"Is there any proof" versus "are there any proofs"

Solution 1:

If you begin the sentence with the singular copula (is) you are expected to make the object agree in number. Breaking down the SO sentence to its essentials, we have:

Is there any proofs?

This is grammatically incorrect. We can make these agree in number in two ways (as your own examples do):

Is there any proof?

Are there any proofs?

Either is correct. "Proof" or "proofs" doesn't matter as long as the number agrees with the number of the copula.

Solution 2:

"Proof" is usually treated as a mass noun, and so has no plural:

"I have proof that ... "

"There is no proof that ... "

"You haven't any proof that ... "

It can be used as a count noun, but usually only in special senses, such as a formal (mathematical or logical) proof:

"His book contains several new proofs of these theorems".

I would find it strange to read "They produced several proofs of his innocence".

Solution 3:

My grammar book (English Grammar, David Daniels and Barbara Daniels) reports that the indefinite pronoun any is either singular or plural.

Someone asked him for a match, but Joe didn't have any.
Do you have any tips to pass on?
I don't have any choice.

In your example, I would use "Is there any concrete-solid proof of this space odyssey?" because if there isn't a single proof, then there aren't two proofs either.

Solution 4:

You're more likely to encounter the plural in formal logic, maths, etc., where a given proposition may have multiple proofs. In other contexts it's more common to lump all the supporting evidence together as (singular) proof.