Which mathematicians have influenced you the most? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-19T07:14:59Z http://mathoverflow.net/feeds/question/5499 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most Which mathematicians have influenced you the most? Jose Brox 2009-11-14T13:28:17Z 2011-09-02T18:01:44Z <p>There are mathematicians whose creativity, insight and taste have the power of driving anyone into a world of beautiful ideas, which can inspire the desire, even the <em>need</em> for doing mathematics, or can make one to confront some kind of problems, dedicate his life to a branch of math, or choose an specific research topic.</p> <p>I think that this kind of force must not be underestimated; on the contrary, we have the duty to take advantage of it in order to improve the mathematical education of those who may come after us, using the work of those gifted mathematicians (and even their own words) to inspire them as they inspired ourselves.</p> <p>So, I'm interested on knowing who (the mathematician), when (in which moment of your career), where (which specific work) and why this person had an impact on your way of looking at math. Like this, we will have an statistic about which mathematicians are more akin to appeal to our students at any moment of their development. Please, keep one mathematician for post, so that votes are really representative.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5501#5501 Answer by Jose Brox for Which mathematicians have influenced you the most? Jose Brox 2009-11-14T13:46:24Z 2009-11-16T17:05:59Z <p>Who: Leonhard <strong>Euler</strong>.</p> <p>When: As a highschool student.</p> <p>Where: On the book "Euler: the master of us all" by William Dunham.</p> <p>Why: The amount of creativity and genius dispersed among the so-different works of Euler continues to amaze me just now, so it only could have a devastating effect on me 10 years ago. He not only addressed a lot of distinct topics, he layed the foundations of many branches of mathematics and solved with ease many problems that were interesting me at that moment of my life. I learned a lot from him: he really deserves the title of "master of us all".</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5510#5510 Answer by Georges Elencwajg for Which mathematicians have influenced you the most? Georges Elencwajg 2009-11-14T14:42:41Z 2009-11-16T17:06:57Z <p>Otto <strong>Forster</strong>.<br /> He is the most brilliant expositor I have ever met. I cherish the notes I took a long time ago of courses he gave in Italy and France, in perfect Italian and French. He wrote a wonderful course on Analysis (in three volumes) which has been the reference in German Universities for 30 years, something like Rudin in the States. His book on Riemann surfaces (both compact and non compact) is a masterful blend of Algebra, Topology and Analysis, with tools ranging from cohomology of sheaves to difficult potential theory. He is a brilliant researcher and has made important contributions to complex geometry and also to algebra (Forster-Swan). Working with him was a wonderful experience and he had the generosity of letting me co-sign articles to which my contribution was negligible compared to his. I am very happy of this opportunity to express my gratitude to and admiration for this genuine scholar and real gentleman.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5519#5519 Answer by Anton Petrunin for Which mathematicians have influenced you the most? Anton Petrunin 2009-11-14T15:44:11Z 2010-01-10T21:51:27Z <p><strong>Gromov</strong>.</p> <p><img src="http://owpdb.mfo.de/photoSmall?id=8240" alt="Gromov 1982" /></p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5530#5530 Answer by B. Bischof for Which mathematicians have influenced you the most? B. Bischof 2009-11-14T16:47:53Z 2010-09-26T12:49:49Z <p><strong>Erdős</strong></p> <p>Sophomore year when I decided that I didn't like physics classes I just happened to be reading "The Man Who Loved Only Numbers" by Hoffman. Between this and "How to Read and Do Proofs" by Solow, I saw mathematics as something much more beautiful. This combined with reading about Erdos style of mathematics made me really attracted to research and led to my first REU experience. It was all downhill from there.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5533#5533 Answer by Jimmy Miller for Which mathematicians have influenced you the most? Jimmy Miller 2009-11-14T17:00:53Z 2009-11-16T17:06:29Z <p>G.H. <strong>Hardy</strong>. Reading "A Mathematician's Apology" in high school really changed the way I think about mathematics.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5539#5539 Answer by Andy Putman for Which mathematicians have influenced you the most? Andy Putman 2009-11-14T18:07:13Z 2009-11-16T17:09:56Z <p><strong>Thurston</strong>. When I was a graduate student, Thurston's work really inspired me to appreciate the role of imagination and visualization in geometry/topology.</p> <p>A prominent mathematician once remarked to me that Thurston was the most underappreciated mathematician alive today. When I pointed out that Thurston had a Fields medal and innumerable other accolades, he replied that this was not incompatible with his thesis.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5542#5542 Answer by Emily Peters for Which mathematicians have influenced you the most? Emily Peters 2009-11-14T18:12:04Z 2009-11-16T17:10:25Z <p>John <strong>Baez</strong>. "This week's finds in mathematical physics" is a great playground for young mathematicians. I was a graduate student when I first found it, and I really loved the links between various TWFs and the math they discussed. Not only does he show you the breadth of modern math, he also gives you bridges between the various areas. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5550#5550 Answer by Jon Awbrey for Which mathematicians have influenced you the most? Jon Awbrey 2009-11-14T18:58:20Z 2009-11-14T18:58:20Z <p><a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Peirce%5FCharles.html" rel="nofollow">Charles Sanders Peirce</a>, his <em>Collected Papers</em>, first encountered in the less-traveled Library of Congress from B to BD corner of the math library my freshman year, and compelling me to the prodigal expense of $35.00 in late 1960-ish dollars to buy <a href="http://www.hup.harvard.edu/catalog/PEICOB.html" rel="nofollow">Volumes 3 &amp; 4 bound as 1</a>. Every year that goes by is a year I add to the number of years his thought was ahead of his time.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5559#5559 Answer by Gerald Edgar for Which mathematicians have influenced you the most? Gerald Edgar 2009-11-14T19:43:34Z 2009-11-14T19:43:34Z <p>Does <strong>Martin Gardner</strong> count, even though he is not a mathematician?</p> <p>I read all of the "Mathematical Games" columns in <em>Scientific American</em> when I was maybe 12 or 14. And this was a non-trivial task ... I would ride my bicycle to the public library one afternoon a week to read a few more columns (the school library didn't have it). So it took maybe a year to read them all.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5598#5598 Answer by Skeptic for Which mathematicians have influenced you the most? Skeptic 2009-11-15T01:27:35Z 2009-11-16T17:07:29Z <p>Silvanus P. <strong>Thompson</strong>: "Calculus Made Easy" (old simian proverb... "what one fool can do, so can another").</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5639#5639 Answer by Erik Davis for Which mathematicians have influenced you the most? Erik Davis 2009-11-15T19:06:53Z 2009-11-16T17:09:07Z <p>Gian-Carlo <strong>Rota</strong>. I really wish I could pinpoint the moment that I came across some of his work, but I can't. And I've only just begun graduate work so it's impossible to be really honest about what sort of impact he has had on me... only time can tell.</p> <p>But nonetheless, his writings are truly inspiring. It's tough to describe the wonder they have given me. Rota began as a functional analyst (PhD under Jacob Schwartz, of the Dunford &amp; Schwartz fame) and moved over to algebraic combinatorics in the 1960s. One of his first papers that has stuck in my mind is "The Number of Partitions of a Set" in which he applies the techniques of the so-called 'umbral calculus' (which he also worked to rigorously formulate) to beautifully establish some combinatorial results. He's credited as setting the field of algebraic combinatorics on solid ground via his seminal papers On the Foundations of Combinatorial Theory. But it's not just the technical results -- his writing is just plain fun to read. </p> <p>Given my personal interests, I really appreciate that although Rota did so much work in combinatorics he always seemed to lean back towards his roots in functional analysis &amp; probability. In fact, his goal to find the true nature of classical results in analysis and probability led him to a great deal of good work in combinatorics, e.g. his work on the Rota-Baxter algebra inspired by his ambition to understand "the algebra of indefinite integration", and his work on the foundations of probability with the ambition to understand the middle ground between the discrete and the continuous. Moreso than most people he is willing to put his position out there and speak <em>about</em> mathematics rather than just speak mathematics. A great example of this is his book "Indiscrete Thoughts" -- definitely worth reading. You may not agree with many things he says but it's wonderful to be allowed a glimpse into the mind of a man such as Rota.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5671#5671 Answer by Harrison Brown for Which mathematicians have influenced you the most? Harrison Brown 2009-11-16T04:12:02Z 2009-11-16T17:08:03Z <p><strong>Poincaré</strong>. Not so much for his mathematical writings (although what I've found in English, or struggled through in French, has been uniformly interesting [if dated, and/or, um, in a language I barely understand]) but for his thoughts on the philosophy and psychology of math. After the already-mentioned John Baez, the first thing I'll implore anyone who bothers to ask to read is "Intuition and Logic in Mathematics," fin-de-siecle thinking and all.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5717#5717 Answer by timur for Which mathematicians have influenced you the most? timur 2009-11-16T17:20:51Z 2009-11-16T17:20:51Z <p><strong>Terence Tao</strong>. He is one of many who influenced me the most. I don't have to mention how superb his blog and publications are. From his writings I found analysis of PDE as a fascinating subject and I am really happy that I found this topic not too late. It amazes me how much he produces.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/5828#5828 Answer by Dmitri Pavlov for Which mathematicians have influenced you the most? Dmitri Pavlov 2009-11-17T15:19:12Z 2009-11-17T15:19:12Z <p>Alexander <strong>Grothendieck</strong>. See, for example, his passage about opening a nut. This was very inspiring for me and was one of the key reasons that led me to abandon computer science and start studying math. I also very much like the way he uses geometric intuition in algebraic geometry, it helped me a lot and not only in algebraic geometry.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/6245#6245 Answer by Martijn for Which mathematicians have influenced you the most? Martijn 2009-11-20T10:16:58Z 2009-11-20T10:16:58Z <p>Herbert <strong>Federer</strong>: his work on geometric measure theorey radiacally changed my view on differential geometry. Besides that, it is extremely practical when studying geometric flows.