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The philosophy article "Intuition and Convergence" confronts a disturbing observation:: When someone actually needs to evaluate a limit, he usually does so by directly violating the definition of "limit"  ("Logic and Knowledge", Ed, Cellucci et al.,Cambridge Scholars, 297-323, 2011).

The philosophy article  "Mathematicians'  Proof" explains to philosophers what actual mathematicians do that we call "proof"   (To appear in "From an heuristic point of view:  in honor of Carlo Cellucci").

The "Faulhaber" article, in "Elementary Mathematics,"  uses a simple trick to explain a surprising fact about the sums of powers of the first n integers..

The "memoir" about "jews" , "Under-represented then Over-represented," is about Jews in U.S. mathematics.
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The twins are trying to get into Prep. (College Math J)   44k v. 5 Feb 20, 2012, 9:43 PM Reuben Hersh
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"Rhetoric and mathematics." About rhetorical math and mathematical rhetoric--good and bad.  1310k v. 4 May 28, 2012, 10:28 AM Reuben Hersh
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Two sticks lying across each other on the ground, once upon a time. (College Math J)   60k v. 5 Feb 20, 2012, 9:43 PM Reuben Hersh
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A tragic love affair. (The Mathematical Intelligencer)   909k v. 5 Feb 20, 2012, 9:42 PM Reuben Hersh
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The Ideal Mathematician--a little weird, but also a little too familiar.  78k v. 3 Feb 20, 2012, 10:05 PM Reuben Hersh
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The Unreasonable Effectiveness, in the simplest possible cases. Published in "18 unconventional essays on the nature of mathematics."   37k v. 4 Feb 20, 2012, 10:05 PM Reuben Hersh
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Mathematics is True Facts About Imaginary Objects!  3938k v. 3 Mar 3, 2012, 3:09 PM Reuben Hersh
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Rather too aggressive and polemical for its intended audience to tolerate. Published in Gian-Carlo Rota's "Advances in Mathematics."   2639k v. 4 Feb 20, 2012, 10:05 PM Reuben Hersh
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Delivered at MAA regional meetings, published in "The Mathematical Intelligencer".  937k v. 3 Feb 20, 2012, 10:04 PM Reuben Hersh
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Published in Paul Ernest's "Philosophy of Mathematics Education"  36k v. 5 Feb 20, 2012, 10:04 PM Reuben Hersh
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Restaurants, theaters, and mathematical life. Published first in "Eureka", then in "Synthese".    682k v. 5 Mar 3, 2012, 3:11 PM Reuben Hersh
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Easier than the way of Heron and/or Archimedes. Originally published in MAA "Focus."   185k v. 4 Mar 3, 2012, 3:11 PM Reuben Hersh
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Mathematics is more like a soaring eagle than a Manhattan skyscraper. With a deconstructed proof of Heron's area theorem. Published by Polimetrica, Milan.    53k v. 6 Mar 3, 2012, 3:12 PM Reuben Hersh
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From the revived online J. of Humanistic Math.  171k v. 4 Feb 20, 2012, 9:40 PM Reuben Hersh
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From the revived online J. of Humanistic Math.  637k v. 4 Feb 20, 2012, 9:40 PM Reuben Hersh
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Minnesota Math Enthusiast. Co-author Kristin Umland.   61k v. 4 Feb 10, 2012, 10:38 PM Reuben Hersh
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We confuse our students by giving common words like "line" and "curve" technical meanings different from their common meanings. American Mathematical Monthly.  260k v. 6 Feb 20, 2012, 9:51 PM Reuben Hersh
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Published in "Educational Studies in Mathematics."   1645k v. 5 Feb 20, 2012, 9:38 PM Reuben Hersh
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In E. Knuth, "Proof in Secondary Math Education"  30k v. 3 Mar 3, 2012, 3:00 PM Reuben Hersh
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Rejected by the Monthly. Published by Alvin White in his Humanistic Math J.   617k v. 4 Feb 20, 2012, 9:39 PM Reuben Hersh
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A visit to Budapest, with interviews, seeking to understand the famous "Hungarian miracle."  The Mathematical Intelligencer.  2273k v. 4 Feb 20, 2012, 9:51 PM Reuben Hersh
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Under-represented, then Over-represented. College Math J, Jan. 2011. Included in "Best Mathematical articles of 2011", Princeton U. Press   598k v. 7 Mar 3, 2012, 3:13 PM Reuben Hersh
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Some encounters with Paul, and an exposition of forcing. The Mathematical Intelligencer, 2011.   336k v. 5 Feb 20, 2012, 9:52 PM Reuben Hersh
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Ford Prize winning memoir by Ray Lorch, my editing. American Mathematical Monthly.  1563k v. 5 Feb 20, 2012, 9:52 PM Reuben Hersh
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Written in response to a request for "a definition of mathematics", published by Polimetrica in Milan.    34k v. 6 Mar 3, 2012, 2:59 PM Reuben Hersh
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American Mathematical Monthly.  371k v. 3 Feb 20, 2012, 9:53 PM Reuben Hersh
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phenomenological report of a derivation of Heron's area formula, for a conference in Brussels  552k v. 3 May 16, 2012, 2:29 PM Reuben Hersh
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Overview of some maverick philosophizing. "18 Unconventional Essays on the Nature of Mathematics."   Springer.  49k v. 5 Mar 3, 2012, 3:14 PM Reuben Hersh
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What we do is not what we say......................... What we say is not what we do. (From "Logic and Knowledge", ed. C. Cellucci et al.)  1138k v. 7 Feb 20, 2012, 9:34 PM Reuben Hersh
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From "Proof and other dilemmas" edited by Bonnie Gold, published by MAA.    74k v. 5 Mar 3, 2012, 3:04 PM Reuben Hersh
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Assistance for philosophers of mathematical practice (to appear in the Cellucci Festschrift "From an heuristic point of view")    138k v. 5 Feb 20, 2012, 9:54 PM Reuben Hersh
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For Ulf Persson, European Mathematical Newsletter, June 2008.   135k v. 4 Feb 10, 2012, 11:02 AM Reuben Hersh
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A merger of Markov chains and groups of linear operators, applied to solve PDE's and their singular perturbations. The Mathematical Intelligencer.   1511k v. 6 Mar 3, 2012, 3:19 PM Reuben Hersh
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An elementary explanation of which differential operators are elliptic, hyperbolic, or parabolic, and why. American Mathematical Monthly.   1132k v. 4 Mar 3, 2012, 2:58 PM Reuben Hersh
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For any well-posed initial-value problem, we present stable difference approximations of accuracy as high as you like. SIAM J Numerical Analysis. Co-author Tosio Kato   927k v. 5 Mar 3, 2012, 3:17 PM Reuben Hersh
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Readable exposition of my results on general mixed initial-boundary value problems, for hyperbolic, parabolic and other types of PDE's. In "Hyperbolic Equations and Waves," Springer.  478k v. 4 Mar 3, 2012, 2:51 PM Reuben Hersh
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Detailed exposition on random evolutions. Rigorous derivation of the diffusion approximation to random transport with infinitesimal mean free path. Rocky Mountain Mathematics Journal.    2761k v. 5 Mar 3, 2012, 3:33 PM Reuben Hersh
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Introducing Lie group methods, we solve Cauchy's problem for hyperbolic PDE's with polynomial coefficients, and other operator equations with non-commuting coefficients. J. Diff. Eq., with Stan Steinberg.    1299k v. 6 Feb 21, 2012, 4:56 PM Reuben Hersh
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Random evolutions can solve many hyperbolic pde's, and obtain singular perturbations of them. Lectures on Partial Differential Equations, Tulane. Springer.     54k v. 7 Mar 3, 2012, 3:15 PM Reuben Hersh
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Transform one problem into another, by operator-valued integral transforms  Lectures on Partial Differential Equations, Tulane. Springer.   1013k v. 5 Mar 3, 2012, 3:15 PM Reuben Hersh
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Ambiguity is the soul of mathematics!!(by William Byers.) Notices, AMS   146k v. 4 Feb 18, 2012, 3:36 PM Reuben Hersh
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Introducing him to readers of the Mathematical Intelligencer, back in 1978.  657k v. 3 Feb 10, 2012, 10:51 AM Reuben Hersh
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A famous French philosopher elevates surreal numbers to metaphysics. Math. Intelligencer   52k v. 4 Feb 18, 2012, 3:35 PM Reuben Hersh
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Bulletin AMS  31k v. 3 Feb 10, 2012, 10:52 AM Reuben Hersh
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College Math J.  32k v. 4 Feb 10, 2012, 11:40 AM Reuben Hersh
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College Math J.  42k v. 3 Feb 10, 2012, 11:40 AM Reuben Hersh
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Biography of Grisha Perelman. Math. Intelligencer  37k v. 3 Feb 10, 2012, 10:53 AM Reuben Hersh
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David Ruelle, on how mathematicians think. SIAM Review   34k v. 4 Feb 18, 2012, 3:37 PM Reuben Hersh
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3 collections of articles by the self-appointed father of the H-bomb, reviewed for the Mathematical Intelligencer.   238k v. 4 Feb 19, 2012, 2:50 PM Reuben Hersh
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Everything is really vague! SIAM Review.    37k v. 5 Feb 18, 2012, 3:38 PM Reuben Hersh
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Co-author Richard J. Griego  1467k v. 3 Feb 8, 2012, 9:24 PM Reuben Hersh
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Co-author Paul J. Cohen  2845k v. 3 Feb 8, 2012, 9:24 PM Reuben Hersh
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Co-author Martin Davis.  3465k v. 3 Feb 8, 2012, 9:24 PM Reuben Hersh
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Chauvenet Prize winner, co-authored with Martin Davis.   2204k v. 4 Feb 20, 2012, 10:00 PM Reuben Hersh
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