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译文url: My name is Leif and I wanted to ask you on your opinion on something-forgive me if this seems strange or random.
the fact that you graduated high school and university and earned your doctorate so young), I’m wondering if you think you possess something that only a few others have in terms of intellectual ability or not.
I have always believed that if someone applies himself and puts in enough time, effort, concentration, and perseverance they can accomplish whatever they set their mind to.
I am not saying I don’t believe some people are naturally more gifted at certain things or develop stronger skills or have stronger talents than others.
I just think it’s possible to achieve levels of excellence and brilliance even in your weak areas through consistent practice. After all, they made their share of mistakes and setbacks but did not give up and they were not superhuman or genetically enhanced as far as I know..
I find that “playing” with a problem, even after you have solved it, is very helpful for understanding the underlying mechanism of the solution better.
For instance, one can try removing some hypotheses, or trying to prove a stronger conclusion. It’s also best to keep in mind that obtaining a solution is only the short-term goal of solving a mathematical problem.
However, I don’t see why it’s not possible for me to develop mathematical abilities as strong as my linguistic abilities or even pursue a career in astronomy (which I love) or physics or even pure mathematics.
And I know you say similar things on your career advice blog, and I know it’s important to be realistic and plan for graduate school and beyond I just really don’t like how people put this label of genius or prodigy on certain people to (in my opinion) make them seem able to achieve things that most other people cannot–even the levels of Einstein or Mozart.
Solving homework problems is an essential component of learning a mathematical subject – it shows that you can “walk the walk” and not just “talk the talk”, and in particular identifies any specific weaknesses you have with the material.
It’s worth persisting in trying to understand how to do these problems, and not just for the immediate goal of getting a good grade; if you have a difficulty with the homework which is not resolved, it is likely to cause you further difficulties later in the course, or in subsequent courses.