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href="/nlab/show/foundations">Structural Foundations</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/logic">logic</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/internal+language">internal language</a></li> <li><a class="existingWikiWord" href="/nlab/show/classical+mathematics">classical mathematics</a></li> <li><a class="existingWikiWord" href="/nlab/show/constructive+mathematics">constructive mathematics</a></li> <li><a class="existingWikiWord" href="/nlab/show/predicative+mathematics">predicative mathematics</a></li> <li><a href="http://ncatlab.org/nlab/list/foundational+axiom">category:foundational axiom</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/set+theory">set theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/structural+set+theory">structural set theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/category+theory">category theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Categories+and+Sheaves">Categories and Sheaves</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topos+theory">topos theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Sheaves+in+Geometry+and+Logic">Sheaves in Geometry and Logic</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/higher+category+theory">higher category theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/higher+topos+theory">higher topos theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Higher+Topos+Theory">(∞,1)-topos theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/models+for+%E2%88%9E-stack+%28%E2%88%9E%2C1%29-toposes">models for ∞-stack (∞,1)-toposes</a></li> <li><a class="existingWikiWord" href="/nlab/show/cohomology">cohomology</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/homotopy+theory">homotopy theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/stable+homotopy+theory">stable homotopy theory</a></li> <li><a class="existingWikiWord" href="/nlab/show/rational+homotopy+theory">rational homotopy theory</a></li> </ul> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topology+and+geometry">Topology and Geometry</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/geometry">geometry</a> (general list), <a class="existingWikiWord" href="/nlab/show/topology">topology</a> (general list)</li> <li><a class="existingWikiWord" href="/nlab/show/general+topology">general topology</a></li> <li><a class="existingWikiWord" href="/nlab/show/differential+topology">differential topology</a></li> <li><a class="existingWikiWord" href="/nlab/show/differential+geometry">differential geometry</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/synthetic+differential+geometry">synthetic differential geometry</a></li> <li><a class="existingWikiWord" href="/nlab/show/symplectic+geometry">symplectic geometry</a></li> </ul> </li> <li><a class="existingWikiWord" href="/nlab/show/algebraic+geometry">algebraic geometry</a></li> <li><a class="existingWikiWord" href="/nlab/show/noncommutative+algebraic+geometry">noncommutative algebraic geometry</a></li> <li><a class="existingWikiWord" href="/nlab/show/noncommutative+geometry">noncommutative geometry</a> (general flavour)</li> <li><a class="existingWikiWord" href="/nlab/show/higher+geometry">higher geometry</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/algebra">Algebra</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/universal+algebra">universal algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/higher+algebra">higher algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/homological+algebra">homological algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/group+theory">group theory</a>, <a class="existingWikiWord" href="/nlab/show/ring+theory">ring theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/representation+theory">representation theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/algebraic+approaches+to+differential+calculus">algebraic approaches to differential calculus</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/counterexamples+in+algebra">counterexamples in algebra</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/analysis">analysis</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/nonstandard+analysis">nonstandard analysis</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/functional+analysis">functional analysis</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/operator+algebras">operator algebras</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Fourier+transform">Fourier transform</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Lie+theory">Lie theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/infinity-Lie+theory+-+contents">higher Lie theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/probability+theory">probability theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/discrete+mathematics">discrete mathematics</a></p> </li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#overview'>Overview</a></li> <li><a href='#spaces_categories_topology_sheaves_topoi_cohomology_'>Spaces, categories, topology, sheaves, topoi, cohomology, …</a></li> <li><a href='#general_history_of_mathematics'>General history of mathematics</a></li> <li><a href='#wiki_collection_and_encyclopaedia_articles'>Wiki, collection and encyclopaedia articles</a></li> <li><a href='#researchers_and_institutes_for_history_of_mathematics'>Researchers and institutes for history of mathematics</a></li> <li><a href='#lab_entries_with_historical_information'><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>Lab entries with historical information</a></li> <li><a href='#other_literature'>Other literature</a></li> </ul> </div> <h2 id="overview">Overview</h2> <p>For the moment, we list here only a few works in the history of mathematics: some with a focus on fields particularly emphasised in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>Lab, and some general. <a href="https://en.wikipedia.org/wiki/History_of_mathematics">Wikipedia</a> has a nice list of general works.</p> <h2 id="spaces_categories_topology_sheaves_topoi_cohomology_">Spaces, categories, topology, sheaves, topoi, cohomology, …</h2> <ul> <li>Mathieu Bélanger. <em>Grothendieck et les topos : rupture et continuité dans les modes d’analyse du concept d’espace topologique</em>, thesis, Université de Montréal 2010 <a href="https://papyrus.bib.umontreal.ca/jspui/bitstream/1866/4759/2/Belanger_Mathieu_2010_these.pdf">pdf</a></li> <li><a class="existingWikiWord" href="/nlab/show/Pierre+Cartier">Pierre Cartier</a>, <em>A mad day’s work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry</em>, Bull. Amer. Math. Soc. <strong>38</strong> (2001), 389-408, <a href="http://www.ams.org/bull/2001-38-04/S0273-0979-01-00913-2/S0273-0979-01-00913-2.pdf">pdf</a></li> <li>Ralf Krömer, <em>Tool and object: A history and philosophy of category theory</em>, Birkhäuser 2007</li> <li><a class="existingWikiWord" href="/nlab/show/John+Bell">John Bell</a>, <em>The development of categorical logic</em> (<a href="http://publish.uwo.ca/~jbell/catlogprime.pdf">pdf</a>)</li> <li>Jean-Pierre Marquis, Gonzalo E. Reyes, <em>The history of categorical logic 1963–1977</em>, 111 pp. <a href="https://www.webdepot.umontreal.ca/Usagers/marquisj/MonDepotPublic/HistofCatLog.pdf">pdf</a></li> </ul> <h2 id="general_history_of_mathematics">General history of mathematics</h2> <ul> <li>C. B. Boyer, <em>A history of mathematics</em>, 2nd ed. rev. by Uta C. Merzbach. New York: Wiley, 1989</li> <li><a class="existingWikiWord" href="/nlab/show/Felix+Klein">Felix Klein</a>, <em>The development of mathematics in 19th century</em></li> <li>Julian Lowell Coolidge, <em>A history of geometrical methods</em>, 1940, Dover Phoenix Editions, Oxford University Press 1940.</li> <li>J. Gray, <em>The real and the complex: a history of analysis in the 19th century</em>, Springer Undergraduate Mathematics Series</li> <li>Dirk Jan Struik, <em>A concise history of mathematics</em></li> <li><a class="existingWikiWord" href="/nlab/show/Umberto+Bottazzini">Umberto Bottazzini</a>, <em>Il flauto di Hilbert: Storia della matematica</em>, UTET Università, 473pp.; <em>The higher calculus: A history of real and complex analysis from Euler to Weierstrass</em>, Springer 1986</li> <li>B. L. van der Waerden, <em>Geometry and algebra in ancient civilizations</em>, Springer 1983 <a href="https://books.google.hr/books?id=-pTzCAAAQBAJ">gBooks</a></li> <li><a class="existingWikiWord" href="/nlab/show/Alexandre+Borovik">Alexandre Borovik</a>, M. G. Katz, <em>Who gave you the Cauchy–Weierstrass