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This is for Toby: in the article on Errett Bishop, it is stated, “Before [his interest in constructive mathematics], he had an ordinary career in approximation theory.” This sounds rather odd to me; most accounts I have read have said his career in (for example) function algebras and in several complex variables – not to mention approximation theory – was extraordinary and brilliant. (Quite a few people with no interest in his constructive mathematics hailed him as an authentic genius in these areas.) Would you clarify this, please?
Some very impressive testimony regarding the mathematical (analytic) prowess of Bishop can be found here.
By ‘ordinary’ I meant not focussed on constructive mathematics.
I’ve edited the sentence slightly, but you should add more if you like.
You mean, then, a career in classical or ordinary approximation theory, not a classical career in approximation theory! The latter sounds bizarre to me! Just to underscore this, wouldn’t it sound weird to say “a non-constructive career in approximation theory”, when you mean “a career in non-constructive approximation theory”?
Goodness, you’re right!
That’s fun. Let’s see, what kind of careers can we envision:
A perverse career in sheaf theory.
A pointless career in topology.
An unbounded career in chain complex theory.
A simple career in group theory
An empty career in set theory. (Nah, then better a career in empty set theory ;-)
Okay, I better stop now.
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