Nine scientists participated in the Mad Scientist Competition, and they each placed between first and ninth. After the competition, they each made the following statements. Since they are scientists, they only ever make a statement if they believe it to be true. However, each scientist is either mad or sane. A mad scientist believes that the truth value of any statement is the opposite of its actual truth value.

**Alan Turing**: At least one of me and Lise Meitner is in a Fibonacci position.**Albert Einstein**: Exactly one of me and Lise Meitner is mad.**Emmy Noether**: Isaac Newton thinks that Enrico Fermi, Kevin Carde, Lise Meitner and I are in the prime-numbered places.**Enrico Fermi**: I got fifth!**Isaac Newton**: Albert Einstein thinks he got sixth.**Jane Goodall**: I think that Enrico Fermi, Isaac Newton, and Kevin Carde got the first three places.**Kevin Carde**: Alan Turing thinks that his placement is a multiple of mine.**Lise Meitner**: The number of mad scientists is prime or even (or both).**Robert Hooke**: Kevin Carde thinks that I did worse than Albert Einstein but better than Alan Turing.