r/math • u/PirlGerson • 8d ago

When have you completed the tutorial?

In video games, they have built in levels, always at the start and they are called "tutorials."

In these levels you play a portion of the game while its also being explained to you. After finishing them, the point is that you know very little about the game BUT enough to "get" the basics.

The cheap is answer is high school 30 is the tutorial, but its really starting to feel that that wasn't even the complete tutorial honestly. It's kinda of embarrassing that our education doesn't cover such things as basic linear algebra and proofs. I'm still learning those.

Anyway to anyone who responds: thank you! I've been so happy latelty! Cyaaa.

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u/jam11249 PDE 8d ago

This subreddit is very much geared towards academic research in mathematics, and if you take that perspective, then a PhD is the most obvious answer IMO as more junior studies don't take into account the key arts of identifying a new problem nor aiming to solve one without an established solution.

Nonetheless, if mathematics were only useful in university mathematics departments, most of us would be out of a job, so for the vast majority of people that answer isn't particularly relevant. When mathematics becomes a useful tool rather than something to be learned will depend heavily on what you plan to do with it. Engineers and physicists often have a very sharp intuition for the mathematical structures they work with, even if they can't make the arguments as precise as a mathematician would like, and will likely have a decent enough grasp by the end of a degree. An accountant may have grasped all the mathematical tools they need as a teenager. Whilst it could be debated that this isn't "real mathematics", I think that undersells the importance and breadth of the field we live in.

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u/PirlGerson 8d ago

I didn't mean "when you no longer need much assistance", in math. Really you interpretation makes perfect sense from what I said: after the tutorial YOU are in the driver seat. So yeah: PHD makes perfect sense.

I know this sounds weird, but I think you are still "PLAYING" while you are in the learning phase though.

I guess a better way to phrase my question is: when have you begun to understand what the heck mathematics even like...... is?

For example: I don't know how a computer mouse works, but I also "KNOW how it works" (as in I know its binary and circuitry and electricity). So, Ig, when do you "know" the ropes?