I believe that the Chern character and the Todd class play an important role in the Atiyah-Singer index theorem* (c. 1963), for which among other things Atiyah won a Fields medal in 1966. —Dan ————————————————————————————————————————————————————————— * https://www.maths.ed.ac.uk/~v1ranick/papers/gilkey3.pdf Henry Baker wrote: ----- As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right?? -----