I came across this statement in [the autobiography by Saunders Mac Lane](http://rads.stackoverflow.com/amzn/click/1568811500).



> 
> It was the interaction between solenoids and group extension that got our collaboration started, and this first work of collaboration revealed much else to be done, some stimulated by a result of Heinz Hopf. It can be best summarized by a striking proof that 2 is more than 1 plus 1. 
> 
> 
> 


Ref: pp 346-347 [1](http://rads.stackoverflow.com/amzn/click/1568811500)


Where can I find the above mentioned proof? I tried google but failed.



Where is a proof of "2 is more than 1 plus 1" said by Saunders Mac Lane?
The paper Mac Lane is referring to must be "Group Extensions and Homology" from May, 1942. (This fits the description about "interactions between solenoids and group extensions".) The main result in that paper is a form of the universal coefficient theorem for cohomology. I don't see how this can be interpreted as saying that 2 is more than 1 plus 1.


However, the paragraph in Mac Lane's autobiography from which you've quoted begins:



> 
> All these examples of collaboration must yield in size and consequence to my long continued work with Eilenberg. He and I came together on a problem that combined our expert knowledge in topology and algebra. The combination turned out to be very fruitful, leading to our many joint papers and covering discoveries such as the cohomology of groups, homological algebra, Eilenberg-Mac Lane spaces, and category theory ....
> 


I infer that the "1 plus 1" being referred to is "Eilenberg plus Mac Lane" and the "more than 1 plus 1" is "Eilenberg-Mac Lane". And the proof, as they say, is in the pudding.


