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Question: What are some explicit examples of major mathematical results understandable by an intelligent lay person ?

Here are few I managed to google:

Euclid - infinitude of primes.

Cantor - the real numbers are uncountable.

Anthony
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    "Hindsight is 20/20". I think this question is contradictory. If something led to "major implications" it can't have been a trivial result. At the very least, it only appears trivial to us, when we are armed with a lot of modern concepts and language which didn't exist at the time of the discovery – Yuriy S Oct 30 '18 at 17:32
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    Related: https://math.stackexchange.com/questions/2398642/conjectures-or-intuitions-that-turned-out-wrong-in-an-interesting-or-useful-wa – Ethan Bolker Oct 30 '18 at 18:06
  • @HansLundmark corrected. – Anthony Oct 30 '18 at 18:25
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    To the edited question: now this makes sense, though the term "intelligent" is subjective. Maybe you mean "a person with basic understanding of mathematics and logic"? I know a lot of very intelligent people who would have a hard time understanding Cantor's argument, neither would they want to – Yuriy S Oct 30 '18 at 19:31

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As in the comment by Yuriy S, trivial is not the word we want to use.

That said, the proof that $\sqrt{2}$ is irrational is easily understandable and had profound implications. It was thought that all numbers could be expressed as the ratio of two integers yet this one could n0t. This is profound because we knew that the diagonal of a unit square has a length equal to $\sqrt{2}$ and yet this number couldn't exist under the assumptions of the day.

This lead to the concept of an irrational number and eventually, the real numbers.

John Douma
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