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/6843#6843 Answer by Spinorbundle for Which mathematicians have influenced you the most? Spinorbundle 2009-11-25T20:59:51Z 2009-11-25T20:59:51Z <p>Sir Michael <strong>Atiyah</strong>. </p> <p>Besides his great technical work (his collected papers are absolutely magnificent!) especially his great interview <a href="http://video.google.de/videoplay?docid=-5911099858813393554&amp;ei=r5UNS8LvKYe62wL_9Lj8CA&amp;q=Sir+Michael+Atiyah+beauty+of+math&amp;client=firefox-a#" rel="nofollow">"Beauty in Mathematics"</a> was very inspiring to me. Another inspiring piece is his <a href="http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf" rel="nofollow">"Advice to a Young Mathematician"</a> in the Princeton Companion to Mathematics.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/8062#8062 Answer by ivane for Which mathematicians have influenced you the most? ivane 2009-12-07T01:49:10Z 2009-12-07T01:54:37Z <p>Consider looking forward: <strong>Grisha Perelman</strong>, his strange history <a href="http://en.wikipedia.org/wiki/Grigori_Perelman" rel="nofollow"> wiki G.Perelman</a>. However the first millenium prize awarded. Even note this: Terence Tao said... "well, it's amazing"</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/11376#11376 Answer by Piotr Szymański for Which mathematicians have influenced you the most? Piotr Szymański 2010-01-10T23:18:03Z 2010-01-10T23:18:03Z <p>I should say three of them:</p> <p>a. Philippe Flajolet</p> <p>His work on analytic combinatorics inspired me enough to decide to study mathematics further after having majored in theoretical computer science. He wrote a book along with Sedgewick called analytic combinatorics, not to mention lots of papers on analysis of algorithms using the techniques he developes, he's a Cauchy of modern combinatorics.</p> <p>b. Lucjan Jacak</p> <p>Mathematician &amp; quantum physicist, his lectures from quantum physics have inspired me to study this field for over two years. His most famous work concers quantum dots.</p> <p>c. Bollobas, Kozma, et. al</p> <p>And their work on non-constructive, probabilistic methods in graphs, also neuropercolation theory etc. Somewhat a revolutionary idea.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/11379#11379 Answer by François G. Dorais for Which mathematicians have influenced you the most? François G. Dorais 2010-01-10T23:32:39Z 2010-01-11T00:30:46Z <p>Serge <strong>Lang</strong>'s Algebra was my first serious encounter with mathematics, the event was a very singular defining moment in my life.</p> <p>Back then, I was firmly intent on becoming a poet or, at least, pursuing some kind of literary career. Like most budding poets, I loved books and I liked spending time in the library. I was very curious, I would often wander in a section and pick up a book just to see what that row was about. One day I picked up an old rebound copy of Lang's Algebra. It was dirty purplish grey and it just said <em>Lang: Algebra</em> in half erased white letters. I don't think I had any good reason to pick up that book, it certainly wasn't very attractive, I probably just wondered why one would write such a large tome on algebra. I sat down with the book and read the first page where he defines a monoid and proves the uniqueness of the identity element. I was fascinated. It was so beautiful. I fell in love.</p> <p>I don't think I read much of Lang's book on that day, I probably only had an hour or less to spare, but I went back to the math section later and I picked up more books. The next one was Willard Van Orman <strong>Quine</strong>'s <em>Set Theory and its Logic</em>, which is probably the worst possible way to get introduced to Set Theory but that's how I eventually became a logician instead of a poet.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19364#19364 Answer by Charlie Frohman for Which mathematicians have influenced you the most? Charlie Frohman 2010-03-25T23:56:29Z 2010-03-25T23:56:29Z <p>John Milnor too many great books.</p> <p>Friedhelm Waldhausen for his papers on three manifold topology.</p> <p>William Thurston for his lecture notes on hyperbolic three manifolds.</p> <p>Fathi, Laudenbach and Poeneru for "Travaux de Thurston"</p> <p>Atiyah and Bott, for "Yang-Mills on Riemann Surfaces."</p> <p>Kobayashi for "Differential Geometry of Complex Vector Bundles"</p> <p>Bill Meeks for his lecture notes on Minimal Surfaces.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19370#19370 Answer by Gerry Myerson for Which mathematicians have influenced you the most? Gerry Myerson 2010-03-26T00:38:31Z 2010-03-26T00:38:31Z <p><strong>Andrew Gleason</strong>. An inspiring teacher in Math 55, the 2nd-year advanced calculus course at Harvard, and Math 213, the graduate complex variables course. He had a knack for getting at the essence of anything he lectured about. I have tried (with considerably less success) to do that in my teaching and my writing. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19371#19371 Answer by Gerry Myerson for Which mathematicians have influenced you the most? Gerry Myerson 2010-03-26T00:42:16Z 2010-03-26T00:42:16Z <p><strong>Arnold Ross</strong>. He ran the summer program in Number Theory for high school students at Ohio State University, my first exposure to serious mathematics. His lectures set me on a course from which I've hardly deviated in over 40 years. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19372#19372 Answer by Gerry Myerson for Which mathematicians have influenced you the most? Gerry Myerson 2010-03-26T00:45:59Z 2010-03-26T00:45:59Z <p><strong>Albert H Beiler</strong>. When I was in high school, someone gave me his book, Recreations in the Theory of Numbers. So different from any mathematics I had seen before, and so much fun! From there, it was just a short step to the Ross program....</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19373#19373 Answer by Gerry Myerson for Which mathematicians have influenced you the most? Gerry Myerson 2010-03-26T00:48:43Z 2010-03-26T00:48:43Z <p><strong>Henry Ernest Dudeney</strong>, author of Amusements in Mathematics, another book that set me, in my early teenage years, on the path to mathematics. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19375#19375 Answer by Jeff Breeding for Which mathematicians have influenced you the most? Jeff Breeding 2010-03-26T01:12:07Z 2010-03-26T01:12:07Z <p><strong>Benedict Gross</strong>. I saw him lecture a few times on BSD. His enthusiasm and mastery were very inspirational. It reminded me why I want to be a professional mathematician. I had just finished my general exams the previous semester and felt tired from taking so many classes and preparing for exams. It had put a haze over the beauty of mathematics. Professor Gross made it clear again.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19381#19381 Answer by Jacques Carette for Which mathematicians have influenced you the most? Jacques Carette 2010-03-26T02:04:01Z 2010-03-26T02:04:01Z <p><strong>Leibniz</strong>. Not just for his mathematics (calculus, amazing insights in logic, semantics) but he was just an incredible polymath, with deep work in law, history, linguistics, chemistry, physics, metaphysics, politics, engineering, sociology, he founded 'library science', and on and on. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19394#19394 Answer by Douglas Zare for Which mathematicians have influenced you the most? Douglas Zare 2010-03-26T05:09:48Z 2010-03-26T05:09:48Z <p>Carl Friedrich <strong>Gauss.</strong></p> <p>The breadth and beauty of his work amazed me when I was a student, and it still inspires me. </p> <p>He started by building on much less than what many of us take for granted: His doctoral dissertation was the Fundamental Theorem of Algebra. His work covered deep, essential results in many areas, from number theory (quadratic reciprocity, conjecture of prime number theorem) to geometry (Gaussian curvature) to statistics (least squares) to probability (Gaussian distribution). It is difficult to imagine these areas without his fundamental contributions. He also contributed to physics and astronomy. </p> <p>Even though Gauss explored many areas, he took the time to revisit old results, looking for different and more satisfactory proofs. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19739#19739 Answer by James for Which mathematicians have influenced you the most? James 2010-03-29T16:51:16Z 2010-03-29T16:57:07Z <p><strong>Who:</strong> H. S. M. Coxeter.</p> <p><strong>When:</strong> When I was an undergraduate.</p> <p><strong>Why:</strong> Not only was he a prince among mathematicians, but he was also a gentleman of the first rank. Several of his books also inspired me. Moreover, by transitivity, he was (for me) clearly the most influential.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/20354#20354 Answer by Tran Chieu Minh for Which mathematicians have influenced you the most? Tran Chieu Minh 2010-04-05T02:54:21Z 2010-04-05T08:59:44Z <p><strong>Gödel</strong> I was captivated by his belief of a platonic mathematical world and the belief that human can understand such a thing.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/20359#20359 Answer by Pietro KC for Which mathematicians have influenced you the most? Pietro KC 2010-04-05T03:20:53Z 2010-04-05T03:20:53Z <p>Taking into account the butterfly effect, I guess <strong>Roger Penrose</strong> would have influenced me the most. At first I was into physics and taught myself some calculus to understand it better; but it was more a tool than an end in itself. Then, at about 14, I read <em>The Emperor's New Mind</em> and was totally blown away by the ideas and proofs around Gödel's and Turing's work. Previously I had no idea the human mind could be so powerful!</p> <p>It definitely pushed me into mathematics, and to this day I am very logically and discretely inclined.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/20372#20372 Answer by Ulrich Pennig for Which mathematicians have influenced you the most? Ulrich Pennig 2010-04-05T08:48:37Z 2010-04-05T08:48:37Z <p><strong>John Willard Milnor</strong> for his books about "Morse Theory" and the "h-cobordism theorem" (I think it is a crime that it isn't printed anymore) and for writing papers in a way that they are quite self-contained and readable. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/20578#20578 Answer by Changwei Zhou for Which mathematicians have influenced you the most? Changwei Zhou 2010-04-07T01:24:39Z 2010-10-19T17:11:53Z <p>Bernhard <strong>Riemann</strong>.</p> <p>The idea of the Riemann Surface and manifolds stroke me when I was a high school student. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/20603#20603 Answer by Carter Tazio Schonwald for Which mathematicians have influenced you the most? Carter Tazio Schonwald 2010-04-07T07:15:17Z 2010-07-06T09:40:39Z <p>In terms of style of math, I'm not quite sure yet. However, I think that it is certainly true for me, and no doubt for countless others, <strong>one's advisors</strong> role is one of the most crucial influences one may have.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/24583#24583 Answer by ogerard for Which mathematicians have influenced you the most? ogerard 2010-05-14T06:52:36Z 2010-07-06T09:43:31Z <p><strong>Louis Comtet</strong>, through his book "Analyse Combinatoire vol 1 and 2", now republished in english translation with additions and corrections as "Advanced Combinatorics".</p> <p>When ? My first year in Paris University while I was attending boring courses in Analysis and Linear Algebra that were very inferior to what I have been exposed in high school the year before.</p> <p>These two little pocket books were relatively easy and cheap to find and gave a wealth of packed information and links to the existing litterature on combinatorics. Combinatorial Mathematics were not in fashion in France in the 1970s, neither in the 1980s. Among many things I liked were the fancy notations, the diagrams, the density of results, the careful index, the intersection with so many other mathematical theories such as set theory, differential equations, topology, group theory. And it was also my first contact with a slightly formalized graph theory, Eulerian numbers, integer partitions, multiple summation, etc.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/24653#24653 Answer by Andrew L for Which mathematicians have influenced you the most? Andrew L 2010-05-14T19:44:21Z 2010-07-06T09:46:55Z <p>The graduate advisor at Queens College of the City University Of New York, <strong>Nick Metas</strong>, was and continues to be my greatest influence.</p> <p>I first had a conversation on the phone with Nick over 15 years ago when I was a young chemistry major taking calculus and just becoming interested in mathematics. We spoke for over 3 hours and we were friends from that moment on.</p> <p>It was Nick who indocrinated me into the ways of true rigor through his courses and countless conversations,and the equal cardinality of the stories he's told. Nick is a true scholar and my enormous knowledge of the textbook literature and research papers from the 1960's onward,I learned from Nick.My learned capacity for self-learning got me through the lean years at CUNY during my illnesses,when there wasn't much of a mathematics department there.</p> <p>In relation to the reference to Gian-Can Rota above,I am Rota's mathematical grandson through Nick. Nick loved Rota and his eyes light up when he speaks of his dissertation advisor and friend from his student days at MIT. I hope someday there's someone famous I can feel that way about. But no one's influenced me more then Nick. </p> <p>Nick's has been my friend and advisor for all things mathematical and he celebrated his 74th birthday yesterday quietly in his usual office hour,with dozens of students asking him for advice or just listening to his wonderful stories and jokes. Regardless of what happens,it will be Nick who's influence on me as a mathematician, student and mentor who's shaped me the most. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/24656#24656 Answer by Dan Piponi for Which mathematicians have influenced you the most? Dan Piponi 2010-05-14T20:19:44Z 2010-05-14T20:19:44Z <p><strong>JH Conway</strong>. He has published work in a diverse set of interesting fields. I first met his name when looking for cool computer programs to write as a kid (ie. the Game of Life) but since then his name kept appearing in mathematics that I found interesting, whether it's Monstrous Moonshine or the properties of finite state automata. He has this incredible knack for turning anything he touches into fun - whether it's knot theory, group theory, quadratic forms, or, more obviously, combinatorial games. As well as working at the frontiers of mathematics he's discovered accessible but surprising and beautiful recreational mathematics, like <a href="http://www.cut-the-knot.org/proofs/checker.shtml" rel="nofollow">Conway's soldiers</a>. All in all, an amazing guy. Once of my regrets in life is being too lazy to attend his lectures on finite simple groups when I was an undergraduate.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/25454#25454 Answer by Burhan for Which mathematicians have influenced you the most? Burhan 2010-05-21T03:36:53Z 2010-05-21T03:36:53Z <p><strong>Srinivasa Ramanujan.</strong> He does not figure that much in my work right now. But studying his notebooks (via Bruce Berndt's studies) when I was a teenager taught me how to appreciate beautiful mathematics. From that moment on, I was hooked. I knew I had to be a mathematician.</p> <p>As for those whose lives or personalities inspired me, or whose style of thinking influenced my methodology, too many to count...</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/25504#25504 Answer by Dan for Which mathematicians have influenced you the most? Dan 2010-05-21T17:12:08Z 2010-05-21T17:12:08Z <p>Raymond <strong>Smullyan</strong>, in elementary school. His book "Alice in Puzzleland" was a childhood favorite of mine and is what and inspired a life long interest in math.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30571#30571 Answer by secret_mathematician for Which mathematicians have influenced you the most? secret_mathematician 2010-07-05T00:08:10Z 2010-07-05T00:08:10Z <p><strong>Lou van den Dries</strong></p> <p>Frankly speaking.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30652#30652 Answer by DamienC for Which mathematicians have influenced you the most? DamienC 2010-07-05T19:19:15Z 2010-07-05T19:19:15Z <p><strong>who</strong>: <a href="http://www.ihes.fr/~maxim/indexF.html" rel="nofollow">Maxim Kontsevich</a></p> <p><strong>when</strong>: when I was a PhD student, and onwards. </p> <p><strong>why</strong>: probably because of my main research interest when I was a PhD student, namely deformation quantization. Also because before moving to (many) other subjects Kontsevich has formulated a lot of very reasonnable conjectures and guessed a lot of possible developpments in the field. Some of them I have been following. Even now, I am still thinking quite often about a few questions he raised . </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30663#30663 Answer by Daniel Asimov for Which mathematicians have influenced you the most? Daniel Asimov 2010-07-05T20:10:59Z 2010-07-06T09:42:22Z <p>(I think that for a question like this with the answers being entirely personal, the voting is of little or no significance.)</p> <p>For me there are so many that I hardly know where to begin. Initially, <strong>Martin Gardner</strong>. Among those I knew personally: my undergrad profs (espcially I.M. <strong>Singer</strong>) who taught me what math is. Then Bill <strong>Thurston</strong>, with whom I shared an office in grad school. Stephen <strong>Smale</strong>, my de facto co-thesis advisor.</p> <p>Notably <strong>Gauss</strong>, <strong>Riemann</strong>, <strong>Klein</strong>, <strong>Poincaré</strong>, <strong>Milnor</strong>.</p> <p>Above all, my thesis advisor, Morris <strong>Hirsch</strong>, with whom I've had a continuing connection since 1970.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30666#30666 Answer by Asaf Karagila for Which mathematicians have influenced you the most? Asaf Karagila 2010-07-05T20:19:39Z 2010-07-06T09:39:53Z <p>I have quite a few on my list. </p> <p><strong>Newton</strong> and <strong>Leibniz</strong> since the day I learned they were 22/19 (respectively) when they invented the calculus, <strong>Riemann</strong> as well (one of my teaching assistants was mad about him as well... it caught on)</p> <p><strong>Gödel</strong> after I'd took a course focusing on completeness and incompleteness, as well after you read his biographies.</p> <p>Saharon <strong>Shelah</strong>, after one of my professors that did his Ph.D. under Shelah told me a lot about him. Finished his master degree in one year, Ph.D. in two. Invented so much... he's a real inspiration for me.</p> <p><strong>Grothendieck</strong> is a personal inspiration from another end. Not as a mathematician but as a human being. The fact he was able to get up and leave everything. That is amazing for me.</p> <p>And while we're at it, Albert <strong>Einstein</strong> since I was 21 and read the book <em>Ideas and Opinions</em>.</p> <p>What matters is less the work, but rather the ability to express with clarity a new idea that no one had before. That's what makes a great mathematician in my eyes... at least from where I stand today.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30724#30724 Answer by vamsi krishna for Which mathematicians have influenced you the most? vamsi krishna 2010-07-06T04:42:15Z 2010-07-06T09:37:46Z <p>For me its <strong>Aryanhatta</strong> who estimated the value of pi and proved that it is irrational way back in 400 B.C.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/30934#30934 Answer by Bill Dubuque for Which mathematicians have influenced you the most? Bill Dubuque 2010-07-07T18:34:11Z 2010-07-07T18:34:11Z <p><b>Dedekind</b>, whose championing of concepts (vs. calculation) left a longstanding impression on the way that I conceive mathematics - even long after I first started reading the masters as a student. Back then I had to grovel through the bowels of the MIT libraries but now, with many important historical works easily accessible online, there is no excuse not to <b>read the masters.</b></p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/42810#42810 Answer by zamanjan for Which mathematicians have influenced you the most? zamanjan 2010-10-19T17:30:01Z 2010-10-20T15:58:03Z <p>Vladimir Igorevich <strong>Arnold</strong>.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/42913#42913 Answer by Joe Johnson for Which mathematicians have influenced you the most? Joe Johnson 2010-10-20T17:12:59Z 2010-10-20T17:12:59Z <p>I would have to say equal parts Godel and Raymond Smullyan. When I first started caring about math I picked up both Newman and Nagel's book on the Incompleteness Theorems and Smullyan's "First Order Logic". I then bought as many of the Smullyan puzzle books I could find. I also read Smullyan's "The Tao is Silent", which influenced me as a person.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/52262#52262 Answer by Patrick I-Z for Which mathematicians have influenced you the most? Patrick I-Z 2011-01-16T21:09:03Z 2011-01-16T21:09:03Z <p><strong>Joseph-Louis Lagrange</strong> For his modesty as a human being, and his <a href="http://gallica.bnf.fr/Search?idArk=&amp;n=15&amp;p=1&amp;lang=EN&amp;adva=1&amp;adv=1&amp;reset=&amp;urlReferer=%2Fadvancedsearch%3Flang%3DEN&amp;enreg=&amp;tri=&amp;submit1=Start+search&amp;catsel1=f_creator&amp;cat1=Joseph-Louis+Lagrange&amp;ope2=MUST&amp;catsel2=f_title&amp;cat2=oeuvres&amp;ope3=MUST&amp;catsel3=f_tdm&amp;cat3=&amp;date=daTo&amp;daFr=&amp;daTo=&amp;t_language=fre&amp;sel_provenance_Part=toutPartenaires&amp;sel_provenance_Edist=toutSNE&amp;dateMiseEnLigne=indexDateFrom&amp;firstIndexationDateDebut=&amp;firstIndexationDateFin=&amp;tri=" rel="nofollow">great mathematical work</a>, on almost every field of mathematics, but especially in mechanics.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/52274#52274 Answer by Frank Thorne for Which mathematicians have influenced you the most? Frank Thorne 2011-01-17T00:05:57Z 2011-01-17T00:05:57Z <p>Cliched perhaps, but <strong>my fellow graduate students</strong> when I was in grad school. They're the ones that answered my questions when I got lost, shared their half-baked ideas and listened to mine, showed me just how many interesting fields of math there are and how many different perspectives people can have on the same subject, and cheered me on when things were difficult.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/52280#52280 Answer by jasomill for Which mathematicians have influenced you the most? jasomill 2011-01-17T01:19:34Z 2011-01-17T01:19:34Z <p><strong>Richard Courant</strong>. Several years before I started studying mathematics in earnest, I spent a summer working through his calculus texts. Only recently, on re-reading them, have I come to realize how much my understanding of calculus, linear algebra, and, more generally, of the unity of all mathematics and, to use Hilbert's words, the importance of "finding that special case which contains all the germs of generality," have been directly inspired by Courant's writings.</p> <p>From the preface to the first German edition of his <em>Differential and Integral Calculus:</em></p> <blockquote> <p>My aim is to exhibit the close connexion between analysis and its applications and, without loss of rigour and precision, to give due credit to intuition as the source of mathematical truth. The presentation of analysis as a closed system of truths without reference to their origin and purpose has, it is true, an aesthetic charm and satisfies a deep philosophical need. But the attitude of those who consider analysis solely as an abstractly logical, introverted science is not only highly unsuitable for beginners but endangers the future of the subject; for to pursue mathematical analysis while at the same time turning one's back on its applications and on intuition is to condemn it to hopeless atrophy. To me it seems extremely important that the student should be warned from the very beginning against a smug and presumptuous purism; this is not the least of my purposes in writing this book.</p> </blockquote> <p>Another example: while not a "linear algebra book" <em>per se</em>, I have yet to find a better introduction to "abstract linear algbera" than the first volume of Courant's <em>Methods of Mathematical Physics</em> ("Courant-Hilbert"; so named because much of the material was drawn from Hilbert's lectures and writings on the subject). His one-line explanation of "abstract finite-dimensional vector spaces" is classic: "for <em>n</em> > 3, geometrical visualization is no longer possible but geometrical terminology remains suitable."</p> <p>Lest one be misled into thinking Courant saw "abstract" vector spaces as "$\mathbb{R}^n$in a cheap tuxedo," he introduces function spaces in the second chapter ("series expansions of arbitrary functions"), and most of the book is about quadratic eigenvalue problems, or, as Courant saw it, "the problem of transforming a quadratic form in infinitely many variables to principal axes."</p> <p>As a final example: Courant's expository <em>What is Mathematics?</em> is perhaps best described as an unparalleled collection of articles carefully crafted to serve as an object at which one can point and say "this is." Moreover, while written as a "popularization," its introduction to constrained extrema problems is, without question, a far, far better introduction than any textbook I've ever seen.</p> <p>I should also mention <strong>Felix Klein</strong>, not only because Klein's views on "calculus reform" so clearly influenced both the style and substance of Courant's texts, but since a number of Klein's lectures have had an equally significant influence on my own perspective. For those unfamiliar with the breadth of Klein's interests, I'm tempted to say "his Erlangen lecture, least of all" (not that there's anything wrong with it).</p> <p>Lest my comments be mistaken for a sort of wistful "remembrance of things past," I'd easily place <strong>Terence Tao</strong>'s writings on par with Courant's, for many of the same reasons: clear and concise without being terse, straightforward yet not oversimplified, and, most importantly, animated by a sort of — <em>je ne sais quoi</em> — whatever it is, it seems to involve, in roughly equal proportions: mastery of one's own craft, a genuine desire to pass it on, and the considerable expository skills required to actually do so.</p> <p>Finally, I can't help but mention <strong>Richard Feynman</strong> in this context, and to plug his <a href="http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html" rel="nofollow">Nobel lecture</a> in particular. While not a mathematician <em>per se</em>, Feynman surely ranks among the twentieth century's best examples of a "mathematical physicist" in the finest sense of the term, not merely <em>satisfied</em> by a purely mathematical "interpretation" of physical phenomena, but surprised, excited, and, dare I say, <em>delighted</em> by the prospect! Moreover, he was equally excited about mathematics in general, see, <em>e.g.,</em> the "algebra" chapter in the Feynman Lectures on Physics.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/53460#53460 Answer by Michael Blackmon for Which mathematicians have influenced you the most? Michael Blackmon 2011-01-27T07:04:48Z 2011-01-27T12:59:55Z <ul> <li>Paul <strong>Cohen</strong> &amp; Kurt <strong>Gödel</strong> <ul> <li>They gave us the tools to construct models of set theory.</li> </ul></li> <li>Kenneth Kunen <ul> <li>His book "Set theory: An Introduction To Independence Results" was the book that got me interested in the field I would later call my home.</li> </ul></li> <li>Saharon <strong>Shelah</strong> <ul> <li>His work on forcing, and singular cardinals keep me asking questions, and open up the possibility for questions I didn't even know could be asked.</li> </ul></li> </ul> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/53490#53490 Answer by Harry Gindi for Which mathematicians have influenced you the most? Harry Gindi 2011-01-27T13:32:42Z 2011-01-27T13:32:42Z <p><strong>Dieudonné</strong></p> <p>The number 1 <em>personality</em> behind Bourbaki. Even though he was famous for taking the most extreme positions and was widely dismissed as a radical, his vision of mathematics is one that has largely been adopted by almost all mathematicians everywhere. Reading any piece of mathematical work he wrote, it his hard not to feel the respect and passion he felt for mathematics as a subject.</p> <p><strong>Dan Kan</strong></p> <p>Singlehandedly developed categorical homotopy theory into a full-fledged replacement for the homotopy theory of spaces (Kan complexes, combinatorial homotopy groups, subdivision,$Ex^\infty\$, among many other things) as well as a large part of the foundations of homological algebra (Dold-Kan correspondence), category theory (adjoint functors, Kan extensions), and the modern theory of simplicial localization (with Dwyer) among numerous other achievements. </p> <p>It's said that Kan's breakthrough paper on adjoint functors convinced Eilenberg and Mac Lane that pure category theory was not only a viable mathematical discipline (rather than a language), but also a deep and rich one. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/62988#62988 Answer by Yuri Zarhin for Which mathematicians have influenced you the most? Yuri Zarhin 2011-04-26T00:25:21Z 2011-04-26T00:25:21Z <p>Who: Manin, Parshin, Serre, Tate.</p> <p>When: When I was an undergraduate.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/63003#63003 Answer by Tarun Chitra for Which mathematicians have influenced you the most? Tarun Chitra 2011-04-26T05:34:47Z 2011-04-26T05:34:47Z <p><strong>Nigel Hitchin</strong> has an amazing ability to find a new mathematical structure out of every physical context. His articles and papers are always clear, concise and provide the necessary intuition for the reader to grasp the concept/application while reading the definitions. I have always felt that many mathematics papers ignore the reader and focus on presenting things in such a concise matter that the true meaning is obfuscated. Hitchin never seems to do that and almost holds the reader's hand as he guides him/her through the wonders of mathematical physics. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/63011#63011 Answer by Vicfred for Which mathematicians have influenced you the most? Vicfred 2011-04-26T07:28:52Z 2011-04-26T12:35:20Z <p>I was an (computer systems) engineering student, I decided tu study Mathematics after reading "Whom the gods love" it's a book about the life of <strong>Évariste Galois</strong>. I was thinking about that but reading that book gave me the courage. I also feel that mathematics is not very different from the topics I like about computer science.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/63585#63585 Answer by Dinesh for Which mathematicians have influenced you the most? Dinesh 2011-05-01T07:21:02Z 2011-05-01T07:21:02Z <p>The first inspiration was Gauss's solution of sum of first n natural numbers when i was in high school...I went on to learn his notion of congruence etc which were really breath taking at that time.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/65749#65749 Answer by Nishant Chandgotia for Which mathematicians have influenced you the most? Nishant Chandgotia 2011-05-23T08:46:50Z 2011-05-23T08:46:50Z <p>Walter Rudin: His texts in Analysis are the ones which got me into mathematics. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/65755#65755 Answer by hungrygrad for Which mathematicians have influenced you the most? hungrygrad 2011-05-23T10:44:24Z 2011-05-23T10:44:24Z <p><strong>Colin Adams</strong> Knot theory was the first topic I was really excited about as an undergraduate from reading "The Knot Book." I did an summer program with Colin Adams and got my first glimpse of research, even at an undergraduate level and realized it's what I wanted to do for the rest of my life.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/65761#65761 Answer by John for Which mathematicians have influenced you the most? John 2011-05-23T13:24:39Z 2011-05-23T13:24:39Z <p><strong>Curtis McMullen</strong>. If you have ever seen him give a talk, you'll know what I'm talking about. He has a knack for delivering seemingly complicated ideas with clarity and charm. He is also a brilliant expositor. See Milnor's article on his work <a href="http://www.math.sunysb.edu/~jack/curt.ps" rel="nofollow">here</a>.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/65765#65765 Answer by Saikat Biswas for Which mathematicians have influenced you the most? Saikat Biswas 2011-05-23T14:45:08Z 2011-05-23T14:45:08Z <p><strong>Barry Mazur</strong>. The Eisenstein ideal paper, the one on towers of abelian varieties, as well as his beautiful expositions on visibility, Galois deformations, Kolyvagin systems etc continue to inspire me everyday.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/65804#65804 Answer by Vamsi for Which mathematicians have influenced you the most? Vamsi 2011-05-23T23:16:32Z 2011-05-23T23:16:32Z <p>Simon Donaldson. His proofs involve (to quote wikipedia) a creative use of analysis. I loved his proof of the theorem of Narasimhan and Seshadri.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/66486#66486 Answer by David White for Which mathematicians have influenced you the most? David White 2011-05-30T19:32:36Z 2011-05-30T19:32:36Z <p>As a graduate student, it's hard to say who's influenced me the <em>most</em>. Certainly my advisor seems to be a strong candidate, though others mentioned above have also influenced me. Still, there is an individual who has influenced my mathematical development at several different times in my career so far and who deserves a mention. From my talks with other grad students, I know I am not alone in being grateful for this person's work and his clear way of thinking and writing about mathematics.</p> <p>Who: Keith Conrad</p> <p>Which work: his body of expository papers at <a href="http://www.math.uconn.edu/~kconrad/blurbs/" rel="nofollow">http://www.math.uconn.edu/~kconrad/blurbs/</a></p> <p>When/Why: First, sophomore year of undergrad, in an elementary number theory course. This course and Professor Conrad's writings helped convince me to go to grad school. Then also junior year when I saw him give a talk at a conference and later at my own college. And more recently in the first year of grad school when I learned about tensor products, modules, exterior algebras, Galois theory, and several other topics.</p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/74382#74382 Answer by Victor Miller for Which mathematicians have influenced you the most? Victor Miller 2011-09-02T18:01:44Z 2011-09-02T18:01:44Z <p>Who: G. H. Hardy</p> <p>When: As a high school student</p> <p>Where: The book "Pure Mathematics" -- from which I learned real analysis.</p> <p>Who: Serge Lang</p> <p>When: As a college student</p> <p>Where: At Columbia, Serge Lang was my mathematical mentor. I took Math I C/II C from him (which I'd describe as freshman mathematics for prospective Ph.D.'s -- it was pretty much an undergraduate Abstract Algebra, plus Real Analysis plus more in two semesters). His energy and love of mathematics was inspiring. I know that nobody who met him felt neutral about him. He was incredibly dedicated to his students. If he liked you he would move mountains.</p> <p>Who: Lipman Bers</p> <p>When: As a college student</p> <p>Where: At Columbia, Lipman Bers was my other inspiration. I took Math III C/IV C from him -- sophomore mathematics for prospective Ph.D.'s. Besides being a very lucid lecturer, with fantastic geometric intuition, he was sophisticated and kind -- a prince among men! By example he showed how one could live a mathematical life (at perhaps a bit less than the frenetic pace of Serge Lang).</p>