Are pure mathematicians, e.g., Algebraists, Number Theorists, Geometers, and Topologists, at good U.S. research universities expected to win research grants to fund their work, in order to gain tenure and be promoted?
I see a lot of questions here on Academia SE that talk about the need to win grant-funding, in order to survive in academia, but I'm not sure whether that applies to pure math professors.
At my large R1 state university in the U.S., it might be impossible to get tenure without having an active grant at the time, even with an otherwise excellent record, since mathematics faculty disinterested (or hostile to whatever the specialty or person in question might be) would use this as grounds for doubting the quality. After all, supposedly, all the best people are funded. Supposedly, endorsement by the NSF (or NSA) is an external, objective test of quality. This is certainly a convenient assumption for arguments in certain directions. EDIT: and since a strong super-majority is needed for a "positive" tenure vote, even irrational ranting can sway otherwise uninformed or disinterested people to scuttle the vote.
Issues of external funding are apparently even more identified with research activity by engineers (and experimental scientists), who often dominate the college-wide tenure (and promotion) committees. That is, it is sometimes apparently unimaginable that a person would be doing research without a grant.
Further, at my university, in other hard-science departments, often large grants are allowed to "buy out" faculty from any teaching at all. This is rare in my math department. EDIT: thus, in the minds of some engineers, "teaching" is stigmatized, since in their own depts it's only the disenfranchised who have to do any of it. And then there're the wildly different paper-count standards for experimental science/engineering versus mathematics.
The literal "funding of research" usually is less critical, apart from the expense of travelling to conferences, and extra summer salary.