Mathematics

It is often said that if we ever make contact with extra-terrestrials the only language we might share would be mathematics. Whilst prime numbers or pi might communicate “we are intelligent life forms”, can mathematics really say anything more than this?

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I'm not sure what this "often said" remark is supposed to mean. Mathematics is not a language but a subject-matter. We use language, and different people use different languages at different times, to speak about mathematics. So mathematics isn't any different, in this respect, than anything else, so far as I can see.

That said, perhaps what you have in mind might be that the way aliens conceptualized the world might be so different from the way we did that we could not understand their language. I have no idea if any such speculation might be true, but it presumably would be true that, at least initially, we could no more understand them than I can understand someone who was talking Chinese. And maybe their way of dealing with the world would be so different that we were unsure if they really were intelligent, and they had the same doubt about us. But then, the thought might be, I could take out a stick and start doing the following: Tap twice; rest; tap three times; rest; tap five times; rest; tap seven times; rest; tap eleven times; rest; and so forth. Then perhaps they'd recognize me as doing something involving the sequence of primes and so as doing something intelligent. Perhaps.

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