Title 数学史研究最新動向 ( 数学史の研究 ) Author(s) 林, 知宏 Citation 数理解析研究所講究録 (2002), 1257: Issue Date URL Right Type

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1 Title 数学史研究最新動向 ( 数学史の研究 ) Author(s) 林, 知宏 Citation 数理解析研究所講究録 (2002), 1257: Issue Date URL Right Type Departmental Bulletin Paper Textversion publisher Kyoto University

2 (Tomohiro HAYASHI) Gakushuin Boys Senior High School * 1,,,,, 2, 3 ( ), (a) (b) (c) 3 Social Context, 4,,, * ,,,,

3 \mathrm{n}\mathrm{a}\mathrm{y}\mathrm{r}\overline{\mathrm{l}}\mathrm{z}\overline{1}$ $\mathrm{s}\mathrm{a} \overline{\mathrm{l}}\mathrm{d}$ \star SCIAM \rightarrow 1 [Rommevaux et al 2001]\rightarrow ( Knorr ), [Knobloch und Graf 2000]\rightarrow,, ( ) [ 2OOI]\rightarrow 1(1 ) [Brentjes 2001] Brentjes, Sonja, Two Comments on Euclid s Ilements?: On the Relation $\mathrm{a}\mathrm{l}- between the Arabic Text Attributed to and the Latin Text Ascribed to Anaritius, Centaurus, 43(2001), pp [Hayashi 2000] Hayashi, Takao, The $Caturacint\overline{a}man$ $i$ of Giridharabhatta: ASixteen- Century Sansckrit Mathematical Treatise, SCIAMVS, 1(2000), pp [Hogendijk 2001] Hogendijk, Jan P, The Geometrical Works of Ab\={u} $\mathrm{j}\mathrm{u}\mathrm{r}\mathrm{j}\overline{\mathrm{a}}\mathrm{n}\overline{1},$ SCIAMVS, $2(2001)$, pp a1-d $\mathrm{a}\mathrm{r}\overline{\mathrm{l}}\mathrm{r}$ al- $[\mathrm{h}\emptyset \mathrm{y}\mathrm{r}\mathrm{u}\mathrm{p}2000]\mathrm{h}\emptyset \mathrm{y}\mathrm{r}\mathrm{u}\mathrm{p}$, Jens, Jacobus de Florentia, Tractatus algorismi(1307):the Chapter on Algebra (Vat Lat 4826, fols 36v-45v), Centarus, 42(2000), pp21-69 [Knobloch und Graf 2000] Gottfried Wilhelm Leibniz Hauptschriften zur Versicherungsund Finanzmathematik, herausgegeben von Eberhard Knobloch und J - Matthias Graf von der Schulenburg(Berlin: Akademie Verlag, 2000) [Muroi 2001] Muroi, Kazuo, Reexamination of the Susa Mathematical Text No 12: A System of Quartic Equations, $SC,IAMVS,$ $2(2001)$, pp 3-8 [Rommevaux et al 2001] Rommevaux, S, Djebbar, A et Vitrac, B, Remarques sur 1 histoire du texte des Eliments d Euclide, Archive for History of Exact Sciences, 55(2001), pp

4 15 des \ El\ ements d Euclide de $5^{e}$ [Sutto 2000] Sutto, Jean-Pierre, Le conpendium du livre Francesco Maurolico, Revue histoire des mathimatiques, $6(2000),$ $d$ $\mathrm{p}\mathrm{p}$, [Takahashi 2001] Takahashi, Ken ichi, AManuscript of Euclid s De Speculis: A Latin $\mathrm{y}$ Text of MS 9822 of the Archivo Biblioteca Capitulares de la Catedral, Toledo, SCIAMVS, $2(2001)$, pp [ 2001],, (, 2001 ) 3 31 [Netz ], [Netz 1999b]\rightarrow, $\text{ }\backslash$ [ $1999\mathrm{a}$ ( ) ( ), { 21 ( ) [Decorps-Foulquier 1999] Decorps-Foulquier, Micheline, Sur les figures du traite des Coniques d Apollonios de Perg\ e \ edit\ e par Eutocius d Ascalon, Revue $d$ histoire des math\ ematiques, 5(1999), pp [Netz $1999\mathrm{a}$ ] [Netz $1999\mathrm{b}$ ] Netz, Reviel, Archimedes Transformed: The Case of aresult Stating a Maximum for acubic Equation, Archive for History of Exact Sciences, 54(1999), pp 1-47 Netz, Reviel, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History(Cambridge: Cambridge University Press, 1999) [Netz et al 2001] Netz, Reviel, Saito, Ken and Tchernetska, Natalie, A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 1), $SC_{/}IAMVS,$ $2(2001)$, pp 9-29

