Editing Conjecture (section)

===Other conjectures===
* [[Goldbach's conjecture]]
* The [[twin prime conjecture]]
* The [[Collatz conjecture]]
* The [[Manin conjecture]]
* The [[Maldacena conjecture]]
* The [[Euler's sum of powers conjecture|Euler conjecture]], proposed by Euler in the 18th century but for which counterexamples for a number of exponents (starting with n=4) were found beginning in the mid 20th century
* The [[Second Hardy–Littlewood conjecture|Hardy-Littlewood conjectures]] are a pair of conjectures concerning the distribution of prime numbers, the first of which expands upon the aforementioned twin prime conjecture. Neither one has either been proven or disproven, but it ''has'' been proven that both cannot simultaneously be true (i.e., at least one must be false). It has not been proven which one is false, but it is widely believed that the first conjecture is true and the second one is false.<ref>{{cite journal | first=Ian | last=Richards | title=On the Incompatibility of Two Conjectures Concerning Primes | journal=Bull. Amer. Math. Soc. | volume=80 | pages=419–438 | year=1974 | doi=10.1090/S0002-9904-1974-13434-8 | doi-access=free }}</ref>
* The [[Langlands program]]<ref>{{citation|last=Langlands|first=Robert|title=Letter to Prof. Weil|year=1967|url=http://publications.ias.edu/rpl/section/21}}</ref> is a far-reaching web of these ideas of '[[unifying conjecture]]s' that link different subfields of mathematics (e.g. between [[number theory]] and [[representation theory]] of [[Lie group]]s). Some of these conjectures have since been proved.