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.
Mathematical structure, completely removed from and unrelated to the reality of the physical structure of what it purports to explain?
Of course not. Sooner or later, the "reality test" must be engaged.
Evidently Rosen proposes a direct correspondence exists between the structures of mathematics and the real world. As Einstein did, by the way.
We all know how fruitful that presupposition was to Einstein — even though it took many years before proper experiments could be framed and finally tested. Which, when they could finally be performed, showed that Einstein's theory was correct.
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.