A Century of Smart

A hundred years ago, a theorem was put forth by mathematician/physicist whose work was lauded by Albert Einstein, David Hilbert, and Hermann Weyl that's still of value today -- in fact, it helps answer a lot of questions raised by Einstein's own theory of general relativity.

This genius was a woman named Amalie Emmy Noether, and "Noether's Theorem" was only one of the areas where she contributed to the growth of science in a time when she could barely get a university to pay her to teach, because she was a she. Her main work was in the development of abstract algebra, a division of that discipline which deals with categories and groups instead of just individual variables. The theorem that carries her name was almost a footnote to her career, but it lets physicists connect the concepts of conservation to the symmetries of a system.

When scientists talk about conservation of one value or another, they mean that value describes a total amount that doesn't change, even if the thing being labeled might change form. The law of conservation of energy, for example, says that energy can't be created or destroyed, only transformed. A piece of wood contains potential energy locked up in the structure of its atoms and molecules. When it's set on fire, that energy transforms into heat and light, as well as physical residue -- but the total energy in any "system" containing the wood doesn't change. Other fuels are more efficient at creating the energy and leave less residue. The more efficient you get, the more energy you wind up with, on up the ladder to things like atomic explosions. Since most of the potential energy in the A-bomb fuel becomes energy, it has tremendous explosive power -- this is why no one gets excited if Kim Jong-Il lights a match but they frown upon his scientists playing with plutonium.

Noether's Theorem relates that quality to a system's "symmetry," which in physics terms mean that when something happens a certain way under certain conditions, it will happen that way under the same conditions no matter where or when they are. When I was reading about this there was a split-second where I almost understood exactly what that relationship was, but it didn't stick, so I'll leave you to figure it out if you want to give it a shot.

Noether, a Jewish pacifist, lost her job in 1933 when the Nazis took power and emigrated to the United States. After an operation to remove a cyst in 1935, she seemed to develop a severe infection and died at 53. Her "afterthought" of a theorem will probably be around for a lot longer, unless we somehow discover that conservation or general relativity are incorrect. It seems unlikely, but science is about the strange and unlikely, so who knows.