For any true statement X, a mad scientist will think that X is false. Thus they will think that they think that X is true. Since all scientists are truthtellers, this means that whenever anyone says "I think X," X must be true. Thus based on what Jane Goodall says, Enrico Fermi, Isaac Newton, and Kevin Carde were in the top 3. Enrico Fermi thinks he got fifth, so he is mad. Meanwhile, if Albert Einstein is sane, then Lise Meitner is mad, so the number of mad scientists is 1 or 9; since Enrico Fermi and Lise Meitner are already mad, it must be 9, which is a contradiction. Thus both Albert Einstein and Lise Meitner are mad, which in turn implies that all scientists are mad.
Now it remains to find the ordering. Since all scientists are mad, any statement of the form "So-and-so thinks X" implies that X is true. Thus Enrico Fermi, Kevin Carde, Lise Meitner, and Emmy Noether are in the prime-numbered places, so Enrico Fermi and Kevin Carde are 2nd and 3rd in some order, and Isaac Newton is first. Moreover, Albert Einstein is 6th. Neither Alan Turing nor Lise Meitner are in a Fibonacci position, so Lise Meitner must be 7th and Alan Turing is 4th or 9th. Thus Emmy Noether is 5th. Since Robert Hooke, who isn't in the top 3, did better than Alan Turing, Alan Turing is 9th. Since Robert Hooke did worse than Albert Einstein, the only remaining option is that he is 8th. Thus by elimination, Jane Goodall must be 4th. Since Alan Turing's placement is a multiple of Kevin Carde's, Kevin Carde must have gotten 3rd, and Enrico Fermi must be 2nd. This yields the ordering: