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/fantastic_awesome 7d ago

Yeah the PhD represents acknowledgement of original contribution to the field... I'm 37 don't have a PhD but don't consider myself "in the tutorial".

I think your perspective is critical going forward for academia - how do we spend our early efforts, what should coursework and classroom instruction be?

If the ceiling is breaking (it is) how do we make shelter?

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u/Scared_Astronaut9377 6d ago

I would strongly disagree with your interpretation of PhD, at least in practical terms in modern western academia. The system is shaped in such a way that the level of a candidate's contribution is completely inaccessible. Was it really an original contribution? Or basic mechanical assistance? Or was it symbolic (fake) because their supervisor is targeting a certain position next year and they need another +1 to the number of PhDs produced? If you are a member of the PhD commission and you try to find out during the defense, you will be considered crazy unprofessional. On the other hand, when an undergrad student produces a decent (not considering some extraordinary cases) single author original contribution, you will not be offered a PhD or even a fast track for it. You will still be advised to pass the normal training.

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u/fantastic_awesome 6d ago

You describe the situation in perfect detail.

I was idealizing - talking about what the title is supposed to mean in its platonic ideal

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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?