@Chan-HoSuh Robert Mercer is an electrical engineering PhD who also made significant contributions to Renaissance Tech, but much greater contributions to digital image processing. I did not know about James Ax. Thank you!

I thought only non-mathematicians believed this: "when I am calm and patient I win, but when I lose my temper I lose big time"!

This is lovely, Tom! Le teorie vanno e vengono ma le formule restano. It evokes the same feeling as realizing that Ohm's Law, V=IR remains valid in the classical AND quantum worlds

I agree with both @YemonChoi and Carl-Fredrik. This question is equally or maybe more appropriate for Math SE than MathOverflow. I don't know if it is possible to migrate it. Designating authorship of the question (and answer) as Community Wikis seems reasonable, as an ad hoc measure.

In what way is this an "ideal" question?

Tom, you might want to consider including your third comment in your answer. Rota's sentence structure is poor, and leads to ambiguity. In your comment, you clarify what he said without changing the meaning of his original phrase. The rest of your comment responds directly to the question in its entirety (there are two parts: what Rota meant in the quoted paragraph AND about the connections between symmetric functions to the three terms). Combined, this is a good answer!

@NateEldredge Good point. That is why the excerpted Arnold passage is more wit than advice. In another paragraph, he describes his notion of Russian intelligentsia, especially mathematicians, who work without any regard for compensation. That paper was dated 1997, but I'm guessing that he alluded to a more umm, planned economy than exists in the U.S. or Russia now. I agree with you, that it is essential that a grad student be able to get a decent job, any job. Arnold is brilliant, verbally fluent, but it reads more like a literary magazine (sardonic commentary) than typical AMS material.