most recent 30 from http://mathoverflow.net 2010-03-16T01:28:56Z http://mathoverflow.net/feeds/question/358 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing Anton Geraschenko 2009-10-12T17:12:16Z 2010-02-11T00:56:32Z

<p>This question is basically from <a href="http://math.stanford.edu/~vakil/" rel="nofollow">Ravi Vakil</a>'s web page, but modified for Math Overflow.</p> <p><em>How do I write mathematics well?</em> Learning by example is more helpful than being told what to do, so let's try to name as many examples of "great writing" as possible. Asking for "the best article you've read" isn't reasonable or helpful. Instead, ask yourself the question "what is a great article?", and implicitly, "what makes it great?"</p> <p>If you think of a piece of mathematical writing you think is "great", check if it's already on the list. If it is, vote it up. If not, add it, with an explanation of why you think it's great. This question is "Community Wiki", which means that the question (and all answers) generate no reputation for the person who posted it. It also means that once you have 100 reputation, you can edit the posts (e.g. add a blurb that doesn't fit in a comment about why a piece of writing is great). <strong>Remember that each answer should be about a <em>single</em> piece of "great writing", and please restrict yourself to posting one answer per day.</strong></p> <p>I refuse to give criteria for greatness; that's your job. But please don't propose writing that has a major flaw unless it is outweighed by some other truly outstanding qualities. In particular, "great writing" is not the same as "proof of a great theorem". You are not allowed to recommend anything by yourself, because you're such a great writer that it just wouldn't be fair.</p> <p>Not acceptable reasons:</p> <ul> <li>This paper is really very good.</li> <li>This book is the only book covering this material in a reasonable way.</li> <li>This is the best article on this subject.</li> </ul> <p>Acceptable reasons:</p> <ul> <li>This paper changed my life.</li> <li>This book inspired me to become a topologist. (Ideally in this case it should be a book in topology, not in real analysis...)</li> <li>Anyone in my field who hasn't read this paper has led an impoverished existence.</li> <li>I wish someone had told me about this paper when I was younger.</li> </ul>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/360#360 Scott Carnahan 2009-10-12T17:30:01Z 2009-10-12T17:30:01Z

<p>Canonical submission: Anything by Serre (e.g., Local Fields, Trees, Algebraic Groups and Class Fields,...). Reasons:</p> <ul> <li>I can't get enough of Trees, chapter 2. I spent a year working on automorphic forms on function fields in part because of this book (it didn't work out well, but that's another story).</li> <li>Peer pressure: several people (including my Ph.D. advisor) have told me that if I were to choose a role model for writing style, I should choose him.</li> <li>Mundane reasons: His writing is incredibly clear and concise, but not so brief as to be confusing. He has a keen eye for what is important in a theory or construction. He doesn't waste words having a conversation with the reader or expounding on his philosophy of mathematical practice.</li> </ul>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/361#361 Ilya Nikokoshev 2009-10-12T17:41:06Z 2009-10-12T17:41:06Z

<p>Well, for me <strong>Hartshorne</strong> was really the window into the brave new world &mdash; and yes, it fits several items from 'acceptable reasons'. </p> <p>Though this prize should be shared with everyone else who was creating abstract algebraic geometry and scheme theory in the past century or so (I spare you the history, you already know it :) ) </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/375#375 Chris Schommer-Pries 2009-10-12T20:13:07Z 2009-10-12T20:13:07Z

<p>I've always really enjoyed the papers by Graeme Segal. They are short and I often feel like they have been distilled down into the essence of what is important. I keep going back to them and extracting new nuggets of beauty. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/376#376 Lars 2009-10-12T20:16:17Z 2009-10-12T20:16:17Z

<p>One of the math books I enjoy reading in most is Neukirch's book "Algebraic Number Theory". In my opinion, he presents the material beautifully and with a good degree of generality for a text book. Also, he manages to use language beautifully without loosing mathematical rigor and without compromising clarity (this holds for the german version as well as for the english translation). When I have to look up some fact from algebraic number theory, Neukirch is usually the first book I try.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/377#377 Noah Snyder 2009-10-12T20:19:17Z 2009-10-12T21:59:20Z

<p>Dror's paper <a href="http://front.math.ucdavis.edu/math.GT/0410495" rel="nofollow">Khovanov's homology for tangles and cobordisms</a> is one of the papers I loved back when I hated all math papers. In particular it's a paper that has a really good use of diagrams, a lot of papers use too few diagrams and suffer a lot for it.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/380#380 John D. Cook 2009-10-12T20:30:07Z 2009-10-12T20:30:07Z

<p>Michael Spivak's <a href="http://www.amazon.com/gp/product/0914098918?ie=UTF8&amp;tag=theende-20&amp;linkCode=xm2&amp;camp=1789&amp;creativeASIN=0914098918" rel="nofollow">Calculus</a> made me want to study analysis. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/382#382 Noah Snyder 2009-10-12T20:53:10Z 2009-10-12T20:53:10Z

<p>Silverman and Tate's "Rational Points on Eliptic Curves."</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/387#387 Theo Johnson-Freyd 2009-10-12T21:30:43Z 2009-10-12T21:30:43Z

<p><a href="http://books.google.com/books?id=KvQr9l0wgf8C&amp;lpg=PP1&amp;dq=proofs%20from%20the%20book&amp;pg=PP1#v=onepage&amp;q=&amp;f=false" rel="nofollow">Proofs from the Book</a>, Martin Aigner, Günter M. Ziegler, 2000.</p> <p>Anyone in [mathematics] who hasn't read this [book] has led an impoverished existence.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/390#390 Noah Snyder 2009-10-12T21:59:56Z 2009-10-12T21:59:56Z

<p>Another paper that I really like, because it makes a lot of things that are muddled in the literature very clear, is Sawin's <a href="http://front.math.ucdavis.edu/0308.5281" rel="nofollow">Quantum Groups at Roots of Unity and Modularity</a>. In particular the lesson to learn is that if it takes you a while to sort through which papers use which conventions or to find all the relevant constants attached to Lie algebras, then you really owe it to your readers to put that information in your paper where it's easy to find (preferably in a table).</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/392#392 Reiner Martin 2009-10-12T22:13:48Z 2009-10-12T22:13:48Z

<p>This is not an example of great mathematical writing, but definitely something to know and probably even more useful: Paul Halmos' brilliant essay "How to write mathematics", which you'll find at <a href="http://retro.seals.ch/digbib/view?rid=ensmat-001:1970:16::59&amp;id=browse&amp;id2=browse2" rel="nofollow">http://retro.seals.ch/digbib/view?rid=ensmat-001:1970:16::59&amp;id=browse&amp;id2=browse2</a>.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/491#491 David Brown 2009-10-14T15:05:21Z 2009-10-14T15:05:21Z

<p>The survey paper <em><a href="http://www-math.mit.edu/~poonen/papers/aws2003.pdf" rel="nofollow">Hilbert's Tenth Problem over rings of number-theoretic interest</a></em> by Bjorn Poonen (my advisor) is one of my favorites. He has several survey papers on his web page. My first year of grad school I read many of these and decided I wanted to work with him, so in a sense this paper did `change my life'. </p> <p>In general Bjorn's writing is extremely clear and I have tried to model my own writing on his.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/495#495 Andy Putman 2009-10-14T15:44:27Z 2009-10-14T15:44:27Z

<p>John Hubbard's book on Teichmuller theory is clear, beautiful, inspiring, and (amazingly) essentially self-contained. He has a fantastic ability to take very technical and difficult results and make them seem clear and natural.</p> <p>Bill Thurston wrote a preface for it which can be read here : </p> <p><a href="http://matrixeditions.com/Thurstonforeword.html" rel="nofollow">http://matrixeditions.com/Thurstonforeword.html</a></p> <p>The money quote : "I only wish that I had had access to a source of this caliber much earlier in my career."</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/501#501 Mikael Vejdemo-Johansson 2009-10-14T18:08:17Z 2009-10-14T18:08:17Z

<p>Actually a book that ended up changing my life: Kaczynski, Mischaikow, Mrozek: Computational Homology</p> <p>I read it while working on my master's thesis in computational homological algebra, in order to see what they had to say about efficient implementations of simplicial homology.</p> <p>After reading it, I first realized that algebraic topology has applications far outside what I had seen thus far - and now, a doctorate later, I'm active in the field of Applied Algebraic Topology and Topological Data Analysis.</p> <p>I'm not certain I'd peg it for <em>great writing</em> as such, but the criteria above <em>did</em> state "changed my life".</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/514#514 B. Bischof 2009-10-14T21:49:22Z 2009-10-14T21:49:22Z

<p>John Lee's Introduction to Smooth Manifolds. This book reminded me of all the mathematics I kinda learned in undergrad, prepared me for graduate school, and taught me differential topology. I feel like every undergrad should have this book and work through it on their own.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/538#538 Akhil Mathew 2009-10-15T01:20:18Z 2009-10-15T18:01:09Z

<p>Walter Rudin's <em>Real and Complex Analysis</em> has long been one of my favorites. Like Serre, Rudin seems to strike a nice balance for detail, and his proofs are always slick and fun to read; I became heavily interested in analysis after reading that one.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/579#579 Harrison Brown 2009-10-15T08:04:23Z 2009-10-15T08:04:23Z

<p>I'm not sure whether "expository" writing counts, but I'll go with it anyway...</p> <p>I don't think it would necessarily change the life of anybody who was already into mathematics enough to pay for it, but I very much wish the <em>Princeton Companion</em> had come out when I was younger. You don't get the chance to get your hands dirty with the details of any of the topics the PCM covers, but sometimes you're not looking to get your hands dirty, and there's not much else of any quality that can compare in terms of breadth. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/586#586 Jason Starr 2009-10-15T10:10:23Z 2009-10-15T10:10:23Z

<p>I love Grothendieck's Tohoku paper.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/596#596 unknown (google) 2009-10-15T13:52:17Z 2009-10-15T13:52:17Z

<p>Lazarsfeld's book <em>Positivity in Algebraic Geometry</em> seems to fit the category ``Anyone in my field who hasn't read this paper has led an impoverished existence.'' </p> <p>I agree with Scott on `anything Serre.' His FAC and GAGA are gems; they will change your life.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/608#608 Rex Cheung 2009-10-15T16:22:52Z 2009-10-15T16:22:52Z

<p>Real Analysis by Elias Stein and Rami Shakarchi</p> <p>I absolutely hated analysis until I read the Stein/Shakarchi analysis series (Fourier, Complex, Real Analysis). Now I find the subject to be very beautiful and full of deep ideas, and it is these books that really convinced me.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/622#622 Akhil Mathew 2009-10-15T18:01:50Z 2009-10-18T00:36:06Z

<p>Silverman's <em>The Arithmetic of Elliptic Curves</em> got me interested in that area for some time, too. The exposition is fun to read, with both motivation and rigorous proofs.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/632#632 Qiaochu Yuan 2009-10-15T19:00:52Z 2009-10-15T19:06:50Z

<p>Anyone in combinatorics who hasn't read Gian-Carlo Rota's <a href="http://www.springerlink.com/index/W041888J1J528605.pdf" rel="nofollow">Mobius function paper</a> has led an impoverished life.</p> <p>Edit: Well, really this applies to every paper in <a href="http://www.amazon.com/Gian-Carlo-Rota-Combinatorics-Introductory-Mathematicians/dp/0817637133/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1255633479&amp;sr=8-1" rel="nofollow">Gian-Carlo Rota on Combinatorics</a>, so let me declare that this post is a vote for the entire book, since I now get to add the reason that, if I become a combinatorialist, it will be because of this book.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/644#644 Ilya Grigoriev 2009-10-15T20:02:56Z 2009-10-15T20:02:56Z

