His main mathematical tools were number theory, set theory, and category theory. His aim was to explore and understand complex living systems in nature by reasoning according to the logical dicta of these mathematical structures.
tacticalogic: Mathematical structure, completely removed from and unrelated to the reality of the physical structure of what it purports to explain?
His ability to visualize and resolve complex mathematical problems far exceeded that of his teachers and peers. I doubt very many at all could appreciate the work he was doing.
To make a long story short, Reimann developed a geometry for which there was no practical application. And he died.
Then along came Albert Einstein (1879-1955) who having rocked the physics world with his theory of Special Relativity had a theory (General Relativity) of the warped structure of the space/time continuum...
And he was able to pull Reimannian geometry off-the-shelf to describe that structure and benefit physicists to this very day.
Like Reimann, Rosen has done the theoretical mathematics and he has passed on.
Now I'm looking for a biologist version of Einstein to come along and pull his work off-the-shelf to make the great strides that are needed in biological research.
Oh so sadly, for Rosen died young, at age 64 (of complications of diabetes, I hear)....
Einstein realized that Euclidian geometry — a geometry of "flat" spaces — did not serve the insight he had about the structure of the universe. He realized that a geometry of curved spaces was needed — and found that geometry already created for him, as if ready made, in Bernhardt Reimannn's geometrical model of curved spaces — which had been on the shelf catching dust for lack of practical "external referents" for some 60 years or so by then. Yet Einstein saw that it was what he precisely needed. So he picked it up, dusted it off, and plugged it into his relativity theory. And the rest is history....
Do not distrust the "unreasonable effectiveness of mathematics" ( as Eugene Wigner put it) when it comes to explicating the mysteries of our universe....
Or so it seems to me.
It has been suggested that this unreasonable effectiveness of mathematics is "God's copyright notice on the universe."
I wholly agree with that insight.