[FOM] "Mathematician in the street" on AC

Henrik Nordmark henriknordmark at mac.com
Tue Aug 11 14:47:47 EDT 2009

Regarding the "mathematician in the street" and his/her opinion on AC...

Benedikt Loewe, Francesco Lanzillotti and myself did some preliminary  
empirical research on this subject matter. Alas, it was generally  
difficult to get mathematicians to sit down and fill out our  
questionnaire and thus the data we collected although quite intriguing  
was generally not sufficient to do any proper statistics on it.  
Nevertheless, I personally found it quite rewarding to get some  
empirical data on what the "mathematician in the street" thinks rather  
than merely speculating about it.

I apologize for my vagueness as I do not have the data readily  
available with me, so please take all of this with a grain of salt.
However, off the top of my head, if I remember correctly:

More than half the mathematicians who responded gave a correct and  
precise definition of AC.
(Quite frankly, we thought it might be less than that.)

A very large majority claimed that AC was generally accepted as true.

Despite that, there was roughly a half and half split between those  
who claim that AC is different from the other ZF axioms and those who  

Thus, the general impression we got was that although your  
"mathematician on the street" tends to prefer to think about AC as  
being true, but at the same time there is a certain awareness or  
uneasiness that AC is perhaps slightly different in nature from the  
other axioms.

There were other questions we asked related to AC, however I am only  
relating those which I can currently remember. If you are interested  
in knowing more about this topic, our findings are supposed to be  
published in the near future.

Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam

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