5 16 32 \star (,,, ) [Steda ], [Stedall ], [Stedall 2001]\rightarrow $2000\mathrm{a}$ $2000\mathrm{b}$ (, ) [Jesseph 1999]\rightarrow (,, ) [Dobson 2001], [Guicciardini 1999], [Pourciau ], [Pourciau 2001b]\rightarrow $2001\mathrm{a}$ (,, ) [Ferraro 2000]\rightarrow (11 functional relation, 2:,, formula, analytical expression) $(1arrow 2)$ global continuity [Knobloch 1999]\rightarrow $\mathrm{a}$ $\mathrm{a}$, (, ) 22 ( ) [Dobson 2001] Dobson, Geoffrey J, On Lemma 1and 2to Proposition 39 of Book 3 of Newton s Principia, Archive for History of Exact Sciences, 55(2001), pp [Ferraro 2000] Ferraro, Giovanni, Functions, Functional Relations, and the Laws of Continuity in Euler, $H\dot{u} to\dot{n}a$ Mathematica, 27(2000), pp [Guicciardini 1999] Guicciardini, Niccolo, Reading the Principia: The Debate on Neeoton s Mathematical Methods for Natural Philosophy from 1687 to 1 $7\mathit{3}\theta$(Cambridge: Cambridge University Press, 1999) [Janiak 2000] Janiak, Andrew, Space, Atoms and Mathematical Divisibillity in Newton, Studies in History and Philosophy of Science, 31 (2000), pp [Jesseph 1999] Jesseph, Douglas M $Squar\dot{\mathrm{v}}ng$ the Circle:The War between Hobbes and Wallis(Chicago: The University of Chicago Press, 1999) [Knobloch 1999] Knobloch, Eberhard, Gahleo and Leibniz: Different Approaches to Infinity, Archive for History of Exact Sciences, 54(1999), pp 87-99

6 Absurdum, REJECT} \mathrm{d}\ovalbox{\tt\small REJECT} \mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}$ et \mathrm{d}$ of 17 [Knobloch 2001] Knobloch, Eberhard, $\ovalbox{\tt\small $d$ histoire des sciences, 54(2001), $\mathrm{p}\mathrm{p}$ $\ovalbox{\tt\small REJECT} \mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$ $\mathrm{l}\mathrm{e}\ovalbox{\tt\small chez $ $ REJECT} \mathrm{b}\mathrm{n}\mathrm{i}\mathrm{z},"$ Revue [Loveland 2001] Loveland, Jeff, Buffon, the Certainty of Sunrise, and the Probabilistic Reductio $\mathrm{a}\mathrm{d}$ pp Archive for History of Exact Sciences, 55(2001), [Palmieri 2001] Palmieri, Paolo, The Obscurity of the Equimultiples: Clavius and Galileo s Foundational Studies of Euclid s Theory of Proportions, Archive for History of Exact Sciences, 55(2001), pp [Pourciau ] Pourciau, Bruce, Newton and the Notion of Limit, Historia Mathematica, 28(2001), pp $2001\mathrm{a}$ [Pourciau $2001\mathrm{b}$ ] [Rashed 1999] Pourciau, Bruce, The Integrability of Ovals: Newton s Lemma 28 and Its Counterexamples, Archive for History of Exact Sciences, 55(2001), pp Rashed, Roshdi, Pierre Fermat et les d\ ebuts modernes de l analyse diophantienne, Historia Scientiarum, 9(1999), pp 3-16 [Schneider 2000] Schneider, Ivo, Der Einfluss der griechischen Mathematik auf Inhalt und Entwicklung der mathematischen Produktion deutscher Rechenmeister im 16 und 17 Jahrhundert, Berichte zur Wissenschaflsgeschichte, 23(2000), S [Stedall $2000\mathrm{a}$ ] Stedall, Jacqueline Anne, Ariadne s Thread: The Life and Times of Oughtred s $C_{/}lavis$, Annals of Science, 57(2000), pp [Stedall $2000\mathrm{b}$ ] Stedall, Jacqueline Anne, $\mathrm{r}\mathrm{o}\mathrm{b} [Stedall 2001] Glories: The Posthumous Misfortunes of Thomas Harriot and His Algebra, Archive for History of Exact Sciences, 54(2000), pp Stedall, Jacqueline Anne, Of Our Own Nation: John Waffis s Account of Mathematical Learning in Medieval England, Historia Mathematica, 28(2001), pp

