The author is indicating the final dates at which the knowledge about the theory changed, --- "in 1912"; "in 1915".  The author could have continued: "In the early 60 �s ... ... ".
 
The author is describing deadlines, ("by the early 60 �s"), ("by the time of the end of the early 60 �s").
 
"From the early 60 �s" is very imprecise.  It is not a point in time, because it covers several years.  Consequently, "from" is not suitable.
 
"Over the early 60 �s" is unsuitable, because the author is describing deadlines, but is NOT describing the period over which the event occurred.
 
Indeed, I think that if an English writer had wished to convey the impression of duration, he/she would have  written: "during the early 60 �s".
 
My experience, as a British English speaker, was that the answer jumped off the page at me.  In my opinion, "by" is the most suitable answer.
 
Les