What is the number of species known through paleontological evidence?
Very interesting question.

I remember reading about it in one of Stephen Jay Gould's great books (The Panda's Thumb? The Flamingo's Smile? Wonderful Life: The Burgess Shale and the Nature of History? Dinosaur in a Haystack? Probably in one of these).

He wrote exactly about this question, and the effort made by teams from many different countries to get to an "approximate" result. What really impressed me at the time (fifteen years ago) is that when Chinese scientists were invited to add material for a second analysis, the number of known fossil species doubled!

Please, if anyone find the exact source of this, I'll be glad to read it!

But maybe you can get an idea by looking at the number of fossil species for certain groups, and comparing with the number of estimated/known extant species. Keep in mind the rates of fossilization for each group, and also the fact that Nematoda and Acari might be the most overlooked groups in terms of species number (both seem to parasitize animals through most of the Animal Kingdom).