[363849473754]

>“ There is a facebook group called "Topology Without Tears Readers" where readers of the book can communicate with each other. But this is definitely not a place to ask others to solve your homework problems. If you ask questions like "How do you solve the problem ...." your post will be removed and you will probably be blocked from this group.”

My complaint with this is the audience reading this book aren’t students in classes and likely a lot of them don’t have access to mathematicians or professors. Working with others is a great way to learn how to properly do proofs when first starting out. I think the FB groups / discord groups or whatever communities of learners should discuss their proofs and suss out difficulties or logical errors with each other.

This approach instead seems to assume the learner will know whenever they develop a correct proof but often one can just fool themselves into thinking their proofs are correct or even get utterly stuck. Or it assumes seeing solutions will “rob” the readers of learning.

Also, who really cares? Most of the people working through this book aren’t getting a grade from it. If they want to rob themselves of learning something just by seeing solutions without thinking first, then that’s on them.

Otherwise, beyond that complaint this seems like a good resource and it’s impressive it’s all free. I’d also recommend another topology book that’s free https://topology.mitpress.mit.edu/, albeit it’s more advanced.

[vector_spaces]

This is my complaint with a lot of math circles, such as the Math Stackexchange, where the amount of policing the motives of askers makes the site a very hostile place to newer users. Treat users and students in general like adults. Assuming bad faith at the outset makes math communities feel elitist and stifling rather than welcoming and playful.

[dav_Oz]

I’ve observed the phenomenon and I think it boils down to being poorly communicated on both sides.

An essential part of reasoning in mathematics comes from the experience of being repeatedly stuck.

Walking through an exciting “maze” for 20 minutes or a few hours most sufficiently motivated people can manage but it get’s harder and harder to endure when days or even weeks pass by and you feel like you have done an exhaustive inventory of every single item of your reasoning, uncountable times, feeling utterly lost. For my part I cannot even imagine being stuck on a single problem for years on end.

So, when there seems to be a reluctance to give away the answer, it is because a big part of mathematics is building up an arsenal of strategies to tackle different problems, and this is best taught through a variety of of build-up problems themselves which really challenge you at your current skill set. This of course widely differs.

It’s easier to get a good estimate if you know something about the person’s background but I can see this inquisitiveness coming off as judgemental and elitist. I’ve mostly found when you clearly can state ‘where’ exactly you feel stuck and which approaches you have tried you are heartwarmingly helped. To try to exactly pinpoint “where” your difficulty lies and patiently hitting the wall (building up a tolerance against immediate satisfaction/frustration) is how you will unlock the problems rather sooner than later.

That being said if someone asks me specifically for a solution which I happen to know, I provide it. Mostly because I don’t think you can force the aforementioned insights and I don’t want to put people into the general atmosphere - which I myself despise - of “explaining oneself”.

[actually_a_dog]

Treating people like adults (should) imply being kind rather than nice. While it could certainly be seen as "nice" to just give people solutions to problems, it's not very kind, as it deprives them of working through to the solution. IMO, hints should be encouraged, but only after the hint seeker describes what they've done and how they've approached the problem so far.