Actually, you *can* prove a negative.
A lot of people say "you can't prove a negative", which I think is wrong. You can prove a negative. What you can't do is prevent other people from employing the fallacy of special pleading against an otherwise convincing proof.
Categorical negatives like "there are no Chinamen with blond hair" are difficult to prove, not because they're negative, but because they're very broad statements. Similarly broad positive statements are also difficult to prove for the same reason, such as "all Chinamen have black hair". Unfortunately "you can't prove a negative" is much punchier than "it is difficult to prove a universally true categorical statement".
Update: I just realize that, ironically, "you can't prove a negative" is in itself a broad categorical assertion that's extremely difficult to prove.
Categorical negatives like "there are no Chinamen with blond hair" are difficult to prove, not because they're negative, but because they're very broad statements. Similarly broad positive statements are also difficult to prove for the same reason, such as "all Chinamen have black hair". Unfortunately "you can't prove a negative" is much punchier than "it is difficult to prove a universally true categorical statement".
Update: I just realize that, ironically, "you can't prove a negative" is in itself a broad categorical assertion that's extremely difficult to prove.