Counterfactuals are always difficult, but in this case I am sure that the answer is somewhere between "no" and "after years of hard work". Certainly it wouldn't have happened overnight -- whereas with psychedelics it very literally did happen overnight. Even if the psychedelics were simply a shortcut, there was a lot of benefit in taking them: within a year of my trip I'd completed 15 credits worth of maths courses, and the rest of my education and career benefited accordingly. I'd been trying for years to overcome those anxiety issues organically and was still only a fraction of the way there, so the non-psychedelic path would not have yielded results in time to benefit me in university.
I couldn't describe how fascinating I'm finding your experience! I don't want to burden you with questions, so I'll have parsimony: can you ellaborate on what did your experience with LSD change in your disposition with mathematics? Did it remove an emotional barrier, did it make you somehow solve things quicker, and in what sense did it do so? (were you just quicker, or the same speed but more intuitive?) were you instead more creative?
I'm specially curious because I love math. There's no emotional barrier between me and various fields -- I find so many things fascinating I could get lost for hours absorbing any theory pretty much. But I'm below average at math. My biggest issue, particularly, is that I'm awfully slow and make tons of mistakes. This doesn't go away with any amount of study (at least so far). If I lived isolated and didn't have to be examined and so on, I would happily pace at my snail speed and be happy with that, but since subjects evolve too quickly and most people are too quick for me, I feel pursuing math-intensive fields would be too demanding.
Primarily it instilled that love of math, where previously there had been anxiety and ennui. This was sufficient to get me actually complete the work -- and do some extra work for fun -- which was more than enough to get through the math in my university coursework. I didn't get into more advanced maths in university, and for the fields that I've ended up in (and here I need to omit some otherwise too-revealing biographical details), I'm undoubtedly sub-par at mathematics. When it comes to calculation, I'm still definitely slower and more mistake-prone than my colleagues. I attribute this to avoiding mathematics for my first two decades; if math is a language, then I learned it at an age when having a thick accent is unavoidable. I make up for these deficiencies by being much more stubborn than my colleagues -- just hammering away at problems until they're done -- and also having an excellent intuitive grasp of certain domains, which I can then implement via coding rather than formulae. (I learned to code when I was very young, so that's something which I'm much more natively fluent at). After I've solved a problem via intuition and code, I usually try to prove (or at least investigate) it with proper math, to reassure myself that the solution is efficient and correct. That's far slower and more painstaking, but I eventually get there (and nine times out of ten, my intuition was correct). That's probably the wrong way to do things, but it works. I wouldn't be able to have a job where the math necessarily came first, however!
Thank you so much! You seem to be really sucessful with problems not unlike mine, so evidence that I can just wrestle with problems for long until they yield always boosts my hope. (Probably asking too much, but if you feel like it please send me some of your work on my email)