You should never estimate your skill in something without anything to back this up. I personally believe there are three pillars of mathematical skill: 1. Math competitions 2. Elegant proofs 3. Research If you can do these three well, you can call yourself a good mathematician. For example, over the last few decades, over half of the fields medal recipients have also won a gold medal at the IMO.
I think you hit on something, but it's not even that the question isn't constructive. Often, the judgement is levied from something like the production of original work, but by dint of the nature of this discipline, there is no way of knowing how to obtain your goal - only that you have. Good goals have clear roadmaps that give you a far clearer idea of _where_ to go, even more than _where_ you are. I think that's probably the best advice in these cases: to change your focus from the latter to the former. For more concrete advice, I believe that some goals are made better than others - it's a bit more than subjective preference at play. The way I've tried to live my life is to focus on being a good person first, and to let mathematics be an expression of that. I find it easier to tell whether you're being a good person versus a good mathematician, but that's just me.
How about simply asking if you enjoy math? If it captivates you like music does for many, then go for it! It would be sad to think that you would only learn piano if you could make it in a top-tier orchestra. Studying math opens up a world of opportunities. There are numerous well-paid jobs where you can apply your math skills, and you don't need to be a genius to excel in these roles.
I know we are supposed to be modest and stuff but being just “another” mathematician (another point in the same group in the plane) makes me feel pretty worthless. Nowadays you have to know much of every math field to publish a useful paper which makes things harder.
Actually, no - different mathematicians know different pieces of math even in the same field, which makes collaborations so powerful! As you grow as a researcher, your expertise steadily becomes unique.
Well, now imagine that the first professor does not take your ideas seriously, the second professor is let go from the University in the middle of our research, the third professor just have family problems and can’t concentrate. All of these converges into me being alone with all these mathematical ideas but that just means I have to read and reread books since no one is around anymore. If you are someone who can contribute with an undergraduate and graduate with no problem then you are definitely a useful mathematician.
"Modesty and insecurity are not the same thing." This is a phenomenal point. 👏👏👏
You are really making a change in our community, Mura. Thank you.
Thank you so much! I'll focus more on usefullnes.
Thank you Maria!
You should never estimate your skill in something without anything to back this up. I personally believe there are three pillars of mathematical skill:
1. Math competitions
2. Elegant proofs
3. Research
If you can do these three well, you can call yourself a good mathematician.
For example, over the last few decades, over half of the fields medal recipients have also won a gold medal at the IMO.
How about the ability to teach someone else mathematics? It takes a certain level of knowledge, skill, and ability to do that well.
I think you hit on something, but it's not even that the question isn't constructive. Often, the judgement is levied from something like the production of original work, but by dint of the nature of this discipline, there is no way of knowing how to obtain your goal - only that you have. Good goals have clear roadmaps that give you a far clearer idea of _where_ to go, even more than _where_ you are. I think that's probably the best advice in these cases: to change your focus from the latter to the former.
For more concrete advice, I believe that some goals are made better than others - it's a bit more than subjective preference at play. The way I've tried to live my life is to focus on being a good person first, and to let mathematics be an expression of that. I find it easier to tell whether you're being a good person versus a good mathematician, but that's just me.
I'm no mathematician at all. I just love to learn it on my own.
How about simply asking if you enjoy math?
If it captivates you like music does for many, then go for it!
It would be sad to think that you would only learn piano if you could make it in a top-tier orchestra.
Studying math opens up a world of opportunities.
There are numerous well-paid jobs where you can apply your math skills, and you don't need to be a genius to excel in these roles.
Pretty sure the world of professional music is also extremely competitive, and similar questions are being asked a lot.
If I might not even win a fields medal, what’s the point of this anyway? 😮😂 Thank you, Mura ❤
I know we are supposed to be modest and stuff but being just “another” mathematician (another point in the same group in the plane) makes me feel pretty worthless. Nowadays you have to know much of every math field to publish a useful paper which makes things harder.
Actually, no - different mathematicians know different pieces of math even in the same field, which makes collaborations so powerful! As you grow as a researcher, your expertise steadily becomes unique.
Well, now imagine that the first professor does not take your ideas seriously, the second professor is let go from the University in the middle of our research, the third professor just have family problems and can’t concentrate. All of these converges into me being alone with all these mathematical ideas but that just means I have to read and reread books since no one is around anymore. If you are someone who can contribute with an undergraduate and graduate with no problem then you are definitely a useful mathematician.
I don't have social skills, my ability to talk to someone is limited to comment sections on TH-cam.
I’m a non mathematical genius…