tale? The dual history of rigorous calculus</em>, Found. Sci. <strong>17</strong>, 245–276 (2012) <a href="https://doi.org/10.1007/s10699-011-9235-x">doi</a></li> </ul> <h2 id="wiki_collection_and_encyclopaedia_articles">Wiki, collection and encyclopaedia articles</h2> <ul> <li>The MacTutor History of Mathematics archive: <a href="http://www.gap-system.org/~history">html</a></li> <li>Stanford Encyclopaedia of Philosophy <a href="http://plato.stanford.edu">online</a>, <a href="http://plato.stanford.edu/contents.html">contents</a></li> <li>wikipedia <a href="http://en.wikipedia.org/wiki/History_of_mathematics">history of mathematics</a></li> </ul> <h2 id="researchers_and_institutes_for_history_of_mathematics">Researchers and institutes for history of mathematics</h2> <ul> <li><a href="http://hsm.institut.math.jussieu.fr">hsm</a> at Jussieu</li> </ul> <h2 id="lab_entries_with_historical_information"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>Lab entries with historical information</h2> <ul> <li><a class="existingWikiWord" href="/nlab/show/history+of+cohomology+with+local+coefficients">history of cohomology with local coefficients</a></li> <li><a class="existingWikiWord" href="/nlab/show/historical+notes+on+characteristic+classes">historical notes on characteristic classes</a></li> <li><a class="existingWikiWord" href="/nlab/show/geometry+of+19th+century">geometry of 19th century</a>, <a class="existingWikiWord" href="/nlab/show/Erlangen+program">Erlangen program</a></li> <li><a class="existingWikiWord" href="/nlab/show/%C4%8Cech+methods">Čech methods</a></li> <li><a class="existingWikiWord" href="/nlab/show/philosophy">philosophy</a></li> <li>lots of entries on individuals, including for some of the most influential mathematicians in history, e.g. <a class="existingWikiWord" href="/nlab/show/Alexander+Grothendieck">Alexander Grothendieck</a>, <a class="existingWikiWord" href="/nlab/show/Jacob+Lurie">Jacob Lurie</a>, <a class="existingWikiWord" href="/nlab/show/Maxim+Kontsevich">Maxim Kontsevich</a>, <a class="existingWikiWord" href="/nlab/show/Saunders+MacLane">Saunders MacLane</a>, <a class="existingWikiWord" href="/nlab/show/Bourbaki">Bourbaki</a>, <a class="existingWikiWord" href="/nlab/show/Alfred+Tarski">Alfred Tarski</a> etc.</li> <li><a class="existingWikiWord" href="/nlab/show/list+of+theses+in+category+theory">list of theses in category theory</a>, <a class="existingWikiWord" href="/nlab/show/list+of+lost+manuscripts+in+category+theory">list of lost manuscripts in category theory</a></li> </ul> <h2 id="other_literature">Other literature</h2> <ul> <li>G.A. Miller, <em>Felix Klein and the history of modern mathematics</em>, PNAS 13, 1927, 611-613</li> </ul> <p>The relation of the techniques of the pioneers of infinitesimal calculus and the modern <a class="existingWikiWord" href="/nlab/show/nonstandard+analysis">nonstandard analysis</a> is discussed in</p> <ul> <li>Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, David Sherry, <em>Toward a history of mathematics focused on procedures</em>, <a href="http://arxiv.org/abs/1609.04531">arxiv/1609.04531</a></li> </ul> <p>A collection of articles on XX-century mathematics is in</p> <ul> <li> <p><span class="newWikiWord">Michele Audin<a href="/nlab/new/Michele+Audin">?</a></span> (editor), <em><a class="existingWikiWord" href="/nlab/show/Mat%C3%A9riaux+pour+l%E2%80%99histoire+des+math%C3%A9matiques+au+XXe+si%C3%A8cle">Matériaux pour l’histoire des mathématiques au XXe siècle</a></em> - Actes du colloque à la mémoire de Jean Dieudonné (Nice 1996) Séminaires & Congrès. Numèro 3. Paris (Socièté Mathématique de France). 1998. 283 pp.</p> </li> <li> <p>Glenn Shafer, Vladimir Vovk, <em>The sources of Kolmogorov’s Grundbegriffe</em>, Statistical Science 21(1) <a href="https://dx.doi.org/10.1214/088342305000000467">doi</a> <a href="http://arxiv.org/abs/math/0606533">arXiv:math/0606533</a></p> </li> <li> <p>Israel Kleiner, <em>From numbers to rings: The early history of ring theory</em>, Elem. Math. <strong>53</strong> (1998) 18–35 <a href="https://ems.press/content/serial-article-files/45056">pdf</a></p> </li> </ul> </body></html> </div> <div class="revisedby"> <p> Last revised on September 24, 2024 at 21:49:42. 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