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Anonymous Fri 31 Jan 11:08:59 2020 No.11347898 View Reply Original Report

Quoted By: >>11347950 >>11347958 >>11347964 >>11348003 >>11348615 >>11348920 >>11349403 >>11349419 >>11351490 >>11351492 >>11351523

Is proving theorems in mathematics something that can be learned?

I study mathematics at university and while I'm doing very well in almost every area, I just don't understand proofs and I'm starting to think they can't just be learned like everything else.

Do you think you need some "creativity" that you either have or don't have?

Anonymous

Anonymous Fri 31 Jan 2020 11:34:11 No.11347950 Report

Quoted By: >>11347990 >>11348373 >>11349428

>>11347898
>study mathematics at university
>I just don't understand proofs
those sentences are mutually exclusive

Anonymous

Anonymous Fri 31 Jan 2020 11:37:40 No.11347958 Report

Quoted By: >>11347990 >>11348376

>>11347898
>doing well in almost every area
Buddy's taken Calc 1 and a logic class. All university mathematics are is proofs. Switch degrees.

Anonymous

Anonymous Fri 31 Jan 2020 11:43:49 No.11347964 Report

Quoted By: >>11347990

>>11347898
>Is proving theorems in mathematics something that can be learned?
No, it's genetic, either you are born with the ability or not.

Anonymous

Anonymous Fri 31 Jan 2020 11:54:18 No.11347990 Report

Quoted By: >>11348577

>>11347950
>>11347958
>>11347964
Anons, I don't mean I can't prove anything, I mean I struggle with complex non-straightforward proofs more than anything else. I'm getting 85%+ in almost every module, but proof is very difficult to me.

Anonymous

Anonymous Fri 31 Jan 2020 12:00:20 No.11348003 Report

Quoted By:

>>11347898
>proving theorems.. something that can be learned
Yes. In the same sense that being a good quarterback can be learned.

Anonymous

Anonymous Fri 31 Jan 2020 14:56:15 No.11348373 Report

Quoted By: >>11348570

>>11347950
not mutually exclusive.

Anonymous

Anonymous Fri 31 Jan 2020 14:56:52 No.11348376 Report

Quoted By:

>>11347958
nope.

Anonymous

Anonymous Fri 31 Jan 2020 16:17:05 No.11348551 Report

Quoted By:

What is the final solution to the MQ?

Anonymous

Anonymous Fri 31 Jan 2020 16:23:27 No.11348570 Report

Quoted By: >>11348994

>>11348373
getting enrolled, sitting trough lectures, reading notes does not mean you are studying mathematics.

Anonymous

Anonymous Fri 31 Jan 2020 16:26:33 No.11348573 Report

Quoted By: >>11348661

Yes.

Takes time and exposure, nothing else. Just have to study, dig deep and write as much as possible. That's genuinely the only "fix".

Anonymous

Anonymous Fri 31 Jan 2020 16:27:21 No.11348577 Report

Quoted By:

>>11347990
so you have problem with reading proofs or actually proving things?

Anonymous

Anonymous Fri 31 Jan 2020 16:38:07 No.11348615 Report

Quoted By: >>11348850

>>11347898
Homework proofs are generally pretty formulaic. Each of the question's "givens" has a particular strategy you normally are supposed to apply to it. E.g. in calculus if you have an infinite set of points, then typically you are supposed to apply the Bolzano-Weierstrass Theorem to get a limit point. But you might have to try aplying something else. With practice it gets easier.

It's actually a lot like solving integrals.

Anonymous

Anonymous Fri 31 Jan 2020 16:56:52 No.11348661 Report

Quoted By:

>>11348573
>write as much as possible
how will this teach OP to understand proofs? Wouldn't it help him to stop and just ponder the logic of the argument until he has the whole thing sorted out?

