Is there a checksum that gives the same checksum when in a text file? Let's say I have a text file (crypto.txt). Let's assume the checksum function can be any type of function (MD5, SHA-1, anything else). Is there a way that the checksum value IN the file (crypto.txt contains a string that could be a possible checksum), when put through a checksum program, outputs the exact same value as the content inside the text file?

In case I lost you, here's a quick breakdown:

crypto.txt contains a viable checksum value (said value = x)
checksum of crypto.txt = x


Is this even possible? Is there math that proves it wrong/right?
For a checksum such as CRC16 or CRC32 it is very much possible to have a value over a text that contains the same CRC value (in whatever format, be it binary, hexadecimals or base 64). The proof of this is simple: you can simply put e.g. 32-48 bits counter at the end of the text and wait until you find a CRC. But in practice you can just calculate the value you need to prefix, append or anything in between and get the right CRC - if it is included or not. Checksums such as CRC are not secure.

For secure hash functions this is not possible. It is even computationally not possible to find any message $m$ where the hash value is $h$, for any chosen $h$ (that is not a known hash value). This is a much stronger presumption than the one you are proposing. It is not possible to find $x = \operatorname{H}(a | \operatorname{encode}(x) | b)$ even if you can chose any special value of $a$ and $b$, and any $\operatorname{encode}$ operation.

It is not possible to prove above completely for the simple fact that the security of hash functions cannot be proven. SHA-1 was thought to be secure for a long time, but by now it might be possible to create a text where the hash value is included.