7 et $\star 20$ \rightarrow,, \rightarrow technical, philosophical,,, $arrow$ $\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{y}$ Scholz [ al 1999], [James et al 1999], [Scholz et al 2001], [Hendricks et al 2000] \rightarrow 1910, $\sim 20$ [Hawkins 2000]\rightarrow 1925\sim 6 (,,, ) [Callender and Weingard 2000], [James et al 1999], [Ullrich 2000]\rightarrow $\vdash$, 23 ( ) [Callender and Weingard 2000] Callender, Craig and Weingard, Robert, Topology Change and the Unity of Space, Studies in History and Philosophy of Modern Physics, 31 (2000), pp [Ferraro 1999] [Fisch 1999] Ferraro, Giovanni, The First Modern Definition of the Sum of adivergent Series: An Aspect of the Rise of 20th Century Mathematics, Archive for History of Etact Sciences, 54(1999), pp Fisch, Menachem, The Making of Peacock s Treatise on Algebm: ACase of Creative Indecision, Aoehive for History of Exact Sciences, 54(1999), pp [Gluchoff and Hartmann 2000] Gluchoff, Alan and Hartmann, Frederick, On a Much Underestimated Paper of Alexander, Archive for History of Exact Sciences, 55(2000), pp 1-41 [Grattan-Guinness 2000] Grattan-Guinness, Ivor, The Search for Mathematical Roots $\mathit{1}\mathit{8}7\theta- \mathit{1}\mathit{9}\mathit{4}\theta$:logics, Set Theories, and the Foundatiorgs of Mathematics $fmm$ Cantor through Russell to Gidel(Princeton, Oxford: Princeton University Press, 2000) [Gray et al 1999]The Symbolic $\mathit{1}\mathit{8}\mathit{9}\theta- Universe: Geometry and Physics Jeremy Gray(Oxford etc : Oxford University Press, 1999) \mathit{1}\mathit{9}s\theta$, edited by

8 19 [Gray 2000] $C_{/}hallenge(\mathrm{O}\mathrm{x}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{d}$ Gray, Jeremy, The Hdbert etc :Oxford University Press, 2000) [Hawkins 2000] Hawkins, Thomas, Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics (New York, etc :Springer Verlag, 2000) [James et al 1999] History of Topology, edited by Ioan Mackenzie James(Amsterdam etc :North-Holland, 1999) [Radu 2000] Radu, Mircea, Justus Grassmann s Contributions to the Foundations of Mathematics: Mathematical and Philosophical Aspects, Historia Mathematica, 27(2000), pp 4-35 [Scholz et al 2001] Hermann Weyl s Raum-Zeit-Materie and a General Introduction to His Scientific Work, edited by Erhard Scholz(Basel, Boston, Berlin: Birkhiuser Verlag, 2001) [Seneta et al 2001] Seneta, Eugene, Parshall, Karen Hunger and Jongmans, Franqois, Nineteenth-Century Developments in Geometric Probability: J J Sylvester, M W Crofton, J -E Barbier and J Bertrand, Archive for History of Exact Sciences, 55(2001), pp [Ullrich 2000] Ullrich, Peter, The Poincar\ e-volterra Theorem: From Hyperelliptic Integrals to Manifolds with Countable Topology, Archive for History of Exact Sciences, 54(2000), pp [van Dalen 1999] van Dalen, Dirk, Mystic, $C_{\mathrm{J}}eometer$, and Intuitionist: The Life of $L$ E J Brouwer, Volume 1The Dawning Revolution(Oxford: Clarendon Press, 1999) [ 2001] (, 2001 ) 4Social Context (Grabiner, Judith V, Is Mathematical Truth Time-Dependent?, American Mathematical Monthly, 81 (1974), pp ) ( [, ) \rightarrow

$$\mathrm{p}\mathrm{p}$ \mathrm{g}\varpi \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{y}$ versus 20, ( ),, [Craik 1999], [Craik 2000], [Crilly 1999], [Goldstein 2000]\rightarrow (, ), (19 ),,$

9 $\mathrm{p}\mathrm{p}$ \mathrm{g}\varpi \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{y}$ versus 20, ( ),, [Craik 1999], [Craik 2000], [Crilly 1999], [Goldstein 2000]\rightarrow (, ), (19 ),, [Beckers 1999], [Beckers 2000], [Beckers 2001]\rightarrow 19 [Remmert1999] \rightarrow, yj [Vucinich 1999], [Vucinich2000]\rightarrow J (,, ), ( ) [ 2001]\rightarrow 3(Social Context ) [Beckers 1999] Beckers, Danny J, Lagrange in the Netherlands: Dutch Attempts to Obtain Rigor in Calculus, , Historia Mathematica, 26(1999), $ $ [Beckers 2000] Beckers, Danny J, Positive Thinking: Conceptions of Negative Quantities in the Netherlands and the Reoeption of Lacroix s Algebra Textbook, Revue $d$ histoire des math\ ematiques, $6(2000)$, pp [Beckers 2001] Beckers, Danny J, Untiring Labor Overcomes All! : The History of the Dutch Mathematical Society in Comparison to Its Various Counterparts in Europe, Historia Mathematica, 28(2001), pp [Craik 1999] Craik, Alex D D, Calculus and Analysis in Early $19\mathrm{t}\mathrm{h}$-Century Britain: The Work of William Wallace, Historia Mathematica, 26(1999), pp [Craik $ 2000] Craik, Alex D D, Analysis in Early $19\mathrm{t}\mathrm{h}$-Century Scotland: John Leslie, William Wallace, and Thomas Carlyle, Historia Mathemaiica, 27(2000), pp

