FOM: What were Kronecker's f.o.m.?

Peter Schuster pschust at
Thu Feb 24 06:11:37 EST 2000

Thanks to Walter Felscher and Julio Gonzalez Cabillon 
for pointing out the correct reference of the dictum 
commonly ascribed to Kronecker 

"Dear God made the whole numbers, 
all the rest is the work of men". 

Walter Felscher wrote

>The following remark appeared on August 7 , 1998, on 
>historia-matematica at  which may be a better 
>place to ask about purely historical matters.

Disregarding whether Kronecker really said this or 
something similar (is Weber not a reliable source?), and 
whether, where, and when it appeared in print, it
is very close to Kronecker's spirit. It is left to 
everyone whether he cares for this spirit, that is,   
constructive mathematics only based on rational numbers, 
and for the way in which Errett Bishop and others put 
this spirit into action, even in areas far away from  
simple rational arithmetic, such as functional analysis. 

Likewise, it is left to everyone and, in particular, to 
the f.o.m. manager whether he might do foundations of 
mathematics without looking at some landmarks in their 
history. It should, however, NOT be left to anyone whether 
foundations keep in touch with mathematical practice, which 
now seems to overtake foundations from the right (UK and 
Commonwealth: left), just in a sense not too far from 
Kronecker's spirit: consider effective, computational, 
empirical methods, etc. Therefore I think that Kronecker's 
view is by no means a purely historical matter. 

Name: Peter M. Schuster
Position: Wissenschaftlicher Assistent
Instituition: University of Munich, Mathematics Department
Research interest: constructive mathematics

More information about the FOM mailing list