At Göttingen, she pursued her passion for mathematical invariance, the study of numbers that can be manipulated in various ways and still remain constant. In the relationship between a star and its planet, for example, the shape and radius of the planetary orbit may change, but the gravitational attraction conjoining one to the other remains the same — and there’s your invariance.

In 1915 Einstein published his general theory of relativity. The Göttingen math department fell “head over ear” with it, in the words of one observer, and Noether began applying her invariance work to some of the complexities of the theory. That exercise eventually inspired her to formulate what is now called Noether’s theorem, an expression of the deep tie between the underlying geometry of the universe and the behavior of the mass and energy that call the universe home.

What the revolutionary theorem says, in cartoon essence, is the following: Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see that it is angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move.

Some of the relationships to pop out of the theorem are startling, the most profound one linking time and energy. Noether’s theorem shows that a symmetry of time — like the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the ball’s trajectory — is directly related to the conservation of energy, our old homily that energy can be neither created nor destroyed but merely changes form.

The connections that Noether forged are “critical” to modern physics, said Lisa Randall, a professor of theoretical particle physics and cosmology at Harvard. “Energy, momentum and other quantities we take for granted gain meaning and even greater value when we understand how these quantities follow from symmetry in time and space.”

Dr. Randall, the author of the newly published “Knocking on Heaven’s Door,” recalled the moment in college when she happened to learn that the author of Noether’s theorem was a she. “It was striking and even exciting and inspirational,” Dr. Randall said, admitting, “I was surprised by my reaction.”