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June 26th, 2014, 12:21 AM   #1
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How revered is B Russell in the math community

As a logician/philosopher it is difficult to find out how revered B Russell is in the math community. As a philosopher in my opinion he's the best. And on the philosophical encyclopedia, plato.standford.com he is the 4th most cited philosopher, but it's difficult to find out how seriously mathematicians take him. In Peter Smith's Godel without Tears, he calls the Principia to be frankly quite sloppily written and several of the axioms are highly dubious. In Russell's autobiography, My Philosophical Development (1959), Russell himself writes that he only knew of 6 people that had the 3rd volume of the PM, implying that most people give up after the first volume. So if we were to make a list of the top 20 mathematicians, then where would Russell fit into that hierarchy in your opinion.
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June 26th, 2014, 02:45 AM   #2
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I must admit that my knowledge of the early 20th century development in the foundations of mathematics, and Russel's contribution in particular, is rather superficial. I think he probably would not make it to the top 20 list of even the 20th century mathematicians. I believe his influence lies in the fact that he participated in and largely started a research direction that is enormously important today. His own theory of types seems no longer relevant even to most logicians, but type theory is very much alive and well. It is the foundation of functional programming and a lot of computer-aided theorem proving. It happened, maybe for historical reasons, that the TYPES mailing list is one of the most popular ones in theoretical computer science announcing conferences almost daily.

I came to the conclusion that mathematical discoveries are (at least) of two sorts. Some are incredibly complex and technical. For example, it takes a couple of months to explain why $\pi$ is transcendental. Others are very simple from the technical standpoint, but contain profound new ideas. For example, Lobachevsky is most famous for inventing non-Euclidean geometry. Nowadays proving that the fifth postulate is independent of the others is as easy as constructing a model with seven points and a few lines. In the nineteenth century it took decades. But authors of both types of advances deserve respect.

You should probably ask this question on more advanced ot specialized forums like Stackexchange.
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June 26th, 2014, 04:50 AM   #3
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Originally Posted by bobsmith76 View Post
As a logician/philosopher it is difficult to find out how revered B Russell is in the math community.
He's a demigod. Very very much.

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Originally Posted by bobsmith76 View Post
So if we were to make a list of the top 20 mathematicians, then where would Russell fit into that hierarchy in your opinion.
10-20ish on my list. I have Gauss, Euler, then everyone else.

Russell and Hilbert were, IMO, the two great mathematicians of their time.
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June 26th, 2014, 09:46 AM   #4
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Thinking about it a little more, I would include Russell in top 20.
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