Celebratio Mathematica

Saunders Mac Lane

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Saunders Mac Lane (1909–2005): His mathematical life and philosophical works

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S. MacLane: Abgekürzte Be­weise im Lo­gikkalkül [Ab­bre­vi­ated proofs in the lo­gic­al cal­cu­lus]. Ph.D. thesis, Georg-Au­gust-Uni­versität Göt­tin­gen (Göt­tin­gen), 1934. Ad­vised by P. Bernays and H. Weyl. An ab­stract was pub­lished (in Eng­lish) in Bull. Am. Math. Soc. 40:1 (1934). phdthesis

S. MacLane: “A lo­gic­al ana­lys­is of math­em­at­ic­al struc­ture,” Mon­ist 45 : 1 (January 1935), pp. 118–​130. JFM 61.​0050.​01 Zbl 0011.​00102 article

S. Mac Lane: “Re­view: Katudi Ono, ‘Lo­gis­che un­ter­suchun­gen über die grundla­gen der math­em­atik’ Journ­al of the Fac­ulty of Sci­ence, Im­per­i­al Uni­versity of Tokyo, I, 3:7 (1938) 329–389,” The Journ­al of Sym­bol­ic Lo­gic 4 : 2 (1939), pp. 89–​90. article

S. Mac Lane: “Re­view: Al­fred Tarski, ‘Der aus­sagen­kalkul und die to­po­lo­gie’, Fun­da­menta Math­em­at­icae 31 (1938), 103–134,” The Journ­al of Sym­bol­ic Lo­gic 4 (1939), pp. 26–​27. article

S. Mac Lane: “Sym­bol­ic lo­gic,” Am. Math. Mon. 46 : 5 (1939), pp. 289–​296. Zbl 0021.​09703 article

S. Mac Lane: “Re­view of M. H. Stone, ‘Ap­plic­a­tions of the the­ory of Boolean rings to gen­er­al to­po­logy’ Trans. Amer. Math. Soc. 41:3 (1937), 375–481,” Journ­al of Sym­bol­ic Lo­gic 4 (1939), pp. 88–​89. article

S. Mac Lane: “Re­view: J.-L. Destouches, ‘Es­sai sur la forme générale des théories physiques’, In­sti­tutul de Arte Grafice ‘Ar­dealul’, Cluj, Ro­mania, 1938,” The Journ­al of Sym­bol­ic Lo­gic 5 : 1 (1940), pp. 23. article

S. Mac Lane: “Re­view: F. Gon­seth, ‘Philo­soph­ie mathématique,’ Ac­tu­alités Sci­en­ti­fiques et In­dus­tri­elles 837, Her­mann, Par­is, 1939,” The Journ­al of Sym­bol­ic Lo­gic 5 : 2 (1940), pp. 77–​78. article

G. Birk­hoff and S. Mac Lane: A sur­vey of mod­ern al­gebra. Mac­mil­lan (New York), 1941. The fiftieth an­niversary of this book was com­mem­or­ated in an art­icle in Math. In­tell. 14:1 (1992). MR 0005093 Zbl 0061.​04802 book

S. Ei­len­berg and S. MacLane: “Nat­ur­al iso­morph­isms in group the­ory,” Proc. Natl. Acad. Sci. U.S.A. 28 : 12 (December 1942), pp. 537–​543. See also art­icle in Gaz. Mat. 29:109–112 (1968). MR 0007421 Zbl 0061.​09203 article

S. Mac Lane: “Re­view: F. Gon­seth, ‘Les en­tre­tiens de Zurich sur les fonde­ments et la méthode des sci­ences mathématiques, 6–9 décembre 1938’ S. A. Leemann frères & Cie., Zurich, 1941,” The Journ­al of Sym­bol­ic Lo­gic 7 : 1 (1942), pp. 35–​37. article

S. Ei­len­berg and S. MacLane: “Gen­er­al the­ory of nat­ur­al equi­val­ences,” Trans. Am. Math. Soc. 58 : 2 (September 1945), pp. 231–​294. MR 0013131 Zbl 0061.​09204 article

S. MacLane: “Book re­view: The de­vel­op­ment of math­em­at­ics,” Am. Math. Mon 53 : 7 (August–September 1946), pp. 389–​390. Book by E. T. Bell (2nd ed., Mc­Graw-Hill, 1945). MR 1526489 article

S. MacLane: “Groups, cat­egor­ies and du­al­ity,” Proc. Natl. Acad. Sci. U.S.A. 34 : 6 (June 1948), pp. 263–​267. MR 0025464 Zbl 0031.​24702 article

S. MacLane: “Of course and courses,” Am. Math. Mon. 61 : 3 (March 1954), pp. 151–​157. MR 1528667 article

S. Mac Lane and G. Birk­hoff: Al­gebra. Mac­mil­lan (New York), 1967. MR 0214415 Zbl 0153.​32401 book

S. Mac Lane: “To­po­logy and lo­gic as a source of al­gebra,” Bull. Am. Math. Soc. 82 : 1 (January 1976), pp. 1–​40. Re­tir­ing Pres­id­en­tial ad­dress. MR 0414648 Zbl 0324.​55001 article

S. Mac Lane: “Ori­gins of the co­homo­logy of groups,” En­sei­gn. Math. (2) 24 : 1–​2 (1978), pp. 1–​29. MR 497280 Zbl 0379.​18012 article

S. Mac Lane: Se­lec­ted pa­pers. Edi­ted by I. Ka­plansky. Spring­er (New York), 1979. With con­tri­bu­tions by Al­fred Put­nam, Ro­ger Lyn­don, Ka­plansky, Samuel Ei­len­berg and Max Kelly. MR 544841 Zbl 0459.​01024 book

