What single word describes the ability to think analytically?

Here's something fancy to impress the ladies: perspicacity.

As in:

"Nathan Rothschild was a man of keen perspicacity and profited immensely from his shrewd decision to employ a courier at the Battle of Waterloo, which lead to his eventually becoming the wealthiest man in all of Britain."

From Wikitionary:

perspicacity (n.)
1. Acute discernment or understanding; insight.
2. The human faculty or power to mentally grasp or understand clearly.
3. (obsolete) Keen eyesight.  

You could use exactitude, thoroughness, precision, or rigor if you mean thinking in the mathematical sense of "analytical thinking".

You could use acumen, discernment, or shrewdness if you mean "analytical thinking" in the sense of "critical thinking".

I personally like shrewdness because of the connotation of "good business sense":

This job requires both creativity and shrewdness.

How about thoroughness, rigor, logic or method? All describe the need for logical thinking, which is probably the main component of analytical thinking.

"Analyticality" fits the bill. (Whether or not it sounds good to many is another question.)

As suggested earlier by @F'x, "rigor" is pretty good, and it plays off of and creates a nice tension with "creativity" .

It suggests rather than capturing whole "the ability to think analytically," so there is conceivably some ambiguity there. But personally I think any ambiguity there is appropriately resolvable by anyone with creativity and the ability to think analytically.