I think you are severely oversimplifying “intelligence” and “productivity” into 1-dimensional quantities. In my experience, “genius” (i.e. the insight that solves a problem) is about acquiring a bag of tricks to throw at new problems, and translating your insight into a solution is the result of practice.
I was actually surprised to read back over the post and see that it was about intelligence; in my memory I had translated it into an article about a one-dimensional scale of ability, which I also imagined including, as a critical component, ability to have effective collaborations.
I guess it was the example of Einstein that brought that to mind. Part of what impressed me the most about his career was that, when he was working on general relativity, he collaborated heavily with a mathematician. Marcel Grossman, I think.
There are two separate simplifying assumptions you can make, when modeling this situation. One is assuming intelligence is the most important factor. The other is assuming that ability is one-dimensional. I suppose that this post makes both of them.
My article is a bit oversimplifying but not because I think intelligence and productivity are “one-dimensional quantities”, but rather because you have to simplify in a blog text—texts with endless qualifications become too long and tedious to read. Also I did say that other characteristics besides intelligence also are important.
Thanks for the link; interesting and sympathetic. I’m not saying you have to be a genius to do math: I’m saying some mathematicians are vastly much more productive than others. And I don’t see anything in Tao’s article that actually contradicts that.
Reading this reminded me of Terrence Tao’s blog post about how you don’t have to be a genius to do math: http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/.
I think you are severely oversimplifying “intelligence” and “productivity” into 1-dimensional quantities. In my experience, “genius” (i.e. the insight that solves a problem) is about acquiring a bag of tricks to throw at new problems, and translating your insight into a solution is the result of practice.
I was actually surprised to read back over the post and see that it was about intelligence; in my memory I had translated it into an article about a one-dimensional scale of ability, which I also imagined including, as a critical component, ability to have effective collaborations.
I guess it was the example of Einstein that brought that to mind. Part of what impressed me the most about his career was that, when he was working on general relativity, he collaborated heavily with a mathematician. Marcel Grossman, I think.
There are two separate simplifying assumptions you can make, when modeling this situation. One is assuming intelligence is the most important factor. The other is assuming that ability is one-dimensional. I suppose that this post makes both of them.
My article is a bit oversimplifying but not because I think intelligence and productivity are “one-dimensional quantities”, but rather because you have to simplify in a blog text—texts with endless qualifications become too long and tedious to read. Also I did say that other characteristics besides intelligence also are important.
Thanks for the link; interesting and sympathetic. I’m not saying you have to be a genius to do math: I’m saying some mathematicians are vastly much more productive than others. And I don’t see anything in Tao’s article that actually contradicts that.