[FOM] Epistemology for new axioms

[Timothy Y. Chow]

Joe Shipman wrote:

> 2) Both sides of the open question can be fruitful in set theory; but
>    I’m not aware of a comparable situation in ordinary mathematics
>    (there aren’t a lot of papers on the consequences of ~RH).

This is perhaps getting off-topic, but the existence of Siegel zeros 
contradicts GRH, and there are some pretty interesting papers about the 
consequences of the existence of Siegel zeros.  For example, Heath-Brown 
has proved that if Siegel zeros exist then the twin prime conjecture 
follows.  There's a nice blog post by Terry Tao on this topic:

https://urldefense.proofpoint.com/v2/url?u=https-3A__terrytao.wordpress.com_2015_08_26_heath-2Dbrowns-2Dtheorem-2Don-2Dprime-2Dtwins-2Dand-2Dsiegel-2Dzeroes_&d=DwIDaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=Yd6zS37d-UWMvpPLZDsivHey-HBek0S4zXvJ6oY44FA&s=7nnt8Xo5kjwLcT7AGfcm2UNZss6Bj_kujIx8o0jWrbA&e= 

Tim