2 ms·
No way. Mathematicians don't assume things to be true even if there are no counterexamples.
by vouaobrasil 17d ago
No way. Mathematicians don't assume things to be true even if there are no counterexamples.
- scrubs 17d agoAgree. I give up isn't the MO of many with graduate degrees.
- bmitc 17d agoGenerally, no, but sometimes, yes. It can be productive to assume something is true and see what happens.
- aleph_minus_one 17d ago> 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...