He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution.

Guldin was noted for his association with the German mathematician and astronomer Johannes Kepler.

[1] Guldin composed a critique of Cavalieri's method of Indivisibles.

[2] Although of Jewish descent, his parents were Protestants and they brought Guldin up in that faith.

In Paolo Casati's astronomical work Terra machinis mota (1658), Casati imagines a dialogue among Guldin, Galileo, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy.