# Saunders Mac Lane

American mathematician

## Saunders Mac Lane's AcademicInfluence.com Rankings

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Mathematics

## Saunders Mac Lane's Degrees

- PhD Mathematics University of Chicago
- Masters Mathematics University of Chicago

## Why Is Saunders Mac Lane Influential?

(Suggest an Edit or Addition)According to Wikipedia, Saunders Mac Lane was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville. He was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space. He was the oldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor at Rice University and Purdue University. Another sister died as a baby. His father and grandfather were both ministers; his grandfather had been a Presbyterian, but was kicked out of the church for believing in evolution, and his father was a Congregationalist. His mother, Winifred, studied at Mount Holyoke College and taught English, Latin, and mathematics.

## Saunders Mac Lane's Published Works

### Published Works

- Categories for the Working Mathematician (1971) (4045)
- Categories for the working mathematician (1971) (2068)
- A survey of modern algebra (1942) (1246)
- Sheaves In Geometry And Logic (1992) (1012)
- General theory of natural equivalences (1945) (663)
- Natural Associativity and Commutativity (1963) (450)
- On the Groups H(Π, n), I (1953) (396)
- On the Groups H(Π, n), II: Methods of Computation (1954) (326)
- Mathematics, Form and Function (1985) (314)
- Cohomology Theory in Abstract Groups. III (1947) (298)
- Coherence in closed categories (1971) (255)
- Categorical Algebra (2007) (243)
- On the 3-Type of a Complex. (1950) (213)
- A construction for absolute values in polynomial rings (1936) (194)
- Cohomology Theory in Abstract Groups. II: Group Extensions with a non-Abelian Kernel (1947) (191)
- Natural Associativity and Commutativity (1979) (181)
- Relations Between Homology and Homotopy Groups of Spaces. II (1945) (173)
- Duality for groups (1950) (168)
- A structural characterization of planar combinatorial graphs (1937) (167)
- A combinatorial condition for planar graphs (1937) (158)
- Reports of the Midwest Category Seminar I (1967) (145)
- Coherence for bicategories and indexed categories (1985) (128)
- Group Extensions and Homology (1942) (120)
- Some Interpretations of Abstract Linear Dependence in Terms of Projective Geometry (1936) (107)
- Category Theory, Homology Theory and their Applications II (1969) (94)
- Homology of spaces with operators. II (1947) (84)
- A construction for prime ideals as absolute values of an algebraic field (1936) (80)
- On the Groups H(Π, n), III: Operations and Obstructions (1954) (79)
- A lattice formulation for transcendence degrees and $p$-bases (1938) (77)
- The universality of formal power series fields (1939) (74)
- Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
- Extensions and obstructions for rings (1958) (68)
- Groups, Categories and Duality. (1948) (68)
- Mathematics: Form and Function. (1987) (63)
- Natural Isomorphisms in Group Theory. (1942) (62)
- Cohomology theory of abelian groups and homotopy theory I. (1950) (61)
- Relations between Homology and Homotopy Groups. (1943) (60)
- Proceedings of the Conference on Categorical Algebra (1966) (58)
- Zero-Dimensional Branches of Rank One on Algebraic Varieties (1939) (58)
- Cohomology and Galois theory. I. Normality of algebras and Teichmüller’s cocycle (1948) (48)
- A brief survey of modern algebra (1953) (45)
- COHOMOLOGY THEORY OF ABELIAN GROUPS (2010) (45)
- Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
- AN ALGEBRA OF ADDITIVE RELATIONS. (1961) (42)
- Coherence in categories (1972) (42)
- AN ALGEBRA OF ADDITIVE RELATIONS. (1961) (40)
- Subfields and Automorphism Groups of p-Adic Fields (1939) (39)
- One universe as a foundation for category theory (1969) (38)
- Determination of the Second Homology and Cohomology Groups of a Space by Means of Homotopy Invariants. (1946) (36)
- The national science board. (1986) (36)
- HOMOLOGY THEORIES FOR MULTIPLICATIVE SYSTEMS (1951) (36)
- Modular fields. I. Separating transcendence bases (1939) (35)
- Review: Henri Cartan and Samuel Eilenberg, Homological algebra (1956) (33)
- The Effect of end Losses on the Characteristics of Filaments of Tungsten and Other Materials (1930) (32)
- Mathematical Models: A Sketch for the Philosophy of Mathematics (1981) (31)
- Topology and logic as a source of algebra (1976) (30)
- Strategies for research. (1994) (28)
- The minimum number of generators for inseparable algebraic extensions (1940) (28)
- Association For Symbolic Logic (2000) (27)
- Algebraic cohomology groups and loops (1947) (27)
- Structure in Mathematics (1996) (27)
- The effect of rearing environment on sexual behavior of young beef bulls. (1983) (24)
- The collected works of J. Richard Büchi (1989) (22)
- The Protean Character of Mathematics (1992) (22)
- Sets, Topoi, and Internal Logic in Categories (1975) (20)
- Hamiltonian Mechanics and Geometry (1970) (20)
- The Uniqueness of the Power Series Representation of Certain Fields with Valuations (1938) (19)
- Cohomology Theory of Abelian Groups and Homotopy Theory II. (1950) (19)
- Applications of categorical algebra (1985) (18)
- A Logical Analysis of Mathematical Structure (1935) (18)
- Closed coherence for a natural transformation (1972) (18)
- Triple torsion products and multiple Künneth formulas (1960) (17)
- Cohomology Theory of Abelian Groups and Homotopy Theory III. (1951) (16)
- DESPITE PYHSICISTS, PROOF IS ESSENTIAL IN MATHEMATICS (1997) (16)
- The milgram bar construction as a tensor product of functors (1970) (16)
- A proof of the subgroup theorem for free products (1958) (16)
- The health of mathematics (1983) (15)
- Carnap on Logical Syntax (1938) (14)
- Is Mathias an Ontologist (1992) (14)
- Infinite Number Fields with Noether Ideal Theories (1939) (14)
- EFFECTS ON TISSUE CULTURES OF INTER-CELLULAR HORMONES FROM INJURED CELLS. (1937) (13)
- On The Homology Theory Of Abelian Groups (1955) (13)
- A conjecture of Ore on chains in partially ordered sets (1943) (13)
- Symmetry of algebras over a number field (1948) (13)
- The Schönemann-Eisenstein irreducibility criteria in terms of prime ideals (1938) (13)
- Some Recent Advances in Algebra (1939) (13)
- Foundations for categories and sets (1969) (12)
- Topology becomes algebraic with Vietoris and Noether (1986) (12)
- The future of universities. (1990) (12)
- Group extensions for 45 years (1988) (11)
- The development and prospects for category theory (1996) (11)
- Projective classes and acyclic models (1967) (10)
- A Late Return to a Thesis in Logic (1979) (10)
- Total reporting for scientific work. (1980) (9)
- Factor-sets of a group in its abstract unit group (1941) (9)
- Extending maps of plane Peano continua (1940) (9)
- IIASA and Modeling (1988) (9)
- Normal algebraic number fields (1941) (8)
- Categorical Foundations of the Protean Character of Mathematics (1997) (8)
- IIASA's Credibility (1988) (8)
- The homology products in (Π (1954) (8)
- The Influence of M. H. Stone on the Origins of Category Theory (1970) (7)
- Edwin Bidwell Wilson. (1973) (7)
- From Whole Numbers to Rational Numbers (1986) (7)
- Conceptual Mathematics: A First Introduction to Categories. By F. William Lawvere & Steven Schanuel (1997) (7)
- Steinitz field towers for modular fields (1939) (7)
- MATHEMATICAL LOGIC IS NEITHER FOUNDATION NOR PHILOSOPHY (1986) (7)
- Eilenberg-Mac Lane: Collected Works (1986) (6)
- Categorical topology and its relation to analysis, algebra and combinatorics : Prague, Czechoslovakia, 22-27 August 1988 (1989) (6)
- The Reasonable Effectiveness of Mathematical Reasoning (1990) (6)
- Infinite Cycles and Homologies. (1941) (6)
- The genesis of mathematical structures, as exemplified in the work of Charles Ehresmann (1980) (6)
- Jobs in the 1930s and the Views of George D. Birkhoff (1994) (6)
- Decker's sharper Künneth formula (1988) (5)
- Review: M. H. Stone, Topological Representations of Distributive Lattices and Brouwerian Logics (1938) (5)
- Opinion: Paradise Lost: The troubled government support of science (1989) (5)
- Samuel Eilenberg and Categories (2002) (5)
- Peer Review and the Structure of Science (1975) (5)
- The PNAS way back then (1997) (5)
- Metric Postulates for Plane Geometry (1959) (5)
- Note on the Relative Structure of p-Adic Fields (1940) (5)
- Saunders Mac Lane: A Mathematical Autobiography (2005) (5)
- PROOF, TRUTH, AND CONFUSION (1991) (4)
- The PNAS way back then. (1997) (4)
- The Work of Samuel Eilenberg in Topology (1976) (4)
- Steinitz Field Towers for Modular Fields (1939) (4)
- A Survey of Modem Algebra: The Fiftieth Anniversary of its Publication (1992) (4)
- Stephen Cole Kleene - a Reminiscence (1996) (4)
- Contrary Statements About Mathematics (2000) (4)
- Abstract Algebra Uses Homomorphisms (1996) (4)
- The Generation of Inseparable Fields. (1941) (4)
- Calculus Is a Disciplin... (1984) (4)
- Possible programs for categorists (1969) (4)
- Review: Alonzo Church, The Present Situation in the Foundation of Mathematics (1940) (4)
- A nonassociative method for associative algebras (1948) (4)
- The Lambda Calculus and Adjoint Functors (2001) (3)
- Group extensions by primary abelian groups (1960) (3)
- Cohomology Groups of Abelian Groups and Homotopy Theory IV. (1952) (3)
- Are we all just specialists (1986) (3)
- Group Extensions By Primary Abelian Groups (1960) (3)
- Normal Algebraic Number Fields. (1940) (3)
- E. the Impact of Modern Mathematics (1954) (3)
- MAA Studies in Mathematics, Volume 2, Studies in Modern Algebra. (1964) (3)
- A general Kummer theory for function fields (1942) (3)
- A formula for the direct product of crossed product algebras (1942) (2)
- A Construction for Absolute Values in Polynomial Rings (1979) (2)
- The origins of mathematical abstraction (1999) (2)
- Abstract Absolute Values Which Give New Irreducibility Criteria. (1935) (2)
- Samuel Eilenberg's work in category theory (1996) (2)
- What ranks for research doctoral programs (1996) (2)
- Of Course and Courses (1954) (2)
- Bornstein Benedykt. Geometrical logic. The structures of thought and space . Bibliotheca Universitatis Liberae Polonae, ser. B, no. 8 (31). Wolna Wszechnica Polska, Warsaw 1939, 114 pp. (1939) (2)
- The Future Role of the Federal Government in Mathematics (1967) (2)
- To the Greater Health of Mathematics (1988) (2)
- Diagnostic ophthalmology. (1997) (2)
- M. H. Stone. Topological representations of distributive lattices and Brouwerian logics. Časopis pro pěsiování matematiky a fysiky , vol. 67 (1937–1938), pp. 1–25. (1938) (2)
- Samuel Eilenberg ( 1913 – 1998 ) (1998) (2)
- THE SUMMER MEETING IN MADISON 1043 (2007) (1)
- Whose mathematical judgment? (1985) (1)
- Hosiasson-Lindenbaum Janina. On confirmation. The journal of symbolic logic, vol. 5 (1940), pp. 133–148. (1941) (1)
- SiC formation on Si3N4 (1995) (1)
- Scientific Exchanges with the Soviet Union (1980) (1)
- Symbolic Logic. (Scientific Books: Introduction to Logic) (1941) (1)
- Hilbert-Bernays on Proof-Theory (1935) (1)
- Review: Edward V. Huntington, Postulates for Assertion, Conjunction, Negation, and Equality (1937) (1)
- What ranks for research doctoral programs? (1996) (1)
- Structures in Categories (1978) (1)
- Can We Buy Quality in Science (1965) (1)
- The cohomology theory of a pair of groups (1961) (1)
- M. H. Stone. Applications of the theory of Boolean rings to general topology. Transactions of the American Mathematical Society , vol. 41 (1937). pp. 375–481. (1939) (1)
- Forms of Space (1986) (1)
- Types of Algebras (1995) (1)
- An unpublished reply. (1980) (1)
- The Travail of the University (1997) (1)
- Geometrical mechanics : lectures (1968) (1)
- Abstract Absolute Values Which Give New Irreducibility Criteria. (1935) (1)
- Sheaves of Sets (1994) (1)
- Circular a-21 reporting systems. (1981) (1)
- Note on some equations without affect (1936) (1)
- Review: Janina Hosiasson-Lindenbaum, On Confirmation (1941) (1)
- Fixed Points and the Extension of the Homeomorphisms of a Planar Graph (1938) (1)
- Review: E. Livenson, On the Realization of Boolean Algebras by Algebras of Sets (1940) (1)
- Algebra [Mac Lane, 1974] (1974) (1)
- Mathematics vs. Numerical Analysis. (1965) (1)
- Itô Makoto. Kakuritu-ron no kôri-taikei ni tuite (An axiom system for probability theory). Journal of the Mathematical Association of Japan for Secondary Education, vol. 20 (1938), pp. 1–9. (1940) (0)
- Journal of Algebra Algebra Editor-in-chief: Graham Higman Contents of Volume 70 (0)
- THE ALGEBRAIC MECHANISM OF FIBER SPACES (1961) (0)
- Book Review: Homological algebra (1999) (0)
- J. Richard Büchi’s Doctoral Students (1990) (0)
- Some major research departments of mathematics (1989) (0)
- Extensions and Resolutions (1995) (0)
- Birkhoff Garrett. Lattices and their applications. Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 793–800. (1939) (0)
- Frink Okrin Jr. Representations of Boolean algebras. Bulletin of the American Mathematical Society, vol. 47 (1941), pp. 755–756. (1942) (0)
- Review: Orrin Frink, Representations of Boolean Algebras (1942) (0)
- Planar Graphs Whose Homeomorphisms can all be Extended for Any Mapping on the Sphere (1937) (0)
- - M. H. A. Newman. Relatively complemented algebras. The journal of the London Mathematical Society , vol. 17 (1942), pp. 34–47. (1942) (0)
- list of Chauvenet Prize winners (2013) (0)
- Algebra [Mac Lane, 1967] (1967) (0)
- Review: M. H. A. Newman, Relatively Complemented Algebras (1942) (0)
- Mathematics and the Question of Cosmic Mind and Other Essays (1936) (0)
- Mathematical "invasion". (1980) (0)
- The Need for Mandatory Retirement for Tenured Faculty (1991) (0)
- Three Comments on Ethics (1992) (0)
- Serge lang Vs. the Bureaucracy— some deeper issues (1984) (0)
- Rosenbloom Paul C.. Post algebras. I. Postulates and general theory. American journal of mathematics , vol. 64 (1942), pp. 167–188. (1942) (0)
- Mori Shinziro. Prime ideals in Boolean rings. Journal of science of the Hirotima University, series A, vol. 9 (1939), pp. 67–71. (1940) (0)
- Over 600 people registered for the meeting , including the following 409 members of the Society : (2007) (0)
- Review: M. H. A. Newman, A Characterisation of Boolean Lattices and Rings (1942) (0)
- Humanized Geometry, An Introduction to Thinking (1936) (0)
- Review: Garrett Birkhoff, Morgan Ward, A Characterization of Boolean Algebras (1940) (0)
- The Ignorance of BourbakiA (1990) (0)
- A proposed “mini-study” of mathematical developments (1975) (0)
- ALLELISM OF SECOND CHROMOSOME LETHALS IN D. MELANOGASTER* (2005) (0)
- Circular A-21 Reporting Systems (1981) (0)
- Chwistek Leon. Sur les fondements des sciences exactes. Philosophie mathematique, by Gonseth F., Actualités scientifiques et induatrielles 837, Hermann et Cie, Paris 1939, pp. 88–91. (1940) (0)
- Modules, Diagrams, and Functors (1995) (0)
- Review: F. Gonseth, Philosophie Mathematique (1940) (0)
- Topoi and Logic (1994) (0)
- Proceedings of the International Symposium on Algebraic Number Theory . Tokyo and Nikko, Japan, September 1955. Science Council of Japan, Tokyo, 1956. 267 pp. (1957) (0)
- Review: Paul Dienes, Logic of Algebra (1939) (0)
- Birkhoff Garrett and Ward Morgan. A characterization of Boolean algebras. Annals of mathematics, ser. 2 vol. 40 (1939), pp. 609–610. (1940) (0)
- To the Greater Health of Mathematics (1988) (0)
- Review: Harry Pollard, The theory of algebraic numbers (1951) (0)
- Groups of Algebras Over an Algebraic Number Field (1943) (0)
- Axiomatic set theory (1964) (0)
- List of officers and members of the Association for Symbolic Logic (1945) (0)
- Symmetry and Braidings in Monoidal Categories (1978) (0)
- Itô Makoto. Kakuritu-ron no kôri-taikei ni tuite . Journal of the Mathematical Association of Japan for Secondary Education, vol. 20 , pp. 1–9 (1940) (0)
- Sununu Diplomacy? (1991) (0)
- NAS-NRC Independence (1997) (0)
- Review: S. Pankajam, On Symmetric Functions of m Symmetric Functions in a Boolean Algebra (1939) (0)
- Categorically, the final examination for the summer institute at Bowdoin College (Maine) 1969 (1970) (0)
- COHOMOLOGY IN ABSTRACT UNIT GROUPS (2010) (0)
- Are we all just specialists? (1986) (0)
- An Unpublished Reply (1980) (0)
- THE CONFERENCE ON ALGEBRA AT CHICAGO. (1938) (0)
- Review: O. Nikodym, On Boolean Fields of Subspaces in an Arbitrary Hilbert Space (1940) (0)
- Mathematical "Invasion" (1980) (0)
- Mathematics vs. Numerical Analysis (1965) (0)
- Serge lang Vs. the Bureaucracy— some deeper issues (1984) (0)
- Annals of Mathematics Group Extensions and Homology* (0)
- Review: Shinziro Mori, Prime Ideals in Boolean Rings (1940) (0)
- Jobs in the 1930s and the Views of George D. Birkhoff (1994) (0)
- The Future of Universities (1990) (0)
- Letters to the editor (1988) (0)
- IIASA and Modeling (1988) (0)
- Alonzo Church. The present situation in the foundation of mathematics. Philosophie mathematique , by F. Gonseth, Actualités scientifiques et induatrielles 837, Hermann et C ie , Paris1939, pp. 67–72. (1940) (0)
- The "Monster" Proof (1980) (0)
- Algebra of Classes (1941) (0)
- Review: Paul C. Rosenbloom, Post Algebras. I. Postulates and General Theory (1942) (0)
- The Ideal-Decomposition of Rational Primes in Terms of Absolute Values. (1935) (0)
- DESPITE PYHSICISTS, PROOF IS ESSENTIAL IN MATHEMATICS (1997) (0)
- The National Science Board (1986) (0)
- Bernays Paul. Bemerkungen zur Grundlagenfrage. Philosophie mathematique , by Gonseth F., Actualités scientifiques et induatrielles 837, Hermann et C ie , Paris1939, pp. 83–87. (1940) (0)
- Group extensions for 45 years (1988) (0)
- Will fermat last? (1994) (0)
- List of officers and Members of the Association for Symbolic Logic (1946) (0)
- Grothendieck Topologies and Sheaves (1992) (0)
- Monads and Algebras (1971) (0)
- The need for mandatory retirement for tenured faculty. (1991) (0)
- Cohomology of Groups (1995) (0)
- Mathematics (1980) (0)
- Homology of Complexes (1995) (0)
- The Mathematical Network (1986) (0)
- Algebra as means of understanding mathematics (1988) (0)
- Functions, Transformations, and Groups (1986) (0)
- Review: John C. Cooley, Outline of Symbolic Logic (1939) (0)
- Complex Analysis and Topology (1986) (0)
- Review: Garrett Birkhoff, Lattices and their Applications (1939) (0)
- The "monster" proof. (1980) (0)
- Pankajam S.. On symmetric functions of m symmetric functions in a Boolean algebra. Proceedings of the Indian Academy of Sciences, section A, vol. 9 (1939), pp. 95–102. (1939) (0)
- The Ideal-Decomposition of Rational Primes in Terms of Absolute Values. (1935) (0)
- Basic Constructions of Topoi (1994) (0)
- Spectral sequences and homotopy : lectures (1953) (0)
- Award for Distinguished Service to Professor Ralph P. Boas, Jr. (1981) (0)
- Review: M. H. Stone, The Representation of Boolean Algebras (1939) (0)
- First Properties of Elementary Topoi (1992) (0)
- Constructions on Categories (1971) (0)
- Book reviews (1981) (0)
- Manifesto on Mathematical Education (1998) (0)
- Sets, Logic, and Categories (1986) (0)
- Reals and Forcing with an Elementary Topos (1992) (0)
- NAS-NRC Independence (1997) (0)
- MacNeille H. M.. Extension of a distributive lattice to a Boolean ring. Bulletin of the American Mathematical Society, vol. 45 (1939), pp. 452–455. (1939) (0)
- Geometric Logic and Classifying Topoi (1994) (0)
- Stone M. H.. The representation of Boolean algebras. Bulletin of the American Mathematical Society , vol. 44 (1938), pp. 807–816. (1939) (0)
- Review: H. M. MacNeille, Extension of a Distributive Lattice to a Boolean Ring (1939) (0)
- Garrett Birkhoff (10 January 1911-22 November 1996) (1998) (0)
- Cohomology of Algebraic Systems (1995) (0)
- The Grand Tour of Europe, 1954 (2005) (0)
- Origins of Formal Structure (1986) (0)
- Linear representation of matroids (1986) (0)
- Relative Homological Algebra (1995) (0)
- Tensor and Torsion Products (1995) (0)
- Some Unique Separation Theorems for Graphs (1935) (0)
- VOL. 29, 1943 MATHEMA TICS: EILENBERG AND MacLANE RELATIONS BETWEEN HOMOLOGY AND HOMOTOPY GROUPS By SAMUEL EILENBERG AND SAUNDERS MACLANE (2005) (0)
- MA THEMATICS : EILENBERG AND MACLANE PROC (0)
- Categories of Functors (1994) (0)
- Review: Makoto Ito, An Axiom System for Probability Theory (1940) (0)
- Cooley John C.. Outline of symbolic logic. Harvard Cooperative Society, Cambridge, Mass., 1938. (1939) (0)
- Point set topology (1950) (0)
- Book Review: Andr\'e Weil: The apprenticeship of a mathematician (1993) (0)
- THE HOMOLOGY PRODUCTS IN KQI, n) (2010) (0)
- Universals and Limits (1971) (0)
- Origins and basic concepts (1986) (0)
- Math teaching, k-12: relevant expertise. (1992) (0)
- MATHEMA TICS: S. MacLANE (2005) (0)
- Review: Alfred Tarski, On Mathematical Logic and the Deductive Method (1938) (0)
- Concepts of Calculus (1986) (0)
- Newman M. H. A.. A characterisation of Boolean lattices and rings. The journal of the London Mathematical Society , vol. 16 (1941), pp. 256–272. (1942) (0)
- MATHEMATICS : CHOW AND KODAIRA ON ANALYTIC SURFACES WITH TWO INDEPENDENT MEROMORPHIC FUNCTIONS (2005) (0)
- Categories, functors and natural transformations (1971) (0)

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