3
$\begingroup$

My question is that : Why are there so many conjectures in elementary number theory and comparatively less in others? This is particularly weird because every topic in maths should have its equal share of conjectures. On the other hand there are so many conjectures in number theory. Also (most of) these conjectures are so easy to state but literally impossible to prove.

I thought of this question because I myself have two open conjectures in number theory.

$\endgroup$
  • 2
    $\begingroup$ maybe a hint about the answer could be, why do you have two open conjectures in number theory and not in other fields? $\endgroup$ – iadvd May 28 '15 at 8:16
  • 1
    $\begingroup$ Where are the numbers of conjectures by field available? What is the ratio of conjectures in number theory to conjectures in the second most conjectural fields of math? And what is the runner up to number theory? $\endgroup$ – Gregory Grant May 28 '15 at 8:19
  • 5
    $\begingroup$ One possible polemic answer: the number of worthwhile conjectures is about equally distributed amongst the various fields of math. $\endgroup$ – Zev Chonoles May 28 '15 at 8:20
  • 2
    $\begingroup$ @Zeb Chonoles I agree ! We have approximately the same number of open problems in all fields. The impression that there are more in Number Theory is coming from the fact that in that area many open problems can be expressed in a language understandable by the laymen. $\endgroup$ – marwalix May 28 '15 at 8:26
  • 1
    $\begingroup$ You may narrow down your question to elementary number theory, for the mathematical concepts involved are more likely to be understood by more people. For example, for people of no math maturity it is very difficult to explain to them the meaning of the phrases such as "for large $n$". $\endgroup$ – Megadeth May 28 '15 at 8:35
3
$\begingroup$

I think there are two ways to answer this question.

  1. I am atleast not sure that there are more in number theory in other fields. However as number theory is close to basic arithmetic at times the conjectures are easier to understand and thus they get more famous, so it simply appears as there are more conjectures than in other fields.

  2. If 1. is false i.e. there are more conjectures in number theory than in other fields, this is probably because questions are easy to ask but seem in general quite hard to proove, as we have seen with Golbachs conjecture, Twin prime conjecture and Fermats theorem. Also, most fields rely more or less on numbers and thus number theory appears when doing their calculations which leads to more conjectures.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy