Sherman Stein (BS' 46)

I retired some 25 years ago because I wanted to see who I am when I do not have the benefit of the cocoon of a university. During this time I've written several books, including two for the public,
"What Did Archimedes Do Besides Cry Eureka?" and "Adventures in Mathematical Reasoning." Also I've published research on the logic of identities, an area in which some of the proofs were provided by computer programs.

I finally answered this elementary question: If multiplication distributes over addition (c(a + b) = ca + cb) and exponentiation distributes over multiplication ((ab)^c = a^c b^c) what functions distribute over exponentiation (f(a^b) = f(a)^f(b))? I had hoped to uncover some new exotic functions but showed that only the two functions f(x) = 1 and f(x) = x have that property. Because the proofs use only elementary calculus I published this in the College Mathematics Journal.

I should mention the years I've spent on the 6th edition of my calculus book. All that remains is another proofreading of text and figures.

In Their Own Words