Word for "Intellectual Prankster"

Solution 1:

Cunning and sly are both very good; but since you ask specifically for impish, may I suggest a word derived from the very archetype of the mischievous imp:

     that shrewd and knavish sprite
Call'd Robin Goodfellow: are not you he
That frights the maidens of the villagery;
Skim milk, and sometimes labour in the quern
And bootless make the breathless housewife churn;
And sometime make the drink to bear no barm;
Mislead night-wanderers, laughing at their harm?
Those that Hobgoblin call you and sweet Puck,
You do their work, and they shall have good luck:
Are not you he?

Puckish, too, is a word often applied to Feynman:

... this play [QED] is a tour-de-force that captures his unique and puckish genius. —Publisher's blurb

Feynman was widely known for his insatiable curiosity and puckish sense of humor. —Colored Reflections (blog)

During this talk Feynman drilled—with impressive prescience and the puckish humor he was well-known for—right to the heart of the question he had raised. —I'm Working on That, Wiliam Shatner

He was puckish—cracking safes, demonstrating the cause of the Challenger disaster on national television with a C-clamp and kindergarten words, naming one of his books in mockery of Princeton's high tea. —Metamerist (blog)

Solution 2:

I think sly fits the bill. The third dictionary.com definition defines it as

playfully artful, mischievous, or roguish

And, in fact, since (according to the comments on your question) you're referring to Richard Feynman, it might be helpful to mention that a number of examples can be found in the wild of people using this exact term to describe Feynman (this is clearly not a scientific survey by any means, but just a collection of examples).

For example, in the introduction to QED A. Zee writes

I chuckled a few times as Feynman got in some sly digs at other physicists.

In a forbes.com article the author refers in passing to

a bit of Richard Feynman sly magic

In a review of a comic featuring Feynman, the reviewer writes

The cover alone almost feels more real than photographs of the man, having boiled down his essence into this inquisitive, sly smirk, the outward representation of the scientific curiosity that drove him every day of his life.

In a scientific paper building upon some of Feynman's work, the author writes

This result came out eight years after Feynman's death, but I can imagine him looking at the equation with a sly smile.

And that's just some of them. A google search reveals a number of other examples.