[FOM] throwing darts at natural numbers (rejoinder to Arnon Avron's reply)

joeshipman@aol.com joeshipman at aol.com
Sun Aug 9 14:25:02 EDT 2009

That can't be right, if you define "mathematician in the streeet" as a 
random person with a Ph.D. in mathematics. Most of the graduate 
cirriculum in pure math (and some of the undergrad curriculum) makes 
regular "unbracketed" use of AC (in the form of Zorn's Lemma, maximum 
principles, constructions involving infinitely many arbitrary choices, 
assuming every vector space has a basis, the Tychonoff theorem, etc.).

I agree that applied mathematicians have no use for AC, but pure 
mathematians are a very important subpopulation of "all mathematicians" 
and they have typically been taught to prove theorems with a toolset 
that relies on AC in many ways.

-- JS

-----Original Message-----
From: T.Forster at dpmms.cam.ac.uk
To: tchow at alum.mit.edu; Foundations of Mathematics <fom at cs.nyu.edu>
Cc: fom at cs.nyu.edu
Sent: Sat, Aug 8, 2009 8:42 pm
Subject: Re: [FOM] throwing darts at natural numbers (rejoinder to 
Arnon Avron's reply)

  I think we are in danger of forgetting that not only do
most mathematicians-in-the-street not believe AC, most of
them have no intuitions about it and cannot state it even
roughly, let alone have any idea how to use it.  After all
most mathematicians are applied mathematicians. Ask yourself:
how many applied people do i know who can correctly state
AC?  We are a charmed circle!

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