Bernoulli’s 1738 kinetic theory is the first mechanistic explanation of gas behaviour. It correctly identifies pressure as momentum transfer and temperature as mean kinetic energy. It derives Boyle’s law from molecular motion. It fails to resolve energy conservation or collision elasticity — gaps that stalled acceptance for a century. Its value lies not in immediate utility but in framing matter as particulate and dynamic — a conceptual pivot that enabled thermodynamics and statistical mechanics.
Kirchhoff’s 1845 circuit laws are two experimentally derived equalities — one for current at junctions, one for voltage around loops — valid only under strict physical assumptions of the lumped-element model.
Lorentz’s transformations were a technically successful but conceptually constrained response to experimental anomalies in electrodynamics. They preserved the aether while making predictions match observation—by introducing local time, length contraction, and time dilation as mathematical corrections. Their algebraic form survived into special relativity, but their physical meaning did not.
Noether's theorem is the rigorous, general proof that continuous symmetries of the action imply conservation laws. It was published in 1918 in Invariante Variationsprobleme. It applies only to smooth, differentiable symmetries in conservative systems. It resolved energy conservation in general relativity. It reshaped theoretical physics’ emphasis toward symmetry.
