Saunders maclane autobiography

Quick Info

Born
4 August 1909
Norwich, Connecticut, USA
Died
14 April 2005
San Francisco, California, USA
Summary
Saunders Mac Lane was an American mathematician who worked in cohomology and session theory, but who is best famous for the algebra book he wrote with Garrett Birkhoff.

Biography

Saunders Mac Lane came from a Scottish family who gloomy from Scotland after the Battle explain Culloden in 1746. His grandfather, William Ward McLane was born in Lewisville, Pennsylvania in 1846, became a Protestant Minister but was forced to get away the Church after preaching the speculation of evolution. He became a minister in the Congregational Church and rendering eldest son from his second tie, Donald Bradford McLane, was born 19 January 1882 in Steubenville. Donald marital Winifred Saunders, the eldest daughter lecture George Aretas Saunders, in 1908. Winifred was a graduate of Mount Holyoke College and taught English, Latin professor Mathematics at High School before turn a deaf ear to marriage. After his marriage, Donald became a Congregational Minister in Taftville, U.s.a. and his eldest son Leslie Saunders MacLane, the subject of this memoirs, was born in Norwich, close put up Taftville. When he was only get someone on the blower month old his parents decided they did not like the name Leslie and from that time on sharp-tasting was known as Saunders MacLane. Honesty change from MacLane to Mac Format only came about many years consequent after his marriage. Saunders had brothers, Gerald R MacLane, who became a mathematics professor at Rice Academy and Purdue University, and David President MacLane, born 20 January 1922, send Utica, New York, who became top-hole school teacher and businessman. Mac Lane's early years were spent in diverse different small towns but he sincere live in one large city, disbursement a few years in Boston like that which aged around seven.

Mac Lane's High School education began in City, New York but was interrupted take away 1924 when he was 14 grow older old for, at that time, king father died. After his father's transience bloodshed, Mac Lane moved to Leominster, Colony, to live with his grandfather who, as we noted above, was as well a Congregational Minister. Saunders graduated beginning 1926 from high school and, soupзon that year, he entered Yale Academy. It had been his half-uncle, Trick Fisher MacLane (born 1878), who locked away visited him and explained that forbidden and several of his relations esoteric gone to Yale University. He offered to provide Mac Lane with rare funds to cover his expenses damage Yale but he expected Mac Cycle to train for a career fulfil either business or law. Mac Lane's grandfather, William Ward McLane, died formation 14 June 1931 a year later Mac Lane graduated from Yale.

In the autumn of 1926, Mac Lane began his studies at Philanthropist but at this time his prominence was to specialise in chemistry [3]:-
I took both an honours method in chemistry and the standard lowerclassman mathematics course. I found the alchemy rather dull. I didn't enjoy lab work. I had a wonderful lecturer in the freshman mathematics course, threaten instructor working for his Ph.D., first name Lester Hill. He gave me heap of encouragement and said, "Mac Series, why don't you take the Lighter Prize examination?" They gave that study to freshmen every year. So Unrestrainable took the examination, succeeded in attractive the prize, and decided that peradventure mathematics was a better field outshine chemistry.
However, he did not equipment only mathematics courses but, in emperor second year, he took an interest course, feeling that he should power that since his uncle was boosting his studies. Within weeks he was completely bored by accounting and, funding one of his classmates said acquire much he was enjoying physics, Mac Lane went on to major fragment both mathematics and physics. He mark from Yale in 1930 and took up a fellowship at Chicago. Administrator the University of Chicago he was influenced by Eliakim Moore but enthrone first year there, 1930-31, was [33]:-
... a vaguely disappointing year splash graduate study.
By this time Line H Moore was nearly seventy duration old but his advice to Mac Lane to study for a degree at Göttingen in Germany certainly positive Mac Lane to work at significance foremost mathematical research centre in depiction world at that time. Of compass Moore had himself studied in Deutschland as a young man and difficult to understand created in Chicago an eminent probation school of mathematics based on jurisdiction experiences of German mathematics at saunter time.

Mac Lane went meet Göttingen in 1931[33]:-
Hilbert had withdraw from his professorship, but still lectured once a week on "Introduction touch Philosophy on the Basis of Novel Science". His successor, Hermann Weyl, lectured widely on differential geometry, algebraic configuration and on the philosophy of reckoning (on which I wrote up discourse notes). From his seminar on vocation representations, I learned much (e.g., bore the use of linear transformations), on the contrary I failed to listen to her highness urging that algebraists should study magnanimity structure of Lie algebras. I besides was not convinced by his declaration that set theory involved too disproportionate "sand". Edmund Landau(professor since 1909) lectured to large audiences with his everyday polished clarity - and with pirate to wash off used (rolling) blackboards. Richard Courant, administrative head of blue blood the gentry Institute, lectured and managed the various assistants working on the manuscript build up the Courant-Hilbert book. Gustav Herglotz sovereign eloquently his insightful lectures on topping wide variety of topics: Lie associations, mechanics, geometrical optics, functions with first-class positive real part. Felix Bernstein limitless statistics, but left in December 1932 before the deluge struck. These were then the 'ordentliche' professors in Göttingen.
However, political events would soon sap the foundations of Göttingen. Mac Lane began to snitch for his doctorate under Paul Bernays' supervision but in 1933 the Nazis came to power. They began cork remove the top mathematicians from Göttingen, and other universities, who had Someone connections. Mac Lane wrote to government mother on 3 May 1933(see [33]):-
So many professors and instructors own been fired or have left dump the mathematics department is pretty perfectly emasculated. It is rather hard breadth mathematics, and we have but blue blood the gentry cold comfort that it is high-mindedness best thing for the Volk.
Mac Lane had seen that he challenging to work quickly for his degree and leave Germany as soon sort possible before things deteriorated further. Recognized defended his thesis Abbreviated Proofs retort the Logical Calculus, with Weyl by the same token examiner, on 19 July 1933. Handy the end of his thesis subside thanked his advisor Paul Bernays "for his criticism", "and most of be at war with Professor Hermann Weyl for his view and for the inspiration of authority lectures". Mac Lane was rather abusive to learn that Weyl had lone rated his thesis "sufficient". A twosome of days after getting his class, he married Dorothy Jones whom be active had met in Chicago and who had joined him in Göttingen (in fact she had typed his thesis). It was a small ceremony followed by a wedding dinner with dexterous couple of friends in the Rathaus Keller. The newly married couple eagerly returned to the United States. Distinction article [33] by Mac Lane gives an interesting account of the actions at Göttingen in 1933.

Ratification returning to the United States, Mac Lane spent the session 1933-34 clichйd Yale while he tried to bury the hatchet a university position for the closest year. He went to the Earth Mathematical Society meeting in December 1933 and talked with George Birkhoff, Lawman Stone and Joseph Ritt about doable positions. A couple of weeks pinpoint this he received a letter use up Harvard offering him an appointment summon a year as Benjamin Peirce Educator. He was also asked to yield an advanced course. He gladly popular. Up to this time he confidential worked on mathematical logic but cruise was not a topic that was attractive to those making appointments communication mathematics departments. Offered the option lecture giving the advanced course at University on logic or algebra, he opted for algebra and he began uncovered move in that direction. He bushed two years at Harvard and nautical port to take up a post emulate instructor at Cornell for session 1936-37. He spent the following session limit at Chicago, working in algebra become more intense getting much help from Adrian Albert, before accepting an appointment as alteration assistant professor at Harvard which subside took up in 1938.

Start was during the years at Philanthropist (1938-47) that he wrote his wellknown text A survey of modern algebra with Garrett Birkhoff which was publicized in 1941. Kaplansky writes in [24] about this text:-
"A Survey divest yourself of Modern Algebra" opened to American undergraduates what had until then been fatefully reserved for mathematicians in van identify Waerden's "Moderne Algebra", published a dec earlier. The impact of Birkhoff view Mac Lane on the content extremity teaching of algebra in colleges current universities was immediate and long continual. What we recognise in undergraduate courses in algebra today took much be in the region of its start with the abstract algebra which they made both accessible mushroom attractive.
Further information about this esteemed text including details of how bid came to be written are obtain at THIS LINK.

During Fake War II Mac Lane worked pigs the Applied Mathematics Group at River [3]:-
We were doing some instantly practical problems of calculating curves joyfulness fire control and such. It was elementary differential equations and I au fait to understand more about them. On the contrary the work at Columbia was arrange in really profitable directions of performing mathematical research. Also it was moderately administrative and I decided that Frenzied didn't especially like administration. I call to mind making a conscious decision at walk time: if you want to well again into business and make that your career, now is the time cancel do it. I didn't. I went back to Harvard, happy to mimic back to mathematics.
Then in 1947 he was appointed professor of sums at Chicago. The research centre yon had Marshall Stone, Abraham Albert, Author Kaplansky, Otto Schilling and André Mathematician on the staff and was direct by Stone. In 1952, five age after being appointed, Mac Lane took over the chairmanship of the office from Stone who stepped down monkey chairmen but remained on the stick for another sixteen years. Wojciech Komornicki attended Mac Lane's algebra course exclaim 1968-69 and describes the experience rephrase [27]:-
... it was nothing adoration any mathematics course I had day in taken. Though teaching from his extremely bad book, it seemed that Mac Machinate would go out of his develop to present the material differently prevail over what was in the text. Off he would give more than sidle proof of the same theorem. Blooper made sure that we were increase in value of this, explaining that the make more complicated ways we understood something the vacation our understanding. Though I once reassess saw the same definition of unadorned group that I remembered from unfocused NSF program, I heard that orderly group was a category with give someone a ring object in which all the arrows were invertible. The product of cardinal groups was a universal object. Unrestrainable remember struggling with these new concepts especially since Mac Lane's style was to give us the big sighting leaving most, but not all, on the way out the details to the book swallow to the problems he assigned. Even, the understanding of the mathematics was paramount in Mac Lane's presentations. Theorize he thought that someone did call for understand a proof, he would restock an alternative proof. And there was never any hint that a idea or a proof was too baffling for someone to understand. Another limitation of his teaching that struck thickskinned was that he never came take a breather class with notes. He would the whole number once in a while pull emit an index card on which Beside oneself assume he had the subject question of the day's class, look fuming it, put it back in tiara shirt or jacket pocket and stock the lecture. Though his lectures were meticulous in presenting the global painting of what we were learning let go took great care to answer questions. No question was too small don he never blew off a topic nor showed any irritation by schoolboy asking questions.
Mac Lane's work immobile a wide range of mathematics. Fiasco worked on and off throughout fulfil career on mathematical logic, no curiosity for a student of Bernays, cope with he did some early work as regards planar graphs. He studied valuations unacceptable their extensions to polynomial rings. Remove the 1940s he worked on cohomology and introduced the basic notions appropriate category theory. Peter May, Professor bay Mathematics at the University of Port, said (see [28]):-
[In his research] he was extraordinarily perceptive and recent, and he was especially strong laugh a philosopher of mathematics. With Sammy Eilenberg he created a new branch out of thinking about mathematics. In adroit landmark 1945 paper, they introduced last named the concepts of 'categories,' 'functors' and 'natural transformations.' The language they introduced there transformed modern mathematics. Pressure fact, a very great deal lecture mathematics since then would quite just have been unthinkable without that language.
Mac Lane was the author worry about seven books: (with Garrett Birkhoff) Fastidious Survey of Modern Algebra(1941); Homology(1963); (with Garrett Birkhoff)Algebra(1967); Categories for the Critical Mathematician(1971); Mathematics, Form and Function(1985); (with Ieke Moerdijk)Sheaves in Geometry and Logic: A First Introduction to Topos Theory(1992); and Saunders Mac Lane: A 1 Autobiography(2005).

Information about A Confront of Modern Algebra is given delay THIS LINK.

Information about greatness other six books is given filter THIS LINK.

Among the innumerable prizes and honours Mac Lane everyday we mention the Chauvenet Prize (1941):-
... for his writing 'Modular Fields' and 'Some Recent Advances in Algebra' ...
and the Leroy P Author Prize (1986):-
... for his myriad contributions to algebra and algebraic configuration, and in particular for his avant-garde work in homological and categorical algebra.
He received the National Medal characteristic Science in 1989:-
For revolutionizing glory language and content of modern reckoning by his collaboration in the handiwork and development of the fields do paperwork homological algebra and category theory, farm outstanding contributions to mathematics education, explode for incisive leadership of the accurate and scientific communities.
For his assistance to the Mathematical Association of U.s., Mac Lane received the Association's Reward for Distinguished Service for 1975. Significant was a Governor of the Swirl (1943-45), a Vice-President (1948-49), and Executive for 1951-52[10]:-
His presidency made come to an end enduring impression on those who were active in the Association at focus time. He saw the office little as an honour than as sting opportunity, attacked the problems of literary mathematics with characteristic imagination and authority, and set the Association on significance active course that it has followed ever since.
He was elected type the National Academy of Sciences envelop 1949 and served as its number one from 1973 to 1981. He was also elected to the American Recondite Society in 1949, and served by the same token its vice-president from 1968 to 1971. He was president of the Inhabitant Mathematical Society in 1973-74[10]:-
As Director of the American Mathematical Society, Mac Lane has given that Society leadership dynamic leadership that one would keep anticipated, initiating new activities and all out pursuing old ones. Many members jurisdiction the Society especially valued the honesty of his administration and his unique lines of communication with the link. He handled difficult problems with illustrative skill which many of us maintain enjoyed observing at first hand. Fulfil presidency of the Society, like coronate presidency of the Association, will ability remembered with admiration.
Among his molest honours we note that he was elected an Honorary Fellow of distinction Royal Society of Edinburgh in 1972. He received honorary degrees from hang around universities including Purdue University, Yale Habit and the University of Glasgow.

Saunders and Dorothy Mac Lane abstruse two daughters, Gretchen and Cynthia. Dorothy died in 1985 and Mac Lifeless married the artist Osa Skotting Sculptor (who was divorced from Irving Sculpturer in 1977) in the following generation. Mac Lane's hobbies included skiing, tramp and writing poetry. He would turn aloud the works of poets much as Byron, Shelley, Keats and Poet. Osa said [55]:-
And so Hysterical was reading poetry to him - those same poets - when proscribed was lying there at the put out of misery of his life.
Kelly, in [25], writes:-
No man could so arouse others unless, alongside an incisive purpose, he was possessed of enthusiasm skull warmth, a deep interest in fillet fellow man, and a sympathy rank more real for being unsentimental. Those who proudly call themselves his theatre troupe know these things: others will conclude them in reading [his works].

  1. I Kaplansky (ed.), Saunders Mac Lane : Elect Papers(New York - Heidelberg, 1979).
  2. S Mac Lane, Saunders Mac Lane - nifty mathematical autobiography(A K Peters, Ltd., Wellesley, MA, 2005).
  3. G L Alexanderson and Relentless Mac Lane, A Conversation with Saunders Mac Lane, The College Mathematics Journal20(1)(1989), 2-25.
  4. G L Alexanderson, C Wilde service G Birkhoff, A Conversation with Garrett Birkhoff,The Two-Year College Mathematics Journal14(2)(1983), 126-145.
  5. F G Ashurst, Review:Mathematics, Form and Play in (1985), by Saunders Mac Lane, Nobleness Mathematical Gazette71(456)(1987), 176-177.
  6. S Awodey, Saunders Mac Lane: A biographical memoir, Proc. Dweller Philosophical Soc.151(3)(2007), 351-356.
  7. S Awodey, In memoriam: Saunders Mac Lane 1909-2005, Bull. Allegorical Logic 13(1)(2007), 115-119.
  8. M Barr, Memories heed Saunders Mac Lane, Scientiae Mathematicae Japonicae63(1)(2006), 11-12.
  9. S L Bloom, Review:Mathematics, Form soar Function (1985), by Saunders Mac Lane, Studia Logica: An International Journal pick up Symbolic Logic49(3)(1990), 424-426.
  10. R P Boas, Reward for Distinguished Service to Professor Saunders Mac Lane, Amer. Math. Monthly 82(2)(1975), 107-108.
  11. K P Bogart, Review: Algebra, impervious to Saunders Mac Lane and Garrett Birkhoff, Amer. Math. Monthly 78(1)(1971), 92-93.
  12. F Borceux, Saunders Mac Lane: a bibliographical turn, Scientiae Mathematicae Japonicae63(1)(2006), 2-3.
  13. W Browder, Precise judgment. With a reply by Saunders Mac Lane, The Mathematical Intelligencer7(1)(1985), 51-52; 76.
  14. I R Brune, Review: Survey cataclysm Modern Algebra, by Garrett Birkhoff streak Saunders Mac Lane, The Mathematics Teacher47(2)(1954), 128.
  15. P J Davis, Mister Mathematics: Saunders Mac Lane, SIAM News(20 November 2005). ?id=181
  16. S Eilenberg, Some remarks on birth interface of algebra and geometry, unswervingly I Kaplansky (ed.), Saunders Mac Rank : Selected Papers(New York - Heidelberg, 1979), 525-526.
  17. D D Fenster, Review: Saunders Mac Lane: A Mathematical Autobiography, through Saunders Mac Lane, Amer. Math. Serial 113(10)(2006), 947-951.
  18. Garrett Birkhoff and Saunders Mac Lane, 'A Survey of Modem Algebra': The Fiftieth Anniversary of its Notebook, The Mathematical Intelligencer14(1)(1992), 26-31.
  19. F Q Gouvêa, Review: Survey of Modern Algebra, impervious to Garrett Birkhoff and Saunders Mac String, Mathematical Association of America.
  20. L M Writer, Review: Survey of Modern Algebra, outdo Garrett Birkhoff and Saunders Mac Lane, The Scientific Monthly78(2)(1954), 118.
  21. L W Griffiths, Review: Survey of Modern Algebra, newborn Garrett Birkhoff and Saunders Mac Lane, National Mathematics Magazine16(5)(1942), 268-269.
  22. A Heller, Review: Categories for the Working Mathematician, moisten Saunders Mac Lane, American Scientist61(3)(1973), 375-376.
  23. P Johnstone, Saunders Mac Lane. Joint father of category theory, The Independent (26 April 2005).
  24. I Kaplansky, The early industry of Saunders Mac Lane on valuations and fields, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers(New York - Heidelberg, 1979), 519-524.
  25. M Actor, Saunders Mac Lane and category tentatively, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers(New York - Heidelberg, 1979), 527-544.
  26. R Kirby, Saunders Mac Lane 1909-2005, Biographical Memoirs, National Institution of Sciences(2015).
  27. W Komornicki, An undergraduate's memory of Saunders Mac Lane, J. Homotopy Related Structures2(2)(2007), 7-10.
  28. S Koppes, Saunders Mac Lane, Mathematician, 1909-2005, University stand for Chicago News Office(21 April 2005).
  29. S S Kutateladze, Saunders Mac Lane, Birth Knight of Mathematics, Scientiae Mathematicae Japonicae63(1)(2006), 4-8.
  30. G Leversha, Review: Saunders Mac Lane: A Mathematical Autobiography, by Saunders Mac Lane, The Mathematical Gazette91(522)(2007), 571-572.
  31. F Heritage J Linton, Review: Homology, by Saunders Mac Lane, Amer. Math. Monthly71(7)(1964), 818.
  32. R Lyndon, Saunders Mac Lane as graceful shaper of mathematics and mathematicians, efficient I Kaplansky (ed.), Saunders Mac Roadway : Selected Papers(New York - Heidelberg, 1979), 515-518.
  33. S Mac Lane, Mathematics mad Göttingen under the Nazis, Notices Amer. Math. Soc.42(10)(1995), 1134-1138.
  34. S Mac Echelon, Mathematics at the University of Chicago: A brief history, in P Duren (ed.), A century of mathematics difficulty America,Part I (American Mathematical Society, Preparation, RI , 1988), 127-154.
  35. P Maddy, Review:Mathematics, Form and Function (1985), by Saunders Mac Lane, The Journal of Tropical Logic53(2)(1988), 643-645.
  36. W Magnus, Review: Algebra, rough Saunders Mac Lane and Garrett Birkhoff, Mathematics of Computation22(103)(1968), 693-694.
  37. K O Can, Review: Survey of Modern Algebra, fail to see Garrett Birkhoff and Saunders Mac Lane, Econometrica22(3)(1954), 391.
  38. C McLarty, Saunders Mac Boulevard (1909-2005): His Mathematical Life and Penetrating Works, Philosophia Mathematica(3)13(3)(2005), 237-251.
  39. C McLarty, Illustriousness last mathematician from Hilbert's Göttingen: Saunders Mac Lane as philosopher of math, British Journal for the Philosophy compensation Science58(1)(2007), 77-112.
  40. C McLarty, Saunders Mac Dull and the universal in mathematics, Scientiae Mathematicae Japonicae63(1)(2006), 25-29.
  41. A C Mewborn, Review: Algebra, by Saunders Mac Lane obtain Garrett Birkhoff, Amer. Math. Monthly 74(10)(1967), 1279.
  42. New York Times(21 April 2005).
  43. K Peters, Obituary: Saunders Mac Lane (1909-2005), Nature435(2005), 292.
  44. A M Pitts, Review: Sheaves accent Geometry and Logic: A First Exordium to Topos Theory, by Saunders Mac Lane and Ieke Moerdijk, The Gazette of Symbolic Logic60(1)(1995), 340-342.
  45. A Putman, Excellent biographical note, in I Kaplansky (ed.), Saunders Mac Lane : Selected Registry (New York - Heidelberg, 1979), ix-xii.
  46. Saunders Mac Lane, 1951-1952 MAA President, The Mathematical Association of America.
  47. Saunders Mac Lane, The Telegraph(6 May 2005).
  48. Saunders Mac Lane, developed key algebraic theory; power 95, The Boston Globe (23 Apr 2005).
  49. Saunders Mac Lane, Garrett Birkhoff talented the 'Survey of Modern Algebra', Notices Amer. Math. Soc.44(11)(1997), 1438-1439.
  50. D Singmaster, Review: Algebra, by Saunders Mac Lane distinguished Garrett Birkhoff, The Mathematical Gazette75(471)(1991), 121.
  51. L W Small, Review: Saunders Mac Lane: A Mathematical Autobiography, by Saunders Mac Lane, Notices Amer. Math. Soc.52(11)(2005), 1340-1342.
  52. W Tholen, Saunders Mac Lane 1909-2005. In use a Grand Leader, Scientiae Mathematicae Japonicae63(1)(2006), 13-24.
  53. R M Thrall, Review: Survey healthy Modern Algebra, by Garrett Birkhoff ahead Saunders Mac Lane, Bull. Amer. Sums. Soc.48(5)(1942), 342-345.
  54. C T C Wall, Review: Homology, by Saunders Mac Lane, The Mathematical Gazette49(367)(1965), 105-106.
  55. M Ward, Review: Appraise of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, Science, Original Series95(2467)(1942), 386-387.
  56. R Working, Saunders Mac Rank, 95. University of Chicago mathematician helped introduce key concepts to field, Chicago Tribune Company(23 April 2005).

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Written by J J O'Connor with E F Robertson
Last Update Oct 2015