Thermodynamics

Der Hauptsatz leads two lives, and anyone who learned German grammar before German physics meets the wrong one first. In a grammar book it is the main clause, the one that can stand on its own, as opposed to der Nebensatz. In a physics lecture it is a law: der erste Hauptsatz says that energy is conserved, der zweite Hauptsatz that heat does not flow from cold to hot by itself. Mathematics adds a third life, der Hauptsatz der Differential- und Integralrechnung, the fundamental theorem of calculus. What holds the three together is the older sense of der Satz as a statement or proposition, the sense that is still alive in der Satz des Pythagoras. So the second law is not das zweite Gesetz in a German textbook but der zweite Hauptsatz, and it declines like any masculine noun: nach dem zweiten Hauptsatz.