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I agree with this advice once you get to a sufficiently high level -- like, working on research problems.

HOWEVER I think there's more nuance: there is tremendous value in having a baseline level of foundational knowledge in whatever domain you're in.

For instance, if someone hasn't learned math to an undergraduate level, and they try to sink their teeth into a math research problem, then they're probably going to spend all their time flailing around and being confused. Waste of time.

A better use of time would be for them to develop a baseline level of mathematical knowledge through a structured curriculum, and then take the leap once they've got their fundamentals down.

Same thing with machine learning. If you want to work on a research problem and you have your ML fundamentals down, then yeah, go ahead and jump right into the research problem. But if you don't even know how gradient descent works, or what an eigenvalue is, how to work with continuous probability distributions, etc., then you're woefully underprepared and you'd be better off just shoring up your foundations first.

Meh? I think a more mercenary approach to learning prerequisites is fine, and frankly better. Use Mathematica or Alpha to show you how equations get from one place to another - those tools are great at the fundamentals. You can skim a calc book, use Mathematica/Alpha to fill in your gaps, and play with toy problems to convince yourself well enough to continue.

The basics are the ones with the most different approaches developed to teach/use them, so they can most easily be skimmed by with cheap modern trickery.

There are some people who can pull that off, and you might be one of them, but they're extreme cases. For the vast, vast majority of students it's not a viable approach.

I really resonate with this. I've also struggled with perfectionist mindset when it comes to learning, especially in mathematics. Recently, I tried to meticulously add math problems to Anki for better retention, only to realize the time cost was too high. This perfectionist mindset often maximizes one variable (retention in my case) at the cost of all others (time as the most important one).

I've grown to really like this Richard Feynman quote: “Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.” It feels like I've been finally granted permission to embrace my natural, messy way of learning.

I have a different advice for aspiring mathematicians. Learn in the way you want. If you enjoy learning the prerequisites or feel like you need to, by all means learn it carefully. There are enough mathematicians on either side of this advice and indeed of most advice. Don't take other people's opinions too seriously. Other people only know what worked or didn't for themselves, they have no idea what will work for you.

> It is tempting to do so because you feel things will come easier to you if you fulfill the prerequisites first. But the problem is that there is just not enough time. AND, it actually may not be even necessary.

I think this is a lesson I am learning. I am going through the book PRML throroughly (which means attempting every single exercise) and writing out the solutions.

I also did the prereqs somewhat rigorously.

It has been incredibly time consuming.

If you take the time to learn everything relevant to your research then you will never have time to do your research.

Passions, feeling special, finding the special one. Do I dare suggest that identifying (or equating(!!!)) these are not just urgent issues for young mathematicians, but young people in general? Or maybe even every one?

Yeah I did a similar thing.

I was a math major and I used to be adamant about reading the chapter perfectly before starting my problem sets.

I mentioned this to my math professor and he’d always say to not be afraid to jump into the problems, that my time was better spent that way.

My take on it is that a) it’s true and b) it works because reading with a purpose is very different than reading as a way of surveying something before you jump into a problem.