Would aliens understand lambda calculus?

Unless you are a sci-fi author or some secret government agency, the question whether aliens would understand lambda calculus is probably not your main practical concern. However, the question is intriguing because it nicely vividly formulates a fundamental question about our formal mathematical knowledge. Are mathematical theories and results about them invented, i.e. constructed by humans, or discovered, i.e. are they eternal truths that exist regardless of whether there are humans to know them?

The question makes for a fantastic late night pub debate, but how can we go about answering it using a more serious methodology? Is there a paper one can read to better understand the problem? Occasionally, a talk or an online comment by a computer scientist comments on this question, but way too often, people miss the fact that the nature of mathematical entities is one of the fundamental questions of philosophy of mathematics. Alas, all those discussions are carefully hidden in the humanities department!

I believe that knowing a bit about philosophy of mathematics is important if we want to have a meaningful debate about philosophical questions of mathematics (sic!) and so I did a talk on this very subject at CodeMesh 2017. This article is slightly refined and hopefully more polished version of the talk for those who, like me, prefer reading over watching. Keep in mind that the question about the nature of mathematical entities is one of the fundamental questions of an entire academic discipline. As such, this article cannot possibly cover all the relevant discussions. Compared to some other writings in this space, this article is, at least, based on a couple of philosophical books that, I believe, have useful things to say on the subject!

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