[gimboland]

> but how did the author learned to love, and more importantly to "fear" the RH? What's there to fear?

It's made abundantly clear: they learned to love it through the course they were fortunate enough to take as an undergraduate, and they learned to fear it later, as a researcher, when they realised that what there was to fear was wasting their career attacking something that was probably just too big and too hard to be sensible for them to attack.

[Tade0]

I understand that the real proof of the RH is the friendships we make along the way, but what would happen if we just acted with the assumption that it is true?

[rfurmani]

There's been a lot of research that has assumed it to be true and built on top of it to find deeper implications.

Still, a number of people who've worked most closely with the Riemann zeta function, even the ones who led the computations and numerical verifications, have expressed doubts on whether the Riemann Hypothesis is actually true: https://arxiv.org/abs/math/0311162

[waynecochran]

This is the difference between a scientist and a mathematician. A scientist would consider the empirical evidence more than sufficient to consider RH to be true.

Of course there is hope that a proof of RH would reveal some deeper understanding -- not merely a conformation.

[hansvm]

I'm not so sure a scientist would consider RH true at this point. Math has a rich history of conjectures appearing true for the first n dimensions, the first k inputs, the first z partial/tangential proofs, etc. The evidence for RH isn't any stronger than that for a plethora of eventually-proven-false conjectures.

Do you know if anyone has tabulated stats on conjecture proofs? That could be a fun dataset to examine.

[jjgreen]

As Richard K. Guy's strong law of small numbers states: There aren't enough small numbers to meet the many demands made of them.