Semmelweis (1818-1865) became a medical assistant at the First Obstetrical Clinic of the Vienna General Hospital in 1846. There were two Obstetrical Clinics in Vienna at that time: the First and the Second Clinic. Their main difference was that the Second Clinic had a much lower mortality rate due to puerperal fever.
The two clinics used in general the same techniques. The First Clinic was to instruct medical students, the Second Clinic was to instruct midwives only. Medical students had access to autoptic exams, while midwives students would not perform them. Semmelweis had a theory that some unknown "cadaverous material" was what caused puerperal fever. He recommended then to wash hands with a solution of chlorinated lime between autopsy work and the examination of patients.
The result was that in April 1847 the mortality rate in the First Clinic dropped a ten-fold and became comparable to the one of the Second Clinic and kept dropping after handwashing was instituted.
Semmelweis could not explain why really this was happening. He had this theory but he could not really explain what was happening with the "cadaverous material". Only Pasteur around 20 years later could come up with the germ theory.
However, even if Semmelweis could not explain it, the numbers were clearly saying that less women were dying. It would have been worth it, to listen to them.
Nobody did. Semmelweis experienced the full hostility of the medical establishement, his contract was not renewed, he edied in an asylum.
... and a lot of women kept dying for the next 30 years or so.
To know more, http://en.wikipedia.org/wiki/Semmelweis gives many more details about this story.