Мы рекомендуем пропустить эти упражнения при первом чтении

[posic]

http://mathoverflow.net/questions/10897/famous-exercise-from-langs-algebra/

Comments

[flaass.livejournal.com]

...the term `abstract nonsense' in this book has a positive character and is used below in the serious sense.

Какая прелесть :) Прямо как в анекдоте: "...в хорошем смысле слова".

[chaource.livejournal.com]

Lots of good mathematicians just have an ego that's way too much inflated. Lots of good mathematics texts can't hide this fact...

[posic.livejournal.com]

What does it have to do with ego? It's just an innocent joke. If it implies anything at all, it is that proofs in basic homological algebra tend to be straightforward (which is true).

[chaource.livejournal.com]

Well, there is a dialog here between the author and the editors of the Russian translation. The author's message is: I assume that the reader is at least as brilliant as I, or at least should be, so that the reader can simply restore all the proofs in homological algebra without much effort. The readers who unable to do so should go back to kindergarten." The editors commented that "We recommend to skip these exercises at first reading", meaning that they dismiss the author's position as childish and know better what the reader should do. None of them says clearly and plainly what they really want to say; this is so because their ego prevents them from expressing themselves straightforwardly and honestly.

In practice, of course, it is not possible to restore all proofs instantly, because (as another comment was saying) not everything is so obvious in homological algebra.

[posic.livejournal.com]

That's common to all jokes. People telling them don't say clearly and plainly what some observers may infer they really want to say. That's what makes jokes so much fun. Of course, the same joke can be interpreted in the almost exact opposite way: it means to instill confidence in the readers, by communicating the message that homological algebra or algebra generally is not at all that hard.

In practice, of course, noone in his right mind can be expected to attempt to complete such an exercise just because it is there in the book, with or without the discouraging footnote by the Russian translation's editors. In fact, I have never heard about anyone trying to do so. If such a person exists, he is certainly expected to realize that he is proceeding at his own risk.

When my brother was studying at 57th school in Moscow, they were given lists of exercises, some of them with stars (meaning difficult), and very few with double stars. Once there was a double-starred exercise asking to prove Dirichlet's theorem about primes in arithmetic progressions. One of the kids completed it, with a liberal use of the available literature, of course. I checked his proof and to the best of my understanding it was correct. We spent many hours discussing it. The kid proceeded to become a research mathematician.

Whether that double-starred exercise meant to tell the pupils that they were less brilliant than their teachers or more brilliant than them is anyone's guess. That its presence tended to help the kids to develop a better understanding of what's worth what in mathematics, I have little doubt. Same applies to Lang's homological algebra exercise. Some other books (perhaps more advanced than Lang's Algebra) are known to include open problems as double-starred exercises.

There are all kinds of mathematics textbooks, some intended for the bright students and some for the more average ones. Lang's Algebra belongs to the former category.

[nikaan.livejournal.com]

Я видел человека, который попытался последовать этому упражнению :) Ему, правда, быстро надоело.

[nikaan.livejournal.com]

Я, когда читал, вопринял как хорошую шутку - и про абстрактную чепуху тоже. Это было как-то очевидно - из общего стиля книги.

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