<p>Anything by John Milnor fits the bill. In particular, "Topology from the differential viewpoint" made me feel that I understand what differential topology is about, and the "h-cobordism theorem" made me feel that it's beautiful. Many other books and papers by him are wonderful; the first that come to mind are "Characteristic Classes", "Morse Theory", lots of things in Volume 3 of his collected papers.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/654#654 Grétar Amazeen 2009-10-15T20:39:03Z 2009-10-15T20:39:03Z

<p>In my opinion Atiyah's paper "vector bundles over an elliptic curve" is a gem that everyone interested in algebraic geometry should read.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/658#658 A.J. Tolland 2009-10-15T20:56:21Z 2009-10-15T20:56:21Z

<p>Atiyah &amp; Bott's paper "The Yang-Mills Equations on Riemann Surfaces" is probably the most satisfying thing I've read. The writing is great, and the ideas are all cool.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/701#701 Jon Yard 2009-10-16T02:14:31Z 2009-10-16T02:14:31Z

<p>This paper changed my life:</p> <p>Vaughan Jones, "Hecke algebra representations of braid groups and link polynomials"</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/704#704 Jon Yard 2009-10-16T02:25:06Z 2009-10-16T02:25:06Z

<p>"Algebraic curves and Riemann surfaces" by Rick Miranda is one of my favorite books. It is full of concrete examples and is full of very clear explanations for everything from the basics of Riemann surfaces and their projective embeddings though sheaf cohomology. Also, it assumes little more than elementary complex analysis. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/736#736 Thomas Riepe 2009-10-16T12:46:44Z 2009-10-16T12:46:44Z

<p>books I enjoyed very much: Mumford "Lectures on Curves on an Algebraic Surface"; Mumford "Curves and their Jacobians"; Mumford "Basics of Torus Embeddings; Examples of the Theory": Chapter 1 in "Smooth Compactification of Locally Symmetric Varieties"; Koblitz "Introduction to Elliptic Curves and Modular Forms"; Deligne SGA 4 1/2 </p> <p>In general I found Bourbaki-seminar texts often very helpfull and readable. Unfortunately many of the newer issues seem not to be free available on the web. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/771#771 hurzilipochtli 2009-10-16T18:03:37Z 2009-10-16T18:03:37Z

<p>Since you wanted to learn writing from examples: J. Kock and I. Vainsencher's book "An Invitation to Quantum Cohomology" is wonderful reading, simply because of its incredibly friendly style. It gives you the feeling that the authors take you by the hand and lead you through their garden of wonders (always uphill of course). The achievement of the book is to give you lots of intuition - for moduli stacks, strategies for proofs in enumerative geometry, the necessity of a virtual fundamental class, how generating functions work... This is something very difficult to do in mathematical writing - in this respect you could compare it to John Baez's blog, only that it is a longer, coherent book on a single subject.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/789#789 Gerald Edgar 2009-10-16T19:56:42Z 2009-10-16T19:56:42Z

<p><em>I wish someone had told me about this paper when I was younger.</em></p> <p>I have had this feeling a few times. For example: Gillman &amp; Jerison, <em>Rings of Continuous Functions</em>.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/1001#1001 Sam Derbyshire 2009-10-18T04:44:26Z 2009-10-18T04:44:26Z

<p>I think Algebraic Topology by Hatcher is one of my early favourites. It starts off being very basic but it manages to mention so much fascinating stuff, and I think the exposition is great. Definitely inspired me and got me interested in algebraic topology.</p> <p>His book in progress "Vector Bundles and Characteristic Classes" is also very nice.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/1033#1033 Anna Varvak 2009-10-18T13:45:09Z 2009-10-18T13:45:09Z

<p>From more introductory texts, some of the most well-written textbooks I came across are</p> <ul> <li>Visual complex analysis, by Tristan Needham</li> <li>Differential equations, by Blanchard, Devaney, and Hall</li> </ul>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/1476#1476 timur 2009-10-20T19:45:59Z 2009-10-20T19:45:59Z

<p>Van der Waerden's Algebra. I became a mathematician because of this book.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/2482#2482 AS 2009-10-25T15:29:50Z 2009-10-25T17:17:49Z

