Hardy / Wright's intro to number theory is highly praised but has no exercises

Conspicuously, Lang's "Algebraic Number Theory" had no exercises in any of the 3 editions I've owned. I don't remember that Weil's "Basic Number Theory" did. Titchmarsh's "The theory of the Riemann zeta" does not. Artin-Tate's "Classfield Theory" does not. I had never thought about the fact that Hardy-Wright does not.

My own experience was contriving examples to illustrate the theorems, and trying to understand the (not always completely explicit) hypotheses or contexts of the theorems. I didn't think of looking for exercises-at-end-of-chapter.

When Lang's and Weil's books appeared, they were the first serious alg no th books in English. Lang's book is itself (as Mariano S-A says about Hardy-Wright, above) one large exercise. Ditto Weil's. What are "exercises" supposed to be, anyway? Derivative filler? Who'd want that?

As far as I know, the "textbook" concept, with exercises included, is a post-WWII invention of U.S. publishers, and/or publishers for the U.S. text-book market, which until recently may have been the dominant force in text-book publishing. Having published textbooks myself, I am well-acquainted with, and somewhat dismayed by, the fixation publishers have with "exercises".

The exercises in Rudin's "Real and Complex", and Lang's "Algebra" are notorious landmarks. One aspect that merits notoriety is that a certain small fraction of them is routine rewriting of definitions/theorems from the chapter, but many require a non-trivial idea. Really, is it true that exercises should test mathematical talent? Seems rather pointless, or even dishonest to make people pay tuition for "education" that is something else.

By this point, I am of the opinion that "the text" should give samples of all questions asked as "exercises", or it's a cheat. Trivial things oughtn't be given as exercises (busywork?), and non-trivial things need models.

Atiyah-MacDonald's "Commutative Algebra" is a crazy extreme case, in my opinion, despite its virtues: perhaps the hardest half (or 2/3) of the results in it are innocently-posed "exercises". Thus, the attractive slimness of the book. But it is a substantial dis-service to leave readers with dubious, un-enlightened, perhaps completely incorrect "solutions" to exercises... if the "exercises" are serious results worth executing well, and with emphasis on the critical features.

In many cases, in my experience, otherwise-conscientious students are too-often entrapped by pointless, make-work exercises, so find themselves feeling they've accomplished something by having spent much time, but, in fact, have not engaged with the central ideas.

The contrived necessity of homework, exams, and grades is very corrupting... Why is mathematics perceived as exclusively a "school subject", and its sense and habits defined by grading systems and publishers? It is bizarre.

In summary, I was at-first-surprised by the question, but soon recovered my equilibrium... and/but had the above reaction. :)

Edit/addendum: incorporating @Pete's comment and @Willie W's... : Indeed, it is not accurate to criticize the idea of "exercises" by noting that too many exercises are bad. It is possible, but very challenging, to give guided-exercises-with-hints in a non-combative, non-challenging fashion. One should try to do so! The false challenge of grading should/must be separated from explanation. To with-hold explanation as a "test" is a bad thing (despite its being standard).

It took me decades, but I only recently realized that the U.S. system has taught everyone to perceive "teachers" as antagonists, not (to say the least) unqualified supporters. Thus, everything said in lecture or notes or text is a potential challenge, a potential expression of doubt that the reader/student/audience understands. The UK system is a bit different, but I do not understand the current mind-set.

Hilariously, my attempts to rise above the corruption of adversarial game-playing grading by promising everyone an "A"... with required [sic] homework have not been as happy as I would have wished: I think the conditioning is too strong, and that combative, adversarial mindset does continue into grad-school. Sigh...

I do also think that discussion of the role of "exercises" deserves attention. Many students (not to mention old people...) misunderstand the "drill".

Edit-2: Thanks to @Gerry M. Indeed! Hardy's "Course..." I'd need to investigate years-of-publication and such, but I know the provenance of that thing needlessly well. My father (a high school math teacher in the U.S. required to obtain a higher degree [sic] in mathematics) endured a night-school course whose text was Hardy's. I was not very old, but old enough to be ... stunned... by the tendentiousness of that text. I had a fair understanding of analysis in the late 1960s, and/but Hardy's text effectively expressed doubt that its reader "had a brain in their body". And would not explain anything to them, either. Ack. I don't hold Hardy morally responsible for that text.

The Bourbaki impulse suggested things ... and publishers solicit. That is not the same as sincere intellectual expressions.

Edit... and about Zygmund, I am truly interested to look at my copy (in my campus office, tomorrow...) That would be an odder (counter-) example than many, to my mind. Relatedly, did Banach's monograph have "exercises"? Did Hausdorff's book? I do srsly think that "textbooks" were not what people were thinking about in those years. Advancing mathematics, monographs, yes. (What kind of "exercises" does EGA have? I'll also look tomorrow...)

Edit-edit: in response to @Bill D's query about my reaction to Hardy's "Course...": (First, certainly Hardy was a very good mathematician.) Surely it's a matter of taste, all the more so about the importance of "logical order" in mathematics, but/and the comparisons one has at hand, or sees as relevant (at least for oneself). Thus, for example, I would not think of comparing Hardy's "Course" to "calculus textbooks", almost all of which make much ado about nothing, not to mention that Hardy was actually a real mathematician, not a textbook writer. For that matter, I do think it's a pity his promotion of big-Oh and little-Oh didn't manage to displace the epsilon-delta version, especially for introductory texts. Nevertheless, in my opinion, it is too careful, and too long. It is (at some level) "logically complete", but I have never been a big fan of logical completeness per se, insofar as this tends to swamp highlights with an ocean of details, all too easily undifferentiated or undifferentiate-able.

Rather than "logical thinking", I think mathematics yields best to "critical thinking", which (to my understanding/experience) is often very different. My choice of charged language would be that critical thinking tries to discern which details matter, and allocate far fewer resources to the others. In contrast, too often a mere "logical order and logical completeness" is alleged to be what we want, and it's not what I want, anyway.

In other words, while I might agree that Hardy's "Course" is vastly better than almost all extant "calculus textbooks", that is very faint praise. I wouldn't recommend that people use those textbooks to actually learn calculus, in any case, since they make it too complicated, too fussy, too deus-ex-machina, too unpersuasive.

And while I'm editing: we aren't usually disappointed when a novel doesn't have attendant exercises, nor when a piece of music doesn't. Why should mathematical writing have exercises? :)

Here is a link to a commutative algebra course by Prof. Kleiman at MIT:

http://web.mit.edu/18.705/www/syl11f.html

It has a link to his new text. It also includes a link to a pdf with problems and solutions.

Pertinent to this question, here is a quote from the syllabus page for the course:

"The solution set will also include solutions to the unassigned problems. Do try to solve each one before reading its solution, in order to better appreciate the issue. And do read the solution even if you think you already know it, just to make sure. Further, some problems have alternative solutions, which may enlighten you."

Perhaps this is a happy pedagogical medium.