10 21 [Crilly 1999] Crilly, Tony, Arthur Cayley as Sadleirian Professor: AGlimpse of Mathematics Teaching at $19\mathrm{t}\mathrm{h}$-Century Cambridge, Historia Mathematica, 26(1999), pp [Goldstein 2000] Goldstein, Joel A, A Matter of Great Magnitude: The Conflict over Arithmetization in 16th-, 17th-, and $18\mathrm{t}\mathrm{h}$-Century English Editions of Euclid s Elements Book Ithrough Historia Mathematica, $\mathrm{v}\mathrm{i}( ),$ 27(2000), pp [Landry-Deron 2001] Landry-Deron, Isabelle, Les Math\ ematiciens $\mathrm{e}\mathrm{n}\mathrm{v}\mathrm{o}\mathrm{y}\acute{\mathrm{e}}_{j}\mathrm{s}$ en Chine par Louis XIV en 1685, Archive for History of Exact Sciences, 55(2001), $\mathrm{p}\mathrm{p}$ [Martini 1999] Martini, Laura, The First Lectures in Italy on Galois Theory: Bologna, Historia Mathematica, 26(1999), pp [Remmert 1999] Remmert, Volker R, Mathematicians at War Power Struggles in Nazi Germany s Mathematical Community: Gustav Doetsch and Wilhelm S\"uss, Revue histoire des math\ ematiques, $5(1999),$ $7-59$ $d$ $\mathrm{p}\mathrm{p}$ [Ribeiro Saraiva 2000] Ribeiro Saraiva, Luis M, A Survey of Portuguese Mathematics in the Nineteenth Century, Centaurus, 42(2000), pp [Vucinich 1999] Vucinich, Alexander, Mathematics and Dialectics in the Soviet Union: The Pre-Stalin Period, Historia Mathematica, 26(1999), pp [Vucinich 2000] Vucinich, Alexander, Soviet Mathematics and Dialectics in the Stalin Era, Historia Mathematica, 27(2000), pp , [Pourciau 2000] \rightarrow {? Gilles, Revolutions in Mathematics(Oxford: Clarendon Press, 1992) \rightarrow [ 2000]\rightarrow (,, 17-18,, )

11 $\text{ }$ 22 4( ), [Bouveresse 2001] Bouveresse, Jacques, Math\ ematiques et logique chez Leibniz, Revue $d$ histoire des sciences, 54(2001), pp [Hendricks et al 2000] Proof Theory: History and Philosophical Significance, edited by Vincent F Hendricks, Stig Andur Pedersen and Klaus Frovin $\mathrm{j}\emptyset \mathrm{r}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{n}$(dordrecht, Boston, London:Kluwer Academic Publishers, 2000) [Glas 2000] Glas, Eduard, Model-Based $\mathrm{d}\mathrm{i}\mathrm{s}\omega \mathrm{v}\mathrm{e}\mathrm{r}\mathrm{y}$ Reasoning and Mathematical : The Case of Felix Klein, Studies in History and Philosophy of Science, 31 (2000), pp [Grosholz and Breger 2000] The Growth of Mathematical Knowledge, edited by Emily Grosholz and Herbert Breger(Dordrecht, Boston, London: Kluwer Academic Publishers, 2000) [Pourciau 2000] Pourciau, Bruce, Intuitionism as a(failed) Kuhnian Revolution in Mathematics, Studies in History and Philosophy of Science, 31(2000), pp [ 2000] ( , 2000 ) ) (

特別寄稿 1931 Kurt Gödel, inexhaustibility Jean Cavaillès,

特別寄稿 1931 Kurt Gödel, inexhaustibility Jean Cavaillès, Title < 特別寄稿 > 数学の無尽蔵性と二つの哲学 -- カヴァイエスとゲーデル -- Author(s) 中村, 大介 Citation 哲学論叢 (2016), 43: 27-39 Issue Date 2016 URL http://hdl.handle.net/2433/219150 Right Type Departmental Bulletin Paper Textversion