<p>Some of my favourite authors are Serre, Mumford, Milnor, Fulton and Neukirch. There names are rather mainstream, I guess. But the most beautiful analysis textbook I ever read must be <a href="http://www.amazon.com/Analysis-Now-Graduate-Texts-Mathematics/dp/0387967885/ref=sr%5F1%5F1?ie=UTF8&amp;s=books&amp;qid=1256484405&amp;sr=8-1" rel="nofollow">"Analysis now"</a>, by Gert Pedersen. Alas, the book is not as well known as it should be.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/3898#3898 Anton Geraschenko 2009-11-03T04:04:19Z 2009-11-03T04:04:19Z

<p>Éléments de géométrie algébrique (EGA) (full text available from <a href="http://www.numdam.org" rel="nofollow">numdam</a>) continues to be an inspirational text for me. I wish I'd started reading it earlier.</p> <p>It's come up in a few <a href="http://mathoverflow.net/questions/2446/best-algebraic-geometry-text-book-other-than-hartshorne/2540#2540" rel="nofollow">other places</a> here on MO. To quote <a href="http://mathoverflow.net/questions/3041/the-importance-of-ega-and-sga-for-students-of-today/3102#3102" rel="nofollow">Jonathan Wise's answer</a> to another question,</p> <blockquote> <p>Virtually every page I've read of EGA/SGA has been useful to me, and almost every page I've skimmed I've later wished I'd read in more detail. The reputation for difficulty is, I think, unfounded. They are certainly abstract, but virtually every detail is present; in many ways, that makes EGA/SGA easier to read than other sources. Opening a volume and reading a sub-paragraph from the middle can be difficult because of all the back-references, but reading linearly can be very pleasant and rewarding. The French language may be a barrier for some, but one doesn't have to "learn French" to learn enough to understand EGA.</p> </blockquote>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/3983#3983 James 2009-11-03T18:22:36Z 2009-11-03T18:22:36Z

<ol> <li><p>The book "Linear Algebra" by Greub; I've always thought his writing here was gorgeous, if a bit Spartan.</p></li> <li><p>Most of John Stillwell's books.</p></li> </ol>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/9577#9577 Kevin Lin 2009-12-23T02:11:47Z 2009-12-23T02:11:47Z

<p>Kontsevich's 1994 paper "Homological Algebra of Mirror Symmetry" has been very inspiring to me. It is full of tantalizing ideas and speculations, and brings so many different aspects of mathematics (and physics!) together into one beautiful tapestry.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/9617#9617 Anirbit 2009-12-23T13:55:17Z 2009-12-23T13:55:17Z

<ol> <li><p>"Differential calculus on Normed Linear Banach Spaces" by Prof.Kalyan Mukherjee</p> <p>This book gave me a very hands-on explorable window into the world of manifolds and Lie groups. Like it shows explicit calculations of derivative of matrix multiplication and determinant maps and also about computing tangents to curves inside Lie groups. </p></li> <li><p>"Topology, Geometry and Gauge Fields" by Gregory Naber. (2 Volumes) </p> <p>Its an exciting book which got me motivated into topology when it explained to me very simply the Heegard decomposition of S^3 and hence Hopf Fibration and how that relates to Dirac Monopoles! Before I read this book I had no clue that I would find mathematics exciting. Especially this revived my childhood interest in geometry. </p> <p>Naber's are books that changed my career decision. </p></li> <li><p>"Global Calculus" by S.Ramanan (in the AMS series)</p> <p>This is a hard book to read initially but it excites the reader a lot and it was great to read alongside when Prof.Ramanan taught me topology and differential geometry. Anyway Prof.S.Ramanan is a great expositor. He could teach topics like modular forms and algebraic curves to a bunch of undergrads in their first complex analysis course in Chennai Mathematical Institute (CMI), India! He really pushes up the possible limits of exposition. </p> <p>Prof.S.Ramanan's lectures in my alma mater CMI, affected my career choices almost as much as Naber's books did.</p></li> <li><p>"Calculus on Manifolds" by Spivak</p> <p>Its treatment of Fubini's theorem and related issues are great. </p></li> <li><p>The writings on group theory by a college senior of mine called Vipul. His wiki "groupprops" is an amazing repository on finite group theory.</p> <p>His extensive efforts into mathematical writing also inspired me into periodically LaTex-ing up interesting things in mathematics as I learn. </p></li> </ol> <p>Can anyone here tell about nice expository writings on topics like Gromov-Witten theory or Reshetkhin-Turaev and Rozansky-Khovanov stuff and how these relate to QFT? Something which shows a lot of examples and may be also explicit calculations. </p> <p>Most sources on Quantum Groups that I have tried looking at start off a bit harshly for the newcomer. I would be greatly interested to read of "great mathematical writing" in these areas. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/9826#9826 Joseph Malkevitch 2009-12-26T21:08:16Z 2009-12-26T21:08:16Z

