I did something like this and ended up just substituting graduate classes for my math and physics requirements while taking regular undergraduate classes for everything else. I made a lot of great friends and was not the only undergrad in those graduate classes. I don't see it as a curse at all. I think the author will be fine if he stays motivated and finds the right peers and the right path.

Agree with everything you said. I also did the same thing basically, undergrad CS and grad math classes.

The author basically did all of undergrad math and physics, and now apparently they're planning to self-study all the grad math. The thing with self-studying is you're taking yourself out of the system, and at some point you have to inject yourself back in. I hope the author is able to do that and doesn't miss out on undergrad college too much, because it's really enjoyable if you find the right friends and you'll look back on it fondly.

I disagree, I think it will provide him with a great foundation for college. As great as online learning is, I don’t think it’s the same as taking a class that you go to multiple times a week and get in person feedback on. It also takes multiple passes at a given subject to properly understand it. I’m sure he’d learn many new things he didn’t quite get from his self study if he enrolled in an actual analysis course or w/e.

this makes sense to me. I skimmed what he took and it says he learned real analysis, a pretty challenging course. It's one thing to listen to the lectures and solve some problems and it's another to be given a difficult homework on a very tight deadline and perform well, same for exams.

I think it's extremely cool though and really a great idea but I am cautious about saying he has the equivalent of those undergraduate degrees.

Yeah, I have unpleasant real analysis memories of frantically taking notes while the lecturer stood facing the blackboard writing down proofs. But, I made it in the end and I have it on good authority now that 1 is indeed bigger than 0!

> it's another to be given a difficult homework on a very tight deadline and perform well, same for exams.

This is the stupid, broken part of school, that only exists as a cost-cutting measure. Real learning and creativity doesn't have this nonsense. It's like saying that living in a nice house is bad because you don't get to smell your poop while you eat. No one needs that. Diego is getting a better education because it isn't being arbitrarily cut short and of track before the going gets good.

I agree with you about it being broken. We’re so focused on grades because they are a believed to be an important part of the credentialing process for getting jobs. An ideal learning environment would likely be something closer to Plato’s academy, imo. Probably not possible under capitalism except for the very rich with a lot of leisure time.

At least in the fields mathematics, physics, and to a lesser extent CS (which has a huge number of students and is becoming like a new business degree), professors view undergraduate degrees as a way to find good students who can go on to graduate school. So there is a tendency to be adversarial in classes. The GPA is one way to measure student aptitude but it's not perfect. Typically more than one metric is taken. If you just love these topics that's a great thing to learn. But if you want to contribute to the fields, it will be hard unless you go through the credentialing process.

> We’re so focused on grades because they are a believed to be an important part of the credentialing process for getting jobs.

Various colleges (ex: Reed, Brown) in the U.S. don't have grades. Their graduates do just fine, afaik.

In defense of grades, they are a good extrinsic motivator for learning boring subjects. Grades are a good consequence for phoning in it. I would probably have skipped reading most of the books I was assigned to read in school if there were no consequences, and would have ended up an (even) less educated person if not for grades.

> At that age it's really risky to do. Really hard to go to college and sit in classes for 4 years if you already know everything.

Or you can do what many of us did, and take more advanced classes.

> I guess you could go straight to grad school or industry, but you miss out on a lot of the social maturity and friendships you develop in college.

There is a standard pathway. Diverging from it doesn't cripple people, at least anyone I know. The pathway was different 100 years ago, or 400 years ago. It's all good.

Personally, though, if I were him, I'd do something different, like a field of engineering. The math and physics will give a huge edge, while he's learning new stuff.

nah, i have plenty of similarly smart friends who are doing just fine. he'll fit right in in some college environments, and he can take the time he's not wasting doing class and pursue real things that matter, like research.

He’s done good work here but implying he’ll be bored for 4 years of college is preposterous.

He could go to any big college where he can take very difficult classes right away, and if he’s somehow still bored he can do research.

I can see both sides of the riskiness of studying the material before taking the course. On the one hand, a person who I see as highly accomplished person in mathematics told me that he did very well in his courses by pre-studying much of their material in the summer before they started, because he was both interested in the subjects and wanted to do well. But on the other hand, I also know of some people who took an introductory language course after previously studying the language, and received worse grades than people new to the language because they didn't put as much effort into the assignments as they didn't see the value (though they did well with minimal preparation for writing assignments).

I think it's better to pre-study, as if you go to the right university, you can take honours-level courses or enter more rigorous, challenging programs, which should still be challenging enough to engage you. Alternatively, if you don't like the challenge (though if you're the type of person to achieve that amount of self-study, you probably would enjoy it), you can take a more normal program and focus on more deeply learning the material over a longer period of time. With the higher grades from deeper learning, you can stand out and earn scholarships and grants to get practical experience by working in a professor's lab.

So, overall, I think it's better to pre-study if you can, as you can keep the benefits while minimizing the risk of boredom by finding ways to challenge yourself. Though in reality, the main issue for someone around 18 is that they might not even know about the risks of boredom, or how to challenge yourself in this way. Hopefully such people who are succeed in self-studying in advance, are around good people who can guide them to find ways to challenge themselves in a healthy way.

Oh no, grades. When you grow up, no one cares about grades.

Haha. The importance of grades depends on your goals: on the one hand, I know two engineering grads who scored multiple great internships with a sub-3.0 GPA, with one landing a very high-paying job thanks to these internships. But on the other hand, a mathematics professor persuasively said to my class that your life can be a lot easier if you do get higher grades. They can help with graduate school admissions, scholarships, and getting certain internships.

So, while grades don't really matter for the vast majority of great employers after graduation, good grades do make it easier to find opportunities earlier on. If it's not overly stressful for a student to achieve higher grades, it's worthwhile to score them for better early career opportunities (e.g. access to top labs and competitive internships).

But if it's too much of a burden for the student, you can be extremely successful career-wise regardless of grades, especially if you work hard and creatively to find ways to gain experience and demonstrate your abilities. For example, one successful former classmate found great internships via networking through their engineering design team, where the companies overlooked their GPA in favour of their demonstrated experience with engineering with the team.

If he can write a good application and gets great scores at his tests (which he should considered how above the required level he is now), he should get a good scholarship and knowing the material should get him noticed pretty quickly which will open opportunities to publish quickly at least in mathematics.

Plus, he clearly is self-motivated and able to study by himself. University will give access to a ton of material and researchers. He should thrive.

Given the opportunity, learning is rarely a wrong choice.

Or he could lead group study sessions. I graduated last year and for many of my classes there were a couple of people like this, and everyone loved them.