Anonymous

Anonymous Fri 31 Jan 2020 18:09:54 No.11348850 Report

Quoted By: >>11348973 >>11349447

>>11348615
I was the boss at doing retardedly ridiculous integrals, but I sucked at proofs in pure math. Specially continuity proofs in any analysis field.
I am a physicist by training, but I studied some pure math stuff in my masters and I just had a hard time doing proofs. I never knew if I could actually make a statement from one step to the other, I had a hard time knowing if a step I was writing was actually valid, or if I was skipping too many steps. Also, the fact that most proofs are just manipulation tricks that give no insight (geometrical or logical) into the problem being stated is absolutely infuriating.

Anonymous

Anonymous Fri 31 Jan 2020 18:39:33 No.11348920 Report

Quoted By:

>>11347898
math student here, yes, I think that the "creativity" that you need for proving non trivial results is something that, far from being innate, can actually be learned. I personally consider that the "key" to learning how to prove is to have a clear understanding of what it is that you're trying to prove beforehand. Don't just start moving formulas around. Start thinking: "well, what would be convenient for my proof to work out the way I want to?" Start with that. If it doesn't work out, bad luck, try something else that seems a little bit less convenient. Of course, sometimes people have "out of nowhere ideas", though afterwards you can always see where they kind of came from. But these ideas start coming to you with practise. To think that "creativity is innate and I don't have it" is just an excuse to not learn this skill.

Also, it is not necessary to always exactly remember every step of every theorem that you're currently using. That's just absurd. Whenever you don't exactly remember a theorem that you know exists, look it up in a book, that's what they're for. Not remembering all proofs for all theorems doesn't mean that you wouldn't be able to figure them out yourself given enough time (of course, you can always try to do this as an exercise). It just means that you're clever and you don't want to do some work that somebody else already did for you.

Hope this helped.

Anonymous

Anonymous Fri 31 Jan 2020 18:42:44 No.11348929 Report

Quoted By:

If you can actually understand it all but not prove it, maybe just fucking stop being an autistic sperg who cant read and write and try to slowly and systematically learn it properly?

Anonymous

Anonymous Fri 31 Jan 2020 19:02:22 No.11348973 Report

Quoted By: >>11350859 >>11351502

>>11348850
These are typical problems/complaints, particularly:
>I had a hard time knowing if a step I was writing was actually valid
This is something that comes with practice, feedback and time. Math-major students have these problems for proofs in general well into their second year of training, and then again somewhat for each new subject. Practice and feedback. You can even post proofs here if you like.

Anonymous

Anonymous Fri 31 Jan 2020 19:12:46 No.11348994 Report

Quoted By:

>>11348570
who claimed it did? take your meds

Anonymous

Anonymous Fri 31 Jan 2020 21:11:34 No.11349403 Report

Quoted By: >>11351461

>>11347898
Proofs=/=deduction.
I bet you can indeed understand proofs, they are a boolean equations that taking past axioms and theorems equal to true on the right. Learn your boolean operators with a logic book or something.
The proofs in books are often a compact ""elegant"" form that doesn't tell you much about how the result was discovered, because that much is kind of irrelevant as long as you can understand that it is true.
Some proofs even took years to arrive like the ones on real analysis, even if people intuitively knew some results nobody proved them without intuition.
Intuition is not a way to do proofs, you find propositions that you want to check for trueness and work your way from there. Just let this sink in, calculus was hundreds of years old before proofs for limits were made.
First step to understand them is making this difference clear.
Where intuition doesn't help you will be around checking the trues and falses, somehow you will end up with a true statement of something counter intuitive and that's part of math.

Anonymous

Anonymous Fri 31 Jan 2020 21:16:33 No.11349419 Report

Quoted By: >>11349434

>>11347898
>I just don't understand proofs
maybe you should switch to physics or computer science, seriously

Anonymous

Anonymous Fri 31 Jan 2020 21:20:36 No.11349428 Report

Quoted By:

>>11347950
so show me the case of studying math without understanding proofs.

