You can try to find the answer on Wikipedia. The smallest number without its own wikipedia entry is 224 (as of today). Despite it being the sum of four consecutive cubes (224 = 8+27+64+125), it only manages to share space with the article on the number 220, appearing in the "221-229" subsection.
Surely that's a lousy criterion! Sooner or later, some bored guy behind a computer is going to write up an article on the number 224, following which, 225 would become the smallest uninteresting number. That's despite it being more interesting than 224... after all it is the sum of five consecutive cubes.
It might be better to ask an actual mathematician. G. H. Hardy, the British mathematician who wrote "A Mathematician's Apology", was visiting his advisee, the great Indian mathematician Ramanujan, at a hospital. Being the typical awkward conversationalist, Hardy began by remarking on the dullness of the license plate number of the taxi he was in -- 1729 --- and was hoping that it would not turn out to be an unfavourable omen. To which Ramanujan replied, "No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways".
Surely that's a lousy criterion! Sooner or later, some bored guy behind a computer is going to write up an article on the number 224, following which, 225 would become the smallest uninteresting number. That's despite it being more interesting than 224... after all it is the sum of five consecutive cubes.
It might be better to ask an actual mathematician. G. H. Hardy, the British mathematician who wrote "A Mathematician's Apology", was visiting his advisee, the great Indian mathematician Ramanujan, at a hospital. Being the typical awkward conversationalist, Hardy began by remarking on the dullness of the license plate number of the taxi he was in -- 1729 --- and was hoping that it would not turn out to be an unfavourable omen. To which Ramanujan replied, "No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways".
I learnt of this lovely anecdote while watching QI, which is short for "Quite Interesting", which is a most interesting show on the BBC where Stephen Fry and four blokes would converse about obscure trivia --- fascinating, funny and most definitely repulsive to the pragmatist.
According to QI, the "correct answer" is 12407. This sleep-inducer holds the distinction of being the smallest number absent from all 200000 sequences in the Online Encyclopaedia of Integer Sequences. That is to say, it's not interesting enough to appear in any number sequence that mathematicians might be interested in.
But surely, that is interesting? To be the smallest uninteresting number is probably one of the most interesting attribute any number can have! And so we have a paradox. If there were a smallest uninteresting number, then it would in fact be interesting by the mere fact that it is so small and so uninteresting. Therefore, there can't be a smallest uninteresting number.
And so what have we gotten ourselves?
For all the math-haters out there, we have a proof that all numbers are interesting.
(I am of course, referring to natural numbers 1,2,3,... As always, the real numbers are a different beast altogether, and one might be able to argue that there are uninteresting real numbers.)
