Although I take my work extremely seriously, I do not actually take myself seriously. Please bear this in mind if you have the misfortune of needing to deal with me; be sure to take everything with a grain of salt.
In case you might be willing to stoop to collaborating with me, just beware that our work would have to go against the grain, hopefully even innovating. Rock the boat? Why not overturn?
James Demmel points out that many revolutionary fast algorithms are "based on approximation — settle for the answer to just 3 digits, or just 15 digits...."
Richard Hamming (circa 1960): "The purpose of computing is insight, not numbers."
Leslie Greengard (circa 2000): "The purpose of computing is numbers — specifically, correct numbers."
(Excellent points! See down below, too.)
First "what," then "how," finally "why" — in that order. Beware of confusing orders (such as the historical order or the logical order).
Most audience members will read only one paragraph or maybe two. Most of the most important will read a page. Some of the most important will read everything. Be sure to keep in mind all three types of audiences.
One rarely encounters people who have developed well-structured world-views and goals, much less missions to fulfill. Almost everyone is optimizing, but only locally, staying stuck in local minima. Remarkably few can bear expending adequate activation energy in order to move very far in the right direction.
It is disconcerting how often people neglect the following rather obvious principles: Objectively, reality is the union of the conclusions of all perspectives, of all the possible (generally subjective) points-of-view. The conclusions derived from different perspectives are usually consistent and complementary, even though the premises leading to those conclusions may be contradictory. The key is to amalgamate the end products of multiple analyses, without needing to reconcile the hypotheses and other means used to obtain those ends.