Anonymous

Anonymous Fri 31 Jan 2020 21:21:30 No.11349434 Report

Quoted By: >>11349494

>>11349419
>computer science
>without understanding proofs
Hmmmm

Anonymous

Anonymous Fri 31 Jan 2020 21:25:01 No.11349447 Report

Quoted By: >>11350859

>>11348850
my proofs teacher in undergrad said something to me once that always stuck with me. It was something to the effect of "whether a proof is good or not depends entirely on who's reading it"

so a proof that looks and seems logically tight to one person would seem confusing to another. it just depends on who's grading it and what they're looking for. Generally in real life things don't need to be proven so meticulously down to the exact details since if you're publishing, other smart people will be reading it and be able to fill in the gaps on their own. proofs in school are pure autism since you're proving things that are usually very obviously true

Anonymous

Anonymous Fri 31 Jan 2020 21:39:28 No.11349494 Report

Quoted By:

>>11349434
I can post final exams from upper division Math courses at top unis if you want to be a faggot. There is a great difference between simplistic combinatorics and algo proofs and doing proofs in a senior level diff geo course.

Anonymous

Anonymous Fri 31 Jan 2020 22:13:31 No.11349592 Report

Quoted By:

The pepes shaking hands should be labeled conservatives.

Anonymous

Anonymous Sat 01 Feb 2020 09:30:44 No.11350859 Report

Quoted By:

>>11348973
While I'm now working in the industry, I am actually studying Stochastic Analysis non my free time, so maybe I'll do some threads here when I'm stuck doing the exercises (proofs).

>>11349447
It's not the fact that I cannot understand the logic, I can see it. But logic involved in each step for most proofs is too short for actually understanding and visualising the statement you're trying to prove. I wasn't mentioning a case "oh, I cannot understand how he went from here to there", I could that when I was studying. It's a question of "why did he manipulate this into that?". You cannot tell me that what is usually called "a book proof" is something for which the quality is in the eye of the beholder. It's not, book proofs are typically condensed results after decades of trying to make things more "elegant" and often the original thought process involved in proving the statement was just substituted by clever tricks.

Anonymous

Anonymous Sat 01 Feb 2020 15:20:24 No.11351461 Report

Quoted By:

>>11349403
This was my point. We cab visualise a lot of results. Check the initial statements, represent them visually (or geometrically) and you might able to infer some of the conclusions. However, the logical proof that is given to students often holds no information that would help us better understand the result being studied.

Anonymous

Anonymous Sat 01 Feb 2020 15:34:24 No.11351490 Report

Quoted By:

>>11347898
No. I tried. Worst thing you can do is try reading one of those "how to solve it" books. It is like reading on how to become Michael Phelps. "just have long arms and swim faster".

Anonymous

Anonymous Sat 01 Feb 2020 15:35:27 No.11351492 Report

Quoted By:

>>11347898
This is honestly everyone's experience with proofs. It's a jump in abstraction like when you go from doing math on numbers to letters in elementary school. Just keep at it and you'll catch it.

Anonymous

Anonymous Sat 01 Feb 2020 15:38:47 No.11351502 Report

Quoted By:

>>11348973
>feedback
that may be the key element of why you can't teach yourself proofs. mathematics seems like something you can learn on your own but it may be a fallacy. like learning a musical instrument. you can learn the guitar (badly but enough to feel good about) but you can't learn how to play the trumpet on your own.

Anonymous

Anonymous Sat 01 Feb 2020 15:46:36 No.11351523 Report

Quoted By:

>>11347898
You can have IQ over 180 but if you non-creative person i guess then you are kinda that type of guy that works like computer, he need a data input before he will do something. It's not like peoples aren't creative at all or at least i hope so it's more about how your own mind is working. If you have internal conversation and solving problems where do you go ? Are you strictly doing it by the rules that you know or you are trying to find out new way to solve the problem. When it comes to me i'm not smart it's just how it is it takes me a long time to connect dots but at the other side i'm creative like maybe it's harming me sometimes because i solve problem and keep overdoing it until i find at least another 10 ways how to solve it again. I just have to use my mind to create a new solutions or otherwise it would be just too much pain for me just not trying something else there are people who are perfectly fine with paths that where set and it's ok as soon as you are happy to do so.

When it comes to math it's just kinda same, you can work on new problems applying methods that are known or trying to create a new one but in this case you will be one who is much more slower when it comes to things that are unknown for you.

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