Interesting question

[bonanova]

Peter and Paul were overheard yesterday at the water cooler. Their conversation went something like this:

Peter: I just love numbers. I find them all interesting.

Paul: What do you mean by that?

Peter: Look at the number six. It's perfect, because 1 x 2 x 3 = 1 + 2 + 3 = 6. And four is interesting because 2 x 2 = 2 + 2 = 4. No other number has that property. Two is the first, and only, even prime number. A really interesting number is 1729 =  1³ + 12³ = 9³ + 10³. It's the smallest number that is the sum of two distinct pairs of cubes. Then there's ...

Paul: But can you consider all numbers interesting? Surely there are many that lack an interesting property of the type you have described. I would call such numbers uninteresting.

With whom do you agree?

[harey]

Well, I know the "official" answer to this problem, but I do not agree with it. Human language is very imprecise, "interesting" is quite subject to interpretation.

I.e. my ex does not find 4 interesting at all. 2+2=2*2=2^2? So what?

[bonanova]

Peter says all numbers are interesting, in the sense of his given examples. Paul says there are uninteresting numbers, in the same sense. Who can make the better case for his position?

[harey]

The list of given examples is not exhaustive nor limiting. You can tailor a property to any number and we can argue ad eternum whether this property is interesting or not. Just my personal opinion

[bonanova]

The list of given examples is not exhaustive nor limiting. You can tailor a property to any number and we can argue ad eternum whether this property is interesting or not. Just my personal opinion

That would argue in favor of Peter's position then. Is there an even stronger argument?

[harey]

Yes, the "official" one.

But as I know it, it would be unfair to publish it. So I will leave it to someone else. We gave some hints now, did not we?