A very intelligent family member of mine has recently decided to send me a large number of books and other resources on mathematics, include Hardy's book. Since this was published in 1921, is it still a useful textbook from which to learn pure mathematics?

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    $\begingroup$ Yes! Mathematics change really little over time and those changes are usually complement old ideas not substitute them. Proven mathematical concepts are true forever. $\endgroup$ – Vinyl_cape_jawa Nov 8 at 16:48
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    $\begingroup$ definitively YES, there are not so many books of this kind, in this sense this book is still fresh. You can get here a version of the book re-written in $\LaTeX$ $\endgroup$ – Masacroso Nov 8 at 16:48
  • $\begingroup$ The material in it is certainly still valid. As for whether it's a good match for you in particular, give it a try; if you don't like it, move on to one of the other dozens of books on introductory real analysis. Even if the math itself doesn't change, there have been changes in notation, writing style, etc. in the intervening century that modern readers may dislike. $\endgroup$ – anomaly Nov 8 at 16:58
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    $\begingroup$ this was published in 1921 --- To clarify, the 1st through 9th editions were published in 1908, 1914, 1921, 1925, 1928, 1933, 1938, 1941, 1944. Assuming the book you have is not a reprint of the 1921 edition and it's in reasonably OK condition, then it's probably somewhat valuable regardless of whether you'd want to study it. In fact, I would probably keep it in as good condition as possible and buy one of the more recently published reprints to study from, if you want to work through it (or at least some of it). Or use a freely available .pdf version. $\endgroup$ – Dave L. Renfro Nov 8 at 17:13

Congratulations to such generous and wise members in your family. My answer is: Yes, of course. This text is great to read and will help to gain a deep and proper understanding of the material.

Hint: In order to better evaluate this treasure, the following might help to come to a decision by yourself:

  • Review 1 by Paramanand Singh, one of the members of this platform.

  • Review 2 from MAA.

  • Proposal: Select two, three sections from Hardy's book which you might find interesting, read them and compare it with corresponding sections from books you are familiar with.


It depends on your taste and interests. Many old books are fantastic, the age is not a problem. I personally dislike Hardy’s book and Hardy himself because I do not believe in “pure Mathematics”. Hardy’s disregard for applications seems to me arrogant and childish. You can learn Math from many other books that include nice motivations from Physics, Engineering etc. The older texts by Hermite, Goursat etc. Are more interesting in my opinion.

  • $\begingroup$ his disregard was far from childish and arrogant. One of his main reasons to disregard the applications was due to the main use on wars and development of weapons. Observe that he lived between the two world wars (I dont downvoted you anyway) $\endgroup$ – Masacroso Nov 8 at 16:55
  • $\begingroup$ I do not understand how you can disregard the infinitely many useful applications of Math because there are bad applications. Hardy was an extremist. He claimed in his "Apology.." that mathematicians over the age of 50 could not be creative and were basically useless. An this despite of the fact that Euler produced relevant Mathematics until his death, that Moebius discovered his band at the age of 68, that Gauss discovered his Theorema Egregium in 1828, and a long etc. $\endgroup$ – GReyes Nov 8 at 17:13
  • $\begingroup$ and Weierstrass at the age of 70, if I remember correctly, proved his approximation theorem. I agree with you that Hardy was, probably, too extremist, anyway In my opinion he was a son of his time $\endgroup$ – Masacroso Nov 8 at 17:21

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