michaellevenson
Member: Rank 8
17 is an interesting number because it is the only prime which is the sum of four consecutive primes: 17= 2+3+5+7. It seems unlikely however that every natural number is interesting.
But every natural number must be interesting, for if this were not so there would be a first uninteresting number. And being the first uninteresting number would make it interesting!
But every natural number must be interesting, for if this were not so there would be a first uninteresting number. And being the first uninteresting number would make it interesting!
When the distinguished number theorist G.H.Hardy was visiting the dying Ramanujan, he told him that his taxi had the apparently boring number 1,729. Ramanujan replied: " No Hardy ! It is very interesting, it is the smallest number expressible as a sum of two cubes in two different ways." 1,729 = 1³+ 12³ or 10³ +9³
' Interesting ' is a relative term, in the present context does it mean interesting to ordinary educated people, to mathematicians or to whom?
If there are any uninteresting numbers there must be a first, and that it was the first uninteresting number would make it interesting. So the next number with no interesting properties will be uninteresting, no, that'll be the new first uninteresting number and therefore interesting. Hence the conclusion that every number is interesting.
However suppose there are uninteresting numbers. In order to characterize the first of these as interesting, we must first characterize it as ground- level uninteresting, uninteresting because it has no remarkable numerical property.
Then it is interesting because it is the first ground- level uninteresting number: call it 2nd- level interesting.
The next uninteresting number will be the first number that is not 2nd- level interesting, and thus 3rd- level interesting, and so on.
The 34th of the original ground-level uninteresting numbers will be 35th -level interesting. The 900th ground- level uninteresting number will be 901st- level interesting. None of this seems very interesting!!
Indeed the first ?th level uninteresting number doesn't seem to be an interesting property any greater than the 1st.
And if that is so , we are not forced to the conclusion that every number is interesting. The only interesting numbers will be those that have notable numerical properties ( the ground- level interesting ), and the first of those that doesn't- if it exists, as it probably does. The first number that theorists say is with no remarkable property is 39. If this is right include 39 among the interesting numbers along with the ground- level interesting ones, the others will be uninteresting.
' Interesting ' is a relative term, in the present context does it mean interesting to ordinary educated people, to mathematicians or to whom?
If there are any uninteresting numbers there must be a first, and that it was the first uninteresting number would make it interesting. So the next number with no interesting properties will be uninteresting, no, that'll be the new first uninteresting number and therefore interesting. Hence the conclusion that every number is interesting.
However suppose there are uninteresting numbers. In order to characterize the first of these as interesting, we must first characterize it as ground- level uninteresting, uninteresting because it has no remarkable numerical property.
Then it is interesting because it is the first ground- level uninteresting number: call it 2nd- level interesting.
The next uninteresting number will be the first number that is not 2nd- level interesting, and thus 3rd- level interesting, and so on.
The 34th of the original ground-level uninteresting numbers will be 35th -level interesting. The 900th ground- level uninteresting number will be 901st- level interesting. None of this seems very interesting!!
Indeed the first ?th level uninteresting number doesn't seem to be an interesting property any greater than the 1st.
And if that is so , we are not forced to the conclusion that every number is interesting. The only interesting numbers will be those that have notable numerical properties ( the ground- level interesting ), and the first of those that doesn't- if it exists, as it probably does. The first number that theorists say is with no remarkable property is 39. If this is right include 39 among the interesting numbers along with the ground- level interesting ones, the others will be uninteresting.
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