Conjecture

『P vs NP経営』歴史的予想。予想は文脈順、各予想内の文献は年代順。出典は『P vs NP経営』v1.0.112 を照合・正規化。

関連: P vs NP経営｜Reference

1. 正十七角形の作図 (Constructibility of the regular heptadecagon)

• Euclid of Alexandria (c. 300 BC). Elements. Ancient Greece.
  • Link
• Gauss, Carl Friedrich (1801). Disquisitiones Arithmeticae. Leipzig.
  • Archive Link

2. ケプラー予想 (The Kepler Conjecture)

• Kepler, Johannes (1611). Strena seu de Nive Sexangula (On the Six-Cornered Snowflake). Germany.
  • Archive Link
• Hales, Thomas C. (1998). “An Overview of the Kepler Conjecture.” arXiv preprint math/9811071.
  • arXiv

3. フェルマーの最終定理 (Fermat’s Last Theorem)

• Fermat, Pierre de (1670). “Observations sur Diophante.” Published in Diophantus’ Arithmetica with commentary by Samuel de Fermat. France.
  • PDF Reprint
• Wiles, Andrew (1995). “Modular elliptic curves and Fermat’s Last Theorem.” Annals of Mathematics, 141(3), 443–551.
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• Breuil, Christophe, Conrad, Brian, Diamond, Fred, & Taylor, Richard (2001). “On the modularity of elliptic curves over ℚ: wild 3-adic exercises.” Journal of the American Mathematical Society, 14(4), 843–939.
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4. 4色問題 (The Four Color Conjecture)

• Guthrie, Francis (1852). “Letter to Augustus De Morgan.” (communicated via Frederick Guthrie).
  • PDF Reference
• Appel, Kenneth, & Haken, Wolfgang (1977). “Every planar map is four colorable. Part I: Discharging.” Illinois Journal of Mathematics, 21(3), 429–490.
  • Project Euclid
• Robertson, Neil, Sanders, Daniel P., Seymour, Paul, & Thomas, Robin (1997). “The four-color theorem.” Journal of Combinatorial Theory, Series B, 70(1), 2–44.
  • PDF Reference
• Gonthier, Georges (2008). “A computer-checked proof of the Four Colour Theorem.” Microsoft Research / INRIA Joint Laboratory Report.
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5. ポアンカレ予想 (The Poincaré Conjecture)

• Poincaré, Henri (1904). “Cinquième complément à l’analysis situs.” Rendiconti del Circolo Matematico di Palermo, 18, 45–110.
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• Perelman, Grigori (2002). “The entropy formula for the Ricci flow and its geometric applications.” arXiv preprint math/0211159.
  • arXiv

6. ヴァイユ予想 (Weil Conjectures)

• Weil, André (1949). “Numbers of solutions of equations in finite fields.” Bulletin of the American Mathematical Society, 55(5), 497–508.
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• Deligne, Pierre (1974). “La conjecture de Weil. I.” Publications Mathématiques de l’IHÉS, 43, 273–307.
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7. ヒルベルトの第10問題とその解決史

• 1900年：ヒルベルトの第10問題（問題の提示）
  • Hilbert, David (1900). “Mathematische Probleme: Reihung der 23 Probleme (Problem 10).” Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 253–297.
• 1931年：算術の決定不可能性（前提の物質化）
  • Gödel, Kurt (1931). “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.” Monatshefte für Mathematik und Physik, 38, 173–198.
• 1936年：停止性問題の提示（計算論の基礎）
  • Turing, Alan M. (1936). “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, Series 2, 42, 230–265.
• 1952年：算術における存在記号の定義可能性（ロビンソンの仮説）
  • Robinson, Julia (1952). “Existential Definability in Arithmetic.” Transactions of the American Mathematical Society, 72(3), 437–449.
• 1953年：帰納的可算述語の代数的表現（先駆的研究）
  • Davis, Martin (1953). “Arithmetical Problems and Recursively Enumerable Predicates.” Journal of Symbolic Logic, 18(1), 33–41.
• 1961年：指数ディオファントス方程式の決定不能性（DPR定理）
  • Davis, Martin, Putnam, Hilary, & Robinson, Julia (1961). “The Decision Problem for Exponential Diophantine Equations.” Annals of Mathematics, Second Series, 74(3), 425–436.
• 1970年：帰納的可算集合のディオファントス的性質（マティヤセヴィチの定理 / DPRM定理の完成）
  • Matiyasevich, Yuri V. (1970). “Диофантовость перечислимых множеств.” Doklady Akademii Nauk SSSR, 191, 279–282. (Enumerable sets are Diophantine; English Translation: Soviet Mathematics. Doklady, 11(2), 354–358).

8. 未解決の予想

リーマン予想 (The Riemann Hypothesis)

• Riemann, Bernhard (1859). “Über die Anzahl der Primzahlen unter einer gegebenen Grösse.” Monatsberichte der Königlichen Preussischen Akademie der Wissenschaften zu Berlin.
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• 未解決 (Unsolved)