4 ms·
You could ask the same “Other than <its value>, what value does <it> have?” question about anything. (The answer is: none. For that matter, how would you answe
by svat 3y ago
You could ask the same “Other than <its value>, what value does <it> have?” question about anything.
(The answer is: none. For that matter, how would you answer questions like: what value does the concept of even-and-odd numbers have? Or, say, Fibonacci numbers: sure the Fibonacci sequence itself might have some applications, but what value does knowing whether or not a certain number is a Fibonacci number have?)
- permo-w 3y agoyou could ask that, and you would be right to untouchable numbers have what seems like a pretty arbitrary definition and yet the article mentions the numbers being studied a thousand years ago, which begs the question: why? why not numbers that can only be produced by adding 3 primes together? why not only numbers that can be produced by multiplying squares greater than 1? there are infinite unique infinite sets of integers. why is this one more interesting than the other infinity to the degree that it's been studied for a thousand years? if it's given that the Fibonacci sequence has uses, then knowing the numbers in that sequence is also obviously going to be useful
- gizmo686 3y ago> why not numbers that can only be produced by adding 3 primes together? Goldbach's weak conjecture: Every odd number greater than 5 can be expressed as the sum of three primes. First proposed in 1742, and proven in 2013 [0]. The original proposal considered even numbers as well, nowadays those are covered by Goldbach's strong conjecture, with a tighter bound of 2 primes. > why not only numbers that can be produced by multiplying squares greater than 1? You mean squares containing at least 2 distinct prime factors? Fully classifying this set of integers would fit well on an undergrad intro to proofs exam. [0] https://arxiv.org/pdf/1501.05438.pdf https://arxiv.org/pdf/1501.05438.pdf
- permo-w 3y agothe actual examples I give are just that, examples. why not numbers that can only be produced as the sum of 17 primes? or 459? or numbers that have the same number of factors as their digits added together does? there are infinite of these constraints that can be invented. why is this one particularly interesting
- naikrovek 3y agoI can't tell if you're really asking, so I'll answer as if you are: learning these things brings greater understanding and greater understanding brings advances in multiple fields. the most fundamental questions are going to be answered (or at least conceived of and worked on) first. answering the most fundamental questions often brings the largest leaps in understanding as well, which is why untouchable numbers are considered more notable than "numbers which can be expressed as the sum of 17 primes", and so on.
- lozenge 3y agoAll the examples you gave before have already been studied and are also particularly interesting. Maths is a huge and well explored field.
- earthboundkid 3y agoBecause Platonism is true and math is a telescope that lets us glimpse at the world of ideals.
- erehweb 3y agoAs an attempt - it's a simple definition, easy to check for small numbers, but leads to some difficult questions - are there infinitely many of them? (found yes by Erdos) How dense are they in the number line? Are there any odd ones > 5? "Numbers that can only be produces as the sum of 459 primes" is not as easy to find examples of, so less aesthetically pleasing to mathematicians.
- romusha 3y agoBecause dees n