and to solve for it symbolically. This person has mastered arithmetic, but algebra remains mysterious to them.

The problem I described above is not your problem, of course, but I think it's analogous to your problem. You're having a difficulty making a transition to the next level of what genuine mathematics is. Please let me affirm this first: Math is hard. It's OK to struggle with it. I have, as has (I believe) every other poster on this board.

If we accept the premise that your most serious problem is a lack of understanding of what math is, I think a close second is a crisis of confidence. You approach this issue with some language that concerns me: you're worried that others are lying to you "just to make [you] feel better," you worry that you "don't have the skills to obtain a lucrative job," and so forth. I will warn you: If you believe these things, they will remain true. You can grow your skills. You can gain new abilities. You have more potential to adapt than you believe.

I could tell you stories about times in my schooling that I doubted myself. I could write pages just about the time I had a panic attack, collapsed on the floor of the bathroom in graduate school, and contemplated my future as a mathematician while trying not to vomit. (Spoiler alert: I now have a PhD and am a tenured professor at a liberal arts university.) I think the most useful thing that I can do right now, though, is just to emphasize that nobody starts out as a finished product. Everyone struggles, and everyone must go through the painful acts of learning and growth.

Only you can decide what the future holds for you in mathematics. I would love to tell you that I believe that every human holds the same capacity for mathematics; however, in truth, I don't know if that's really true. What I do believe, though, is that every human holds the capacity to do enough mathematics, whatever that means for them. Consider the useful analogy of running a mile. I believe that no matter how hard I train, I will never be able to run as fast as Olympiads. I certainly lack the physical qualities needed for that, but I think I probably also lack the grit and determination required to do that. However, I can run a mile in 8 minutes, and in the past, I have worked hard to get that down close to 6 minutes. The point is that even though I never had a future as a professional runner, I shouldn't think of running as something that I'm not good enough to do. I can run as fast as I need to for my purposes, such as chasing my kids around or making it to meetings across campus.

I believe, without knowing much about you, that you can do as much math as you need to do. Only you can decide how much math that is. But I promise you that you will be limited by your own imagination if you allow yourself. It's probably true that you need to change your study habits, and perhaps even your entire approach to mathematics. But you can do those things.

I would strongly encourage you to speak with people you trust about this. Start with friends or family; branch out to an academic or career advisor. Consider also a counselor or therapist, and do not feel shame about doing so. Gather as many opinions as you can. Retain the ones that are useful, and discard those that aren't.

I'm sorry that you don't believe in yourself, and I'm sorry that you're hurting. Please remember that you can adapt -- either by improving your skills in math, or by finding something more suited to your interests and skills.

Aaron Montgomery
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  • I know what math is. But knowing what it is doesn't make me any more capable of doing it. I also hope I know what machine learning research is, or what machine learning should be from a mathematicians' high standards perpsective. –  Oct 03 '19 at 15:37
  • @Germania Understood, and I hope you didn't find my answer to be condescending. The shortest answer to, "Why does it seem like I can't do abstract math?" is in short, "You haven't yet, and it's new." Again, I'm very sorry for the pain and confusion you're feeling. I encourage you to both believe in your capacity to grow, and also to talk frankly with people you trust (ideally someone who knows some math) about this. – Aaron Montgomery Oct 03 '19 at 16:33