> No way. Mathematicians don't assume things to be true even if there are no counterexamples. It depends: there do exist some conjectures for which there don't

> No way. Mathematicians don't assume things to be true even if there are no counterexamples. It depends: there do exist some conjectures for which there don't exist any proofs, but a huge amount of results assuming this conjecture (which is very near to assuming that the conjecture is true). Examples are: - Riemann hypothesis [1] - Generalized Riemann hypothesis (GRH) [2], and potentially also Extended Riemann hypothesis (ERH) [3] - Standard conjectures on algebraic cycles [4] - perhaps Schanuel’s conjecture [5] -- [1] https://en.wikipedia.org/w/index.php?title=Riemann_hypothesis&oldid=1375292396 https://en.wikipedia.org/w/index.php?title=Riemann_hypothesi... [2] https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Generalized_Riemann_hypothesis_(GRH) https://en.wikipedia.org/w/index.php?title=Generalized_Riema... [3] https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Extended_Riemann_hypothesis_(ERH) https://en.wikipedia.org/w/index.php?title=Generalized_Riema... [4] https://en.wikipedia.org/w/index.php?title=Standard_conjectures_on_algebraic_cycles&oldid=1374346010 https://en.wikipedia.org/w/index.php?title=Standard_conjectu... [5] https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conjecture&oldid=1375037872 https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conj...