No master without students.
This is age-old wisdom coming in various iterations and examples. Here are some.
Some great artists were recognized at their time, amassed great fortune and fame, had plenty of contemporary students to teach to and learn from. Others also did great work, but died alone, poor, without recognition, without any direct students.
So, you can seemingly fail as a master during your lifetime. But if you were determined and truly great, you will get redeemed by your future students. Across time. Ultimately, the joke is on them: because you aren't around anymore to be asked questions and the students were "too late" to get the cues, they now need to try extra hard to understand! Haha!
Karate:
Despite, fighting capability and spirit are still very important for further propagation of the art. Masters take this into account and screen for the "warrior heart". Quitters don't win and won't graduate the black belt. Even if they get it while lacking quality, maybe the master's attention slipped and didn't notice the flaw in character. Then they will doubt themselves, see how poor their forms are compared to other black belts, other masters and they will eventually stop wearing the belt, quitting Karate.
When you achieve a "master title" in academia or your "master diploma" as a craftsman (f/m/d), you have demonstrated that you are at the top of your game, know all the relevant stuff and are ready to be released onto the world without training wheels. Some of those masters teach students, take apprentices, become doctors, professors. Others may create such great things, that even without taking direct students, future students will study their work for insights.
So this "math master", instead of getting his name attributed to his works (like most of the masters before and after him), he chose to delay credit (it got attributed anyway, check the linked Wikipedia article) and by choosing a considerate pseudonym spread the idea that even a master must be a perpetual student. Any proper math teacher or professor will explain the name, that the distribution is really called "student" not because a person was named like this, but because the person wanted to highlight that they saw themselves as "eternal math students" and that there always will be something left to study.
Mastery is explored extensively in Star Wars.
Galen Erso (Rogue One) is a master weapon builder, engineer and scientist. He is forced to finish the most powerful weapon ever: the Death Star. Knowing that the evil empire will discard him after, he planned a long-running plot: He built in weak point by design to be found and relayed to the rebels/resistance by his daughter. The rebels then studied it hard and destroyed the Death Star (+ later iterations). Each time with greater ease. They basically achieved "undo evil powerful weapons" mastery, as their master Galen Erso intended with his master work. The incapable evil empire couldn't fix the inherent design flaws, because they weren't masters and also poor students. It took a while, but after the 3rd station got destroyed they got the message and stopped building "just another Death Star"™, but went with a more conservative approach "even bigger fleet". Well, no mastery there either, judging by how it turned out.
Jedi: A Jedi master may take multiple padawans over the course of his life. A padawan may become a master and teach padawans themselves. Potentially, this ensures greater spread and higher numbers. Some may disagree and may part with the Jedi order to instead become...
Sith: Who took mastery to the extreme ("absolutes" so to say, hehe) with the "Rule of Two": At any given time there may be only one Sith Lord with only one Sith Apprentice. To become the lord, the apprentice needs to kill the master. Either by sheer force/power or by great wit/deceit, whatever is more suitable for continuation of the Sith given the circumstances. The apprentice fails when the lord kills them instead. The master grows more powerful with this, too: Learning how the student tried to outplay, what better qualities to look for in the next apprentice. Darth Sidious had and outgrew multiple apprentices until ultimately killed and both sides of the force merged.
As you see, the pattern is pretty omnipresent and told in various forms. To reach as many humans as possible. I'm sure, you can find further examples!
Now we talked a lot about "masters" and "mastery", but little about students. That's because there isn't much to say, if you understood it to this point:
No such thing as "bad students".
That's also common wisdom and it's self-evident from the very word: studere is Latin for "to sincerely try".
So the only task a student has, is to try. Try to understand the masters and their greatness. Try to outshine them. They don't necessarily need to succeed. They may fail, that's fine. They then may look for a different master, a different topic and try again. Others may take their place instead. The only bad student is a student who doesn't try, in which case they aren't a "student" by the very sense of the word. A student giving up, simply ceases to be a student. Not offending any master, any craft or anything really, but themselves. By wasting their own time. A master claiming in front of poorly performing students that "they are wasting the master's time" isn't reflecting enough on what he could learn from the student's failures. At the same time, the master implicitly asks them to try harder.
Thus "bad student" is an inherent oxymoron, while "excellent master" is an obvious tautology. If we don't think like this, e.g. having the need to distinguish between "masters" and "great masters". Then, maybe, we have watered down the term "master" a bit too much.
So, I hope this post corrected the image. Highlighting that obtaining mastery is a perpetual, self-correcting process. Sounds a lot like all of life, huh?
What happens with the masters who aren't good enough and the students who never achieved mastery in anything ever?
Mediocrity will simply be forgotten.
In other words, the opening sentence of this post could be reworded to: If your art, craft etc. dies with you, you were a lesser than all the masters before you! Even if your trade is still relevant to humankind, new students will simply skip past you to the masters before you! The joke is on you there! Ouch!
However, another, positive way to see this: mediocre students will be students forever, always learning, learning from lots of masters. Trying and trying and trying again, to achieve mastery!
The master builders of the pyramids got buried with their pharaohs. Did we forgot how to build pyramids? Yes! Do we know how the pyramids were built? Not quite, but we have some ideas! Do we really need to build further pyramids? Probably not.
Did we learn something anyway? Yeah, for instance:
Did the pharaohs have a bad intention bury their builders with them? We don't know! Maybe it doesn't matter, either!
Form my software engineering life:
I. I once interviewed an applicant for a (senior) software development position. Previously, the candidate worked in a consulting firm literally called "senior dev only" specializing in renting out senior developers to needy companies. I wondered, how that'd work and how they'd know that they are all "senior developers". Was it by age (to fight blatant agism, let's mean "years of experience")? Was by the amount of money they charge gullible companies? The candidate wasn't that good by my judgement, some knowledge at display was outdated. We ended up not hiring the candidate.
II. Similarly, some very capable (by my judgement), senior colleagues left for another company. That company had huge financial backing and was hiring "senior devs only" to finish an ambitious project on a tight one year schedule. I didn't check back again, but here are my assumptions of possible outcomes:
III. So I was teaching "modern" software engineering for one semester (2020-2021 during pandemic) at university, which is a separate blog post still in the making©. The gist is, I worked my way backwards from primary motive of "working software" (duh, surprise!) in the Agile Manifesto. Close to the end of semester, I got evaluated by the students. Besides all the benevolent feedback which I received, the most helpful one was (paraphrased): "Agile is pseudo-scientific mumbojumbo and I wished the lecturer would have instead focussed more on real engineering, not personal anecdotes." Ufff, that hit hard! Quite a revelation! Even if I may have failed that student, it pushed me to try harder. I openly motivated my strategy again, so hopefully the rest of them got the message. Overall, the students tried hard despite the suboptimal Corona situation, did very well in required presentations and the exam.