UKC

In my copy of David Wells "curious and interesting numbers" he says that 51 is the smallest number that is uninteresting. However QI said it was 11630 so who is right?

In reply to Duncan Bourne:

I find the number 16 to be deeply tedious. Don't ever let it near the brandy, or it'll tell the most godawfully racist stories about its cleaner.

51 Is a hoot and a delight.

Martin

In reply to Duncan Bourne:

It'll be something to do with primes or cubes.

1729 is pretty fascinating if you believe Srinivasa Ramanujan

In reply to Duncan Bourne:

There are no uninteresting numbers.

Proof:
Assume there are uninteresting numbers. Let x be the first (lowest value) uninteresting number.

Then x is interesting *because* it is the first uninteresting number. So the assumption that there are uninteresting numbers implies a contradiction.

In reply to Duncan Bourne:

I just cycled to a country pub & had a great pint of 'Sur Votre Velo'

In reply to Duncan Bourne:

How can triple 17 possibly be uninteresting? A jolly useful number if you're a darts player.

In reply to DaveHK:



A friend of mine when I was an undergrad was in the maths department, trying to get into a specific computer room which had a four digit entrance code that he didn't know. He asked a passing postgrad who told him that it was the smallest number that's expressible as a sum of two cubes in two different ways, so he immediately tapped in 1729 and walked in. He only realized later how amazing that scene would have looked to someone who didn't know that pretty much all mathematicians know the Ramanujan taxicab story by heart...

In reply to tom_in_edinburgh:





That's so feeble. It's logical, yes, but it's just so feeble.

In reply to Gordon Stainforth:


I think it's quite a good mathematical joke.

In reply to tom_in_edinburgh:

Ah QI had already discounted that argument due to that very paradox

In reply to Duncan Bourne:

I'm 51 years old this year. There's only a small number of people interested in that - maybe just one.

In reply to DaveHK:


That's where 51 went wrong, crimes and pubes would have been more interesting.

In reply to Duncan Bourne:


Ah indeed: QI, the ultimate authority on all things.

So much so, that they recently had to revise the scores awarded in all previous programmes due to…well, basically because the just-out-of-college researchers they use are a bunch of credulous, lazy smartarses who simply choose the first 'fact' they find online which contradicts the general belief, and run with that.

I wouldn't take anything stated on QI as being definitive.

In the case of the uninteresting numbers argument, the paradox is the argument, so saying that the argument is invalid because it is paradoxical is utterly and completely missing the point.

In reply to Martin W:

Oh I quite agree that the least interesting number is by definition interesting.

However I was wondering why 51 was no longer the first least interesting number (interesting in an earlier edition of the same book it was 39, it is tempting to think that it is a kind of receding mirrors trick, ie the first LIN becomes interesting because it is the first so then the second LIN becomes the first but then that is therefore interesting and so on and so forth. However I can't imagine a publisher upping the anti purely on the basis of that argument)

Leaving aside QI and the ''paradox", 51 is interesting as it is a pentagonal number.

I think QI were using the definition on uninteresting to mean an integer not appearing in any sequence listed in the On-Line Encyclopedia of Integer Sequences.

In reply to Philip:

Ah mystery solved

In reply to Martin W:


It's entertainment ! The fact that it stimulates thinking and interest is a bonus - admittedly a very good one. I reckon one of the best program's from my youth was Johnny Ball's Think of a number and QI is almost a grown up version of that.

As to the researchers - they now have their own podcast - no such thing as a fish - that is also very good.

Also, to paraphrase Brian cox - another entertainer - the more you know, the more you realise you don't know.

In reply to Ramblin dave:

Not heard that story before, thanks for mentioning it

http://en.m.wikipedia.org/wiki/1729_(number)

In reply to Philip:


Well spotted! 51=36+15 (6 squared + 5th triangular number)
Definitely interesting.

In reply to Philip:

I think QI were using the definition on uninteresting to mean an integer not appearing in any sequence listed in the On-Line Encyclopedia of Integer Sequences.

One of the sequences is the list of all numbers not appearing in the OIEIS.

In reply to tom_in_edinburgh:

Yes, but why would there be no uninteresting rationals ? Your proof does not work for them.

In reply to Dror1:


I'm not a mathematician, its not my proof. I think I read it in one of Martin Gardner's books when I was a kid.

My guess is the proof could be made to work for rationals because rationals are a countable set.

It probably doesn't work for real numbers though. There are plenty of boring real numbers

In reply to Duncan Bourne:

It's palindromic in base 2

In reply to tom_in_edinburgh:

The rationals are countable but there is no minimal or maximal number, therefore the proof would depend on the mapping to the naturals, so different mappings would produce different interesting uninteresting rationals in an arbitrary manner, so you would have to define interesting regarding the rationals in a broader way then the naturals, say in relation to the natural mapping.. ('snake' in a grid map)

In reply to Duncan Bourne:

If 51 is truly uninteresting, isn't -51 also uninteresting but smaller?

In reply to Duncan Bourne:

51 has to be interesting. After all it has a UKC thread all of its own.

In reply to Dror1:


Let's have a go

Assume that there exist uninteresting rational numbers x.

Let rational x = n/d, (n whole,d natural, d > 0).

a. There are no uninteresting rational numbers for any chosen value of d (since d is fixed the smallest rational number with denominator d is the one with the smallest n). The smallest uninteresting rational with denominator d is interesting *because* it is the smallest 'uninteresting' rational number with denominator d.

b. Since there no uninteresting rational numbers for all values of d there are no uninteresting rational numbers.

In reply to Ramblin dave:

Not 9191 then?

In reply to Jim Fraser:


Of course, the combination for the sound engineers' cupboard would be 1212...

In reply to tom_in_edinburgh:

not bad..
conclusion all numbers are interesting ? )
cos irrationals are always interesting by default..