- child prodigy. Acquired varying degrees of proficiency with 13 different languages
- appointed Professor of Astronomy at Trinity College, Dublin (age 22)
- theoretical prediction of “conical refraction” by biaxial crystals in 1832 — experimentally verified the same year
- Hamiltonian mechanics: systematic derivation of equations of motion for complicated dynamical systems with multiple degrees of freedom — paved way for development of quantum mechanics
- interpretation of complex numbers as “theory of algebraic couples”
- search for “theory of algebraic triples” led to discovery of Quaternions.

- latter career devoted to (failed) effort to establish quaternions as the “new language of science”