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What motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nealynearly as smart as them in their schooldays?

Many professors in mathematics or theoretical physics got their Ph.D degrees from departments that were much more prestigious than the ones they are working in. So when they train Ph.D students in their current department, (I think)they may have the following comparisons, though they will never speak them out:

"When I was an undergraduate student in Princeton University, I could solve such problems much quickly than you graduate students do".

"When I was taking algebraic topology with *** in Princeton University, we covered the whole book within one semester while you guys...."

At the same time, the students may also have thoughts that they can never make achievements as big as their advisers in the future. For instance, they will get positions in departments that are much less prestigious.

So my question is, what motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nearly as smart or excellent as them? Of course, I am comparing students and they advisers in their schooldays. I know professors just can't refuse students who want to work with them without strong reasons, but what makes them "feel happy" to work with students who are not nearly as good as them?

What motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nealy as smart as them in their schooldays?

Many professors in mathematics or theoretical physics got their Ph.D degrees from departments that were much more prestigious than the ones they are working in. So when they train Ph.D students in their current department, (I think)they may have the following comparisons, though they will never speak them out:

"When I was an undergraduate student in Princeton University, I could solve such problems much quickly than you graduate students do".

"When I was taking algebraic topology with *** in Princeton University, we covered the whole book within one semester while you guys...."

At the same time, the students may also have thoughts that they can never make achievements as big as their advisers in the future. For instance, they will get positions in departments that are much less prestigious.

So my question is, what motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nearly as smart or excellent as them? Of course, I am comparing students and they advisers in their schooldays. I know professors just can't refuse students who want to work with them without strong reasons, but what makes them "feel happy" to work with students who are not nearly as good as them?

What motivates professors to train Ph.D students who aren't nearly as smart as them in their schooldays?

Many professors got their Ph.D degrees from departments that were much more prestigious than the ones they are working in. So when they train Ph.D students in their current department, (I think)they may have the following comparisons, though they will never speak them out:

"When I was an undergraduate student in Princeton University, I could solve such problems much quickly than you graduate students do".

"When I was taking algebraic topology with *** in Princeton University, we covered the whole book within one semester while you guys...."

At the same time, the students may also have thoughts that they can never make achievements as big as their advisers in the future. For instance, they will get positions in departments that are much less prestigious.

So my question is, what motivates professors to train Ph.D students who aren't nearly as smart or excellent as them? Of course, I am comparing students and they advisers in their schooldays. I know professors just can't refuse students who want to work with them without strong reasons, but what makes them "feel happy" to work with students who are not nearly as good as them?

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source | link

What motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nealy as smart as them in their schooldays?

Many professors in mathematics or theoretical physics got their Ph.D degrees from departments that were much more prestigious than the ones they are working in. So when they train Ph.D students in their current department, (I think)they may have the following comparisons, though they will never speak them out:

"When I was an undergraduate student in Princeton University, I could solve such problems much quickly than you graduate students do".

"When I was taking algebraic topology with *** in Princeton University, we covered the whole book within one semester while you guys...."

At the same time, the students may also have thoughts that they can never make achievements as big as their advisers in the future. For instance, they will get positions in departments that are much less prestigious.

So my question is, what motivates professors in mathematics or theoretical physics to train Ph.D students who aren't nearly as smart or excellent as them? Of course, I am comparing students and they advisers in their schooldays. I know professors just can't refuse students who want to work with them without strong reasons, but what makes them "feel happy" to work with students who are not nearly as good as them?