"I hope they not only go on past 'Hogan's' record but keep going toe to toe for a while," New Zealand coach Mike Hesson said yesterday.
So are there any bets among the team on who'll get there first?
"No, we don't gamble in our team."
It was appropriate Williamson and Taylor, who made 60, gave New Zealand the big push towards their seven-wicket victory.
Their 163-run third wicket stand shut the door on Bangladesh's hopes, after they had nabbed two early wickets in the chase for 217.
Williamson has made centuries against all other nine test-playing nations, and got there faster than any of the previous 12 achievers of that feat by some distance.
He was five years younger than the next youngest - Sri Lanka's Kumar Sangakkara - and 19 tests faster than the same player.
The only country missing from Taylor's resume is South Africa, the same opponent Crowe missed out against (he also didn't play Bangladesh in a test).
That might offer Taylor the chance of a two-fer in March - catching Crowe, even eclipsing him, and completing his full set.
All three have double centuries to their name - but only Taylor has two.
Asked to pontificate on how many centuries Williamson, at 26 six years younger than Taylor, might finish with, Hesson demurred: ''Lots. I'd hate to put a number on it.
"He just goes about his work. He wouldn't know he's got 15 hundreds. Hopefully by the end of his career he'll have scored a hell of a lot more."
Hesson liked what he saw from both his leading batsmen at the Basin on Monday.
"They were proactive, always looking to score, which probably took the wind out of their sails a bit.
"Kane was able to score all round the ground against some guys other players struggled to score off.
"We like having him in our team."
Williamson is the shortest odds favourite to eventually become New Zealand's holder of a pile of batting records.
Being first to pass Crowe presents a challenge, but if they both do it they will be immensely satisfied - irrespective of whether they get there first or second.