S. Mac Lane: “Math­em­at­ics,” pp. 104–​110 in “Sci­ence” Centen­ni­al, published as Sci­ence 209 : 4452. Issue edi­ted by P. H. Abel­son and R. Kul­stad. July 1980. MR 576525 Zbl 1225.​00002 incollection

S. Mac Lane: “His­tory of ab­stract al­gebra: Ori­gin, rise, and de­cline of a move­ment,” pp. 3–​35 in Amer­ic­an math­em­at­ic­al her­it­age: Al­gebra and ap­plied math­em­at­ics (El Paso, TX, Novem­ber 1975 and Ar­ling­ton, TX, Oc­to­ber 1976). Edi­ted by J. D. Tar­wa­ter, J. T. White, C. Hall, and M. E. Moore. Math­em­at­ics Series 13. Texas Tech Press (Lub­bock, TX), 1981. MR 641700 incollection

S. Mac Lane: “Math­em­at­ic­al mod­els: A sketch for the philo­sophy of math­em­at­ics,” Am. Math. Mon. 88 : 7 (August–September 1981), pp. 462–​472. MR 628015 Zbl 0468.​00019 article

S. Mac Lane: Math­em­at­ics, form and func­tion. Spring­er (New York), 1986. MR 816347 Zbl 0675.​00001 book

S. Mac Lane: “Con­cepts and cat­egor­ies in per­spect­ive,” pp. 323–​365 in A cen­tury of math­em­at­ics in Amer­ica, part I. Edi­ted by P. Duren, R. A. As­key, and U. C. Merzbach. His­tory of Math­em­at­ics 1. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1988. An ad­dendum to this art­icle was pub­lished in His­tory of Math­em­at­ics, part III (1989). MR 1003181 Zbl 0665.​01002 incollection

S. Mac Lane: “Group ex­ten­sions for 45 years,” Math. In­tell. 10 : 2 (1988), pp. 29–​35. MR 932159 Zbl 0657.​01011 article

S. Mac Lane: “Ad­dendum: ‘Con­cepts and cat­egor­ies in per­spect­ive’,” pp. 439–​441 in A cen­tury of math­em­at­ics in Amer­ica, part III. Edi­ted by P. Duren, R. A. As­key, H. M. Ed­wards, and U. C. Merzbach. His­tory of Math­em­at­ics 3. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1989. Ad­dendum to an art­icle in His­tory of Math­em­at­ics, part I (1988). MR 1025356 incollection

G. L. Al­ex­an­der­son and S. Mac Lane: “A con­ver­sa­tion with Saun­ders Mac Lane,” Col­lege Math. J. 20 : 1 (1989), pp. 2–​25. MR 979840 Zbl 0995.​01520 article

S. Mac Lane and I. Mo­er­dijk: Sheaves in geo­metry and lo­gic: A first in­tro­duc­tion to topos the­ory. Uni­versitext. Spring­er (New York), 1992. A cor­rec­ted re­print was pub­lished in 1994. Zbl 0822.​18001 book

S. Mac Lane: “A mat­ter of tem­pera­ment,” The New York Re­view of Books 42 : 15 (Oct. 5 1995), pp. 56. Let­ter, with reply by Free­man J. Dys­on. article

S. Mac Lane: “Math­em­at­ics at Göt­tin­gen un­der the Nazis,” No­tices Am. Math. Soc. 42 : 10 (1995), pp. 1134–​1138. MR 1350011 Zbl 1042.​01536 article

S. Mac Lane: “Steph­en Cole Kleene: A re­min­is­cence,” Ann. Pure Ap­pl. Lo­gic 81 : 1–​3 (1996), pp. 3–​7. MR 1407050 Zbl 0855.​01030 article

S. Mac Lane: “Struc­ture in math­em­at­ics,” pp. 174–​183 in Math­em­at­ic­al struc­tur­al­ism, published as Philos. Math. (3) 4 : 2. Issue edi­ted by S. Sha­piro. 1996. MR 1397752 Zbl 0905.​18001 incollection

S. Mac Lane: “Van der Waer­den’s ‘Mod­ern al­gebra’,” No­tices Am. Math. Soc. 44 : 3 (1997), pp. 321–​322. MR 1435205 Zbl 1036.​01007 article

S. Mac Lane: “Gar­rett Birk­hoff and the ‘Sur­vey of mod­ern al­gebra’,” No­tices Am. Math. Soc. 44 : 11 (1997), pp. 1438–​1439. MR 1488571 Zbl 0908.​01019 article

S. Mac Lane: “Des­pite phys­i­cists, proof is es­sen­tial in math­em­at­ics,” pp. 147–​154 in Proof and pro­gress in math­em­at­ics (Bo­ston, MA, 12 Feb­ru­ary 1996), published as Syn­these 111 : 2. Issue edi­ted by A. Kanamori. 1997. MR 1465267 Zbl 1052.​00512 incollection

J. Green, J. LaDuke, S. Mac Lane, and U. C. Merzbach: “Mina Spiegel Rees (1902–1997),” No­tices Am. Math. Soc. 45 : 7 (1998), pp. 866–​873. MR 1633722 Zbl 0973.​01070 article

S. Mac Lane: Cat­egor­ies for the work­ing math­em­atician, 2nd edition. Gradu­ate Texts in Math­em­at­ics 5. Spring­er (New York), 1998. Re­pub­lic­a­tion of 1971 ori­gin­al. MR 1712872 Zbl 0906.​18001 book

S. Mac Lane: Saun­ders Mac Lane: A math­em­at­ic­al auto­bi­o­graphy. A K Peters (Welles­ley, MA), 2005. With a pre­face by Dav­id Eis­en­bud. MR 2141000 Zbl 1089.​01010 book