Talking to my 8 yr old about "the greatest mathematician of all time", I said it was probably Gauss in my opinion, but that Gauss was not very kind to his kids (for example, forbidding them to go into mathematics because it would "ruin the family name"). So I recommended Euler as being a better choice (from what I've read, Euler was an all-around good guy).
My son already knows a result of Gauss: the trick that lets you sum the first $n$ integers. So he asked for a result from Euler, but the best I could do was the Euler Totient function. Although my son now knows the totient function, he finds it pretty unmotivated and no where near as cool as the Gauss trick.
Can you suggest something from Euler that might appeal to an 8 yr old? Number theory and calculus are ok, but no groups/rings/fields, no real analysis, no non-Euclidean geometry, etc.
Best Answer
How about Euler's theorem on Eulerian paths in graphs, which originated from his solution to the Königsberg bridge problem?