Speaking of Euler, as I did in the prior post....
It's of course impossible to name the four most important or influential or greatest mathematicians of all time. The arguments could go 'round-and-'round forever without resolution, and math is a surprisingly diverse, robust field where different individuals make all kinds of different contributions.
Nonetheless, one of the math T-shirts I offer at my Zazzle store is "The Fab Four" where I've designated the four I would pick out for such an honor if forced to choose. For the combined breadth, depth, and variety of their contributions they are (with their Wikipedia links):
(1707 - 1783)
Carl Friedrich Gauss
(1777 - 1855)
(1862 - 1943)
G.F. Bernhard Riemann
(1826 - 1866)
I'm leaving out both a lot of hugely important ancient and modern-day mathematicians, but these are just my subjective choices. Who might you choose for a Fab Four? Here's a list of 'greatest mathematicians' as formulated by someone else: