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數學家如何提出可行的猜想
用結果、隨機性、類比協助推理

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訪  談  者　梅哲（Barry Mazur）

作者簡介　梅哲為美國數學家，1959 年畢業於普林斯頓大學，現為哈佛大學教授。梅哲早期研究幾何拓樸，證明廣義旬弗萊猜想（Schoenflies conjecture），後受格羅騰迪克影響，轉往代數數論領域，成為該領域的領導人之一。他在2013 年獲頒美國國家科學獎章。

譯        者　趙學信

譯者簡介　趙學信，網路工程師，兼事翻譯寫作。

本文出處    本文曾以演講的形式在2012 年1 月5 日的AMS-MAA 聯合會議上宣讀。後收於The Mathematical Intelligencer 36（2014）No.1。

延伸閱讀 

• Pólya, George Mathematics and Plausible Reasoning: Vol. I: Induction and Analogy in Mathematics , Mathematics and Plausible Reasoning: Volume II: Patterns of Plausible Inference（ 1954）, Princeton University Press。本書重印多次。臺灣可見譯本有《數學與可信推理 》（林聰源譯），曉園；《數學與似真推理》（簡體，楊迅文等譯），福建人民出版社；《數學與猜想》兩冊（李心燦等譯），臺版：九章、陸版：科學出版社。
• 作者在哈佛大學的網站內除了數學論文外，還有許多科普性或人文性的討論文章。http://www.math.harvard.edu/~mazur/index.html
• Derbyshire, John Prime Obsession - Bernhard Riemann and the Greatest Unsolved Problem in Mathematics（ 2004）。中譯成兩本《質數魔力（上）（下）》（2005），陳可崗譯，天下文化。想理解黎曼假說，這是一本可讀性很高的科普書。
  

參考資料

[ABC] The web is an excellent source for information about this, constantly updated. See for example: http://en.wikipedia.org/wiki/Abc_conjecture and http://www.math.unicaen.fr/*nitaj/abc.html.
[QP] Archimedes, The Quadrature of the Parabola. See pp.233–252 of Archimedes’ Collected Works, (Eng. transl.: T.L. Heath) Cambridge University Press (1897). These pages have also been scanned on the web: http://www.math.ubc.ca/*cass/archimedes/parabola.html.
[AR] Bektemirov, B., Mazur, B., Stein, W., Watkins, M., Average ranks of elliptic curves: Tension between data and conjecture, Bulletin of the American Mathematical Society 44 (2007), 233–254.
[C-L] Cohen, H., Lenstra, H.W., Heuristics on class groups of number fields, pp. 33–62 in Lecture Notes in Math. 1068 Springer (1984); see also https://openaccess.leidenuniv.nl/bitstream/handle/1887/2137/346_069.pdf?sequence=1.
[C1] Connelly, R., A counter-example to the rigidity conjecture for polyhedra, Publ. Math. IHES 47 (1978), 333–338.
[C2] Connelly, R., The rigidity of polyhedral surfaces, Math. Mag. 52 (1979), 275–283.
[CK] Cox, D., Katz, S., Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs 68 A.M.S. Publications (1991).
[G] Gelbart, S., An elementary introduction to the Langlands Program, Bulletin of the A.M.S. 10 (1984), 177–219.
[FME] Mazur, B., Finding meaning in error terms, Bulletin of the A.M.S. 45 (2008), 185–228.
[MPR] Pólya, G., Mathematics and Plausible Reasoning, Volume 1:Induction and Analogy in Mathematics, Princeton University Press (1956); Volume II Patterns of Plausible Inference, Princeton University Press (1968).