<p>The American Mathematical Society awards the Leroy P. Steele Prize, in part for recognition of mathematical exposition:</p> <p>The Leroy P. Steele Prize for Lifetime Achievement The Leroy P. Steele Prize for Mathematical Exposition The Leroy P. Steele Prize for Seminal Contribution to Research</p> <p>These prizes were established in 1970 in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein, and are endowed under the terms of a bequest from Leroy P. Steele. From 1970 to 1976 one or more prizes were awarded each year for outstanding published mathematical research; most favorable consideration was given to papers distinguished for their exposition and covering broad areas of mathematics. In 1977 the Council of the AMS modified the terms under which the prizes are awarded. Since then, up to three prizes have been awarded each year in the following categories: (1) for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students; (2) for a book or substantial survey or expository-research paper; (3) for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research. In 1993, the Council formalized the three categories of the prize by naming each of them: (1) The Leroy P. Steele Prize for Lifetime Achievement; (2) The Leroy P. Steele Prize for Mathematical Exposition; and (3) The Leroy P. Steele Prize for Seminal Contribution to Research. Each of these three US$5,000 prizes is awarded annually.</p> <p>The winners in the area of Mathematical Exposition, including prizes for specific books are listed here:</p> <p><a href="http://www.ams.org/prizes/steele-prize.html" rel="nofollow">http://www.ams.org/prizes/steele-prize.html</a></p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/14327#14327 kakaz 2010-02-05T23:47:34Z 2010-02-05T23:47:34Z

<p>Hugo Steinhaus <a href="http://en.wikipedia.org/wiki/Hugo_Steinhaus" rel="nofollow">http://en.wikipedia.org/wiki/Hugo_Steinhaus</a> book "Mathematical Kaleidoscope" </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/14328#14328 fpqc 2010-02-05T23:57:23Z 2010-02-05T23:57:23Z

<p>One of my all-time favorites for rigour and clarity:</p> <p>Vistoli's Notes on <a href="http://homepage.sns.it/vistoli/descent.pdf" rel="nofollow">Descent</a>. </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/14949#14949 Victor Miller 2010-02-10T21:26:37Z 2010-02-10T21:26:37Z

<p>I'm surprised that nobody's mentioned almost anything by Emil Artin. His little monographs on Galois Theory and the Gamma Function are thrilling to read. They are so clear, and use the minimum necessary (but not more -- to paraphrase Einstein) I found them inspiring. Also his "Algebraic Numbers and Algebraic Functions" and "Geometric Algebra".</p> <p>Another book, is G. H. Hardy's "Pure Mathematics". That's the book that I really learned analysis from (when I told that to Pat Gallagher he exclaimed that I was really lucky) when I was in high school. Reading that cemented my feeling that I wanted to be a mathematician.</p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/14958#14958 Ian Durham 2010-02-11T00:56:32Z 2010-02-11T00:56:32Z

<p><em>Category Theory</em> by Steve Awodey (Oxford Logic Guides 49) is a very clear exposition of the subject.</p> <p>And I know my students hate it, but I really like <em>The Way of Analysis</em> by Robert Strichartz.</p>