[Koshkin]

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

[marktangotango]

I also champion this method; I used solutions manuals as guides until I could internalize and reproduce the logic on my own. I was a particularly dense student though.

[chii]

being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking.

Also, if you can't prove a solution correct, then you haven't solved it!

[threwythrw]

>Also, if you can’t prove a solution correct, then you haven’t solved it!

This is the type of thinking I’m talking about. A beginner can think they “proved a solution correct” but have a subtle or even blantant error that isn’t obvious to them.

Also, if reader wants to just skip to the solutions then that’s their fault. But don’t let such people rob the student that put serious effort into their work from seeing the solution.

[ptd]

Is this a feature or a bug? If it takes you two weeks to apply creative solutions and it take me one week to apply a “rote” solution, what is the benefit?

[gbear605]

The idea is that it might take you longer to learn, but when you are applying it in the real world and hit real world problems that are messy, you’ll be a lot faster

[ptd]

That’s the idea. In practice does it actually work out like that?

[username90]

The main reason to study mathematics is to build and fix your intuition, hence studying rote solutions is a waste of time. It might help you pass the class but it wont help you much at all in other parts of life.

For example, at work nobody will care if you have rote memorized a solution or not since they will have already done the math, you will just apply formulas others have came up with. In order to do anything important with the math (not just solving school problems) you need to have intuition for it.

[threwythrw]

I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. True beginners may think they have solid intuition and a rigorous proof, but without outside validation, may have a blantant or subtle error they cannot see. The point is not to study rote solutions, but to check correctness.

Edit: To your reply below, I’m talking about someone that is self-studying and has no access to a teacher. The suggestion the beginner (without a teacher) should “know” whether or not their solutions are correct is something I disagree with.

I do agree with there are multiple ways to prove something and such a beginner may think their proof is incorrect based on a provided solution, when it may be correct, just different. This is why an instructor is valuable.

[username90]

> I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct.

Yes, which is why you want a teacher until you reach that stage.

> The point is not to study rote solutions, but to check correctness.

Looking at others solutions can in no way prove that your solution is incorrect so I am not sure how those would help you. However having access to others solutions often makes students doubt their own solutions if they don't look very similar, this hampers their growth since they learn to distrust intuitions which are actually correct.

[mindcrime]

It might not prove that your solution is wrong, but it can help show that your solution is correct (if you trust the provided solution), and if you made a silly mistake in your solution then seeing someone else's solution might well help you spot it.

[mindcrime]

Yes, which is why you want a teacher until you reach that stage.

Not everyone has that luxury.

[falcor84]

I absolutely agree. From my experience this is also true for the best professional mathematicians, it seems that generally they have picked a very large toolbox of memorized "tricks" that they can effectively (and intuitively) apply, rather than approaching every problem as if it were an entirely new challenge.