Mathematician!

By: Megan Wilson

•Born on March 23, 1882

•Died April 14, 1935

•Born in Erlangen, Germany

•Father and brother also had careers in mathematics.

•When she was a child, she wasn’t looking at

mathematics, she was looking at languages.

About Emmy Noether

•Noether’s Theorem

Suppose we have a particle moving on a line with Lagrangian L(q,q'), where q is its position and q' = dq/dt

is its velocity. (I'll always use the symbol ' to stand for time derivatives.)

The momentum of our particle is defined to be:

p = dL/dq' The force on it is defined to be F = dL/dq The equations of motion - the so-called Euler-Lagrange

equations - say that the rate of change of momentum equals the force: p' = F That's how Lagrangians work!

Next, suppose the Lagrangian L has a symmetry, meaning that it doesn't change when you apply some

one-parameter family of transformations sending q to some new position q(s).

This means that:

d/ds L(q(s), q'(s)) = 0. Then I claim that C = p dq(s)/ds is a conserved quantity: that is, C' = 0.

Proof - Take the time derivative of our supposed conserved quantity using the product rule: C' = p' dq(s)/ds

+ p dq'(s)/ds Next, use the equation of motion of our particle and the definition of momentum to rewrite the

p' and p terms in this equation: C' = dL/dq dq(s)/ds + dL/dq' dq'(s)/ds Finally, use the chain rule to recognize

that the right side of this equation is d/ds L(q(s), q'(s)) = 0!

Riddle, Larry. "Biographies of Women Mathematicians." Emmy

Noether (1995): n. pg. Web. 29 Jun 2011.

<http://www.agnesscott.edu/lriddle/women/noether.htm>.

Baez, John. "Noether's Theorem in a Nutshell." (2002): n. pg. Web. 30 Jun 2011.

<http://math.ucr.edu/home/baez/noether.html>.