Mathematical trivium

Trivium Mathématique, V. I. Arnold (in French) is a list of 100 problems that Arnold set as a list of mathematical problems that (university) students in physics ought to be able to solve. This is preceded by Arnold stating that the system of oral exams in Russia should be replaced with written exams, and that a system based around the ability to solve certain problems is superior to a system based around the ability to regurgitate certain theorems. He then goes on to give a list of such problems.

As someone who tends to prefer problem-solving to theory-building, I find the following particularly interesting (my translation):

A student who takes more than five minutes to calculate the average of sin ¹⁰⁰ x with a precision of 10% has no mastery of mathematics, even if he has studied nonstandard analysis, universal algebra, supervarieties, or plongement [I don't know this word] theorems.

Go ahead, try that problem! (Curiously, it's not one on the list.) More generally, it's an interesting bunch of questions in various branches of mathematics, biased towards but by no means exclusively in calculus and differential geometry; this is no surprise as it's meant for physicists.

(Why the French version, you ask? The article was originally in Russian; there's an English translation but it's not free. Links to free versions in Russian or English, if they exist, would be appreciated.)

Edit, 12:07 am Sunday: An anonymous commentator provides the English version, and Dmitri Pavlov the Russian.

The mathematician's "you"

Ertl Wins: Down With Witchcraft, by Derek Lowe at In The Pipeline, on this year's Nobel winner in Chemistry. Most chemical reactions take place in some sort of bulk liquid or gas; Ertl's work considers chemistry that occurs on the surface of a solid. The most important example is probably the Haber-Bosch process for creating ammonia from nitrogen and hydrogen.
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Lowe writes:

You can Haber-Bosch yourself some ammonia simply enough – just take iron powder, mix it with some drain cleaner (potassium hydroxide) and stir that up with some alumina and finely ground sand (silica). Heat it up to several hundred degrees and blow nitrogen and hydrogen across it; ammonia gas comes whiffing out the other end. Now, bacteria do this at room temperature in water, down around the roots of bean plants, but bacteria can do a lot of things we can’t do. For human civilization, this is a major achievement, because nitrogen does not want to do this reaction at all.

Megan McArdle's response to this: "Derek Lowe has a highly exaggerated notion of my abilities."

For a moment this struck me as the way a mathematician might use "you" (although the preferred second-person pronoun in mathematical texts is "the reader", as in "This is left as an exercise for the reader." or "The reader can show that...") But it's not quite the same thing. If I'm sitting there reading some mathematics, and I come across something that "the reader" should do, I probably can do it, sitting there in my chair, if I have a large enough supply of paper and coffee. (Whether I will is a different matter; how badly do I want to understand what I'm reading?) But the reader of Lowe's post -- or the reader of a chemistry paper -- can't actually do that. The chemist has to take the author's word for it, in most cases, because it would be prohibitively expensive to check everything they read.

Vladimir Arnold, in an essay "On Teaching Mathematics", said that "Mathematics is the part of physics where experiments are cheap." This is an example of that phenomenon, although I would argue that "physics" should be replaced with some broader term, as more and more areas of knowledge are becoming mathematizable and computing power becomes cheaper and cheaper.