In 1989, Ning Li, of the University of Alabama in Huntsville theoretically demonstrated how a time dependent magnetic field could cause the spins of the lattice ions in a superconductor to generate detectable gravitomagnetic and gravitoelectric fields.
In 1937 Ettore Majorana theoretically demonstrated that all results of the beta decay theory remain unchanged if neutrino coincides with its anti-particle, i.e. if it is a majorana particle.
Unruh demonstrated theoretically that the notion of vacuum depends on the path of the observer through spacetime.
In 1997, Martin and Girard demonstrated theoretically that electric field under a metallic or dielectric tip (belonging to NSOM apertureless technique) can be strongly enhanced if the incident field is along the tip axis.
Andrew Greentree, Jared Cole, and Lloyd Hollenberg of the University of Melbourne, and Charles Tahan of the University of Cambridge demonstrated theoretically how to engineer a phase transition in photons, leading them to change their state so that they do interact with each other in a macroscopic, strongly-correlated way.
In France there are some who maintain that, mathematically, a bird cannot possibly fly; and others who demonstrate theoretically that fishes were never made to live in water.