[danieldyer]

Don't forget Emmy Noether: http://en.wikipedia.org/wiki/Emmy_Noether

"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians."

- Albert Einstein

[ibebrett]

She was brilliant, but lets not go overboard. She's not even the biggest name in the fields of math she contributed to.

[danieldyer]

She's certainly far less well known than many of her contemporaries, but Noether's theorem is an incredibly important tool in theoretical physics, and has been described as "certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem". [1]

[1]: http://en.wikipedia.org/wiki/Emmy_Noether#cite_note-FOOTNOTE...

[stolio]

I don't know what she did for math but Noether's Theorem in physics, that symmetries in nature are connected to conservation laws, is impressive.

No idea how far up the totem pole that puts her.

[ibebrett]

she was involved in commutative algebra. she had a nice little section in my undergrad abstract algebra book. i'm not saying anything negative about her, just that if you are going to list the most brilliant/productive scientists of all time then shes not going to be on the list. she was brilliant of course.