I'm glad you had success but...let's not measure your outlier experience with the rest of the world. Especially in Adv Mathematics.

I'd point you and other HNs to Srinivasa Ramanujan. He is self taught but...he was wrong [1]. He had a brilliant mind but...due to being self taught, he made some critical mistakes.

Being self taught can easily lead the learner to some critical mistakes. Eventually, they may be corrected (and at what 'cost' does this mistake cause an organization or business or those involved) but it's more efficient of someone's time to just learn from another. I'm not saying everyone needs a University Degree. I'm saying that everyone needs a teacher. Everyone. Why? Because instead of 'the blind leading the blind' (you as a 'blind' teacher, leading you as a 'blind' learner). You have the efficiency of being led by a mentor of some kind that can steer you away from faulty concepts that may come in.

It's great that we now have more free/cheap materials than ever before at our disposal but without a mentor or some kind of peer-review, we could be misapplying concepts.

Also, to comment on something you specifically said:

> Because in my companies view, being able to teach yourself all that math is much more impressive than being taught from a University.

Yes, it's 'impressive' but...most don't learn this way. Which is way it's 'impressive'. Also, being self-taught, how do you truly verify what you understand mathematically is accurate and solid? [2] You might be and I'm not going to fault you but learning concepts is one thing but applying them is even more challenging. It's one thing to be 'impressive', it's a whole other thing to have mastery over a topic. And I'm a firm believer mastery is mostly achieved with peer/mentor feedback.

I applaud you but let's not steer others to just teach themselves, without help from others. Let's encourage self taught and peer feedback. It's not one or the other, it's both.

[1] - https://www.youtube.com/watch?v=jcKRGpMiVTw

[2] - I searched for 30 minutes to find this article, that I read, that stated the current environment of Mathematical Research [3]. Namely, it stated that a lot of research is being published that is NOT peer-reviewed because there isn't enough skilled* Mathematicians to review the work. That it's a 'dirty little secret' in the industry that "known" Mathematicians would get a pass (published w/o review) but many others trying new groundbreaking ideas couldn't get their research peer-reviewed. And with the given University culture to publish NEW research and not review, it's understandable how this environment was created. Namely, Einstein gets the fame but it took numerous people to peer-review his work before it was accepted.

[3] - I know this article exists. It's one of the reasons why I'm becoming a Mathematician. I read it in the past 2-3 years. It was a major site (NewScientist or something that focuses on emerging research). If you can find it, I'd be very grateful. I'm now* using Zotero to save all my findings, so hopefully when I quote something I'll have a source. ;)

*(edited) - original said 'not'. I meant 'now I'm using Zotero'. ;). original said 'skill', I meant 'skilled'