Selected Title s i n Thi s Serie s

20 Kolmogoro v i n perspective , 200 0

19 Herman n Grassmann , Extensio n theory , 200 0

18 Jo e Albree , Davi d C . Arney , an d V . Frederic k Rickey , A statio n favorabl e t o th e pursuits o f science : Primar y material s i n th e histor y o f mathematic s a t th e Unite d State s Military Academy , 200 0

17 Jacque s Hadamar d (Jerem y J . Gra y an d A b e Shenitzer , Editors) , Non-Euclidea n geometry i n th e theor y o f automorphi c functions , 199 9

16 P . G . L . Dirichle t (wit h Supplement s b y R . Dedekind) , Lecture s o n numbe r theory , 1999

15 Charle s W . Curtis , Pioneer s o f representatio n theory : Frobenius , Burnside , Schur , an d Brauer, 199 9

14 Vladimi r Maz'y a an d Tatyan a Shaposhnikova , Jacque s Hadamard , a universa l

mathematician, 199 8

13 Lar s Garding , Mathematic s an d mathematicians : Mathematic s i n Swede n befor e 1950 ,

1998

12 Walte r Rudin , Th e wa y I remember it , 199 7

11 Jun e Barrow-Green , Poincar e an d th e thre e bod y problem , 199 7

10 Joh n Stillwell , Source s o f hyperboli c geometry , 199 6

9 Bruc e C . Bernd t an d Rober t A . Rankin , Ramanujan : Letter s an d commentary , 199 5

8 Kare n Hunge r Parshal l an d Davi d E . Rowe , Th e emergenc e o f th e America n

mathematical researc h community , 1876-1900 : J . J . Sylvester , Feli x Klein , an d E . H . Moore ,

1994

7 Hen k J . M . Bos , Lecture s i n th e histor y o f mathematics , 199 3

6 Smilk a Zdravkovsk a an d Pete r L . Duren , Editors , Golde n year s o f Mosco w

mathematics, 199 3

5 Georg e W . Mackey , Th e scop e an d histor y o f commutativ e an d noncommutativ e

harmonic analysis , 199 2

4 Charle s W . M c Arthur, Operation s analysi s i n th e U.S . Arm y Eight h Ai r Forc e i n Worl d

War II , 199 0

3 Pete r L . Dure n e t al. , Editors , A centur y o f mathematic s i n America , par t III , 198 9

2 Pete r L . Dure n e t al. , Editors , A centur y o f mathematic s i n America , par t II , 198 9

1 Pete r L . Dure n e t al. , Editors , A centur y o f mathematic s i n America , par t I , 198 8

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KOLMOGOROV IN PERSPECTIVE

Histor y of Mathematic s •Volum e 20

KOLMOGOROV IN PERSPECTIVE

America n Mathematica l Societ y Londo n Mathematica l Societ y

https://doi.org/10.1090/hmath/020

Editorial Boar d American Mathematica l Societ y Londo n Mathematica l Societ y

George E . Andrew s Davi d Fowler , Chai r Joseph W . Daube n Jerem y J . Gra y Karen Parshall , Chai r S . J . Patterso n George B . Seligma n

Translated fro m th e Russia n b y Harol d H . McFaden .

2000 Mathematics Subject Classification. Primar y 01A70 .

Library o f Congres s Cataloging-in-Publicatio n Dat a Kolmogorov i n perspective / [translate d fro m th e Russian b y Harold H . McFaden] .

p. cm . — (Histor y o f mathematics ; v. 20) Includes bibliographica l references . ISBN 0-8218-0872- 9 (har d cover ; acid-fre e paper ) ISBN 0-8218-2918- 1 (sof t cover ; acid-fre e paper ) 1. Kolmogorov, A . N. (Andrei Nikolaevich) , 1903 - 2 . Mathematicians—Russia (Federation) —

Biography. I . Series . QA29.K627K65 200 0 510/.92—dc21 [B] 00-04416 2

Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s acting fo r them, ar e permitted t o make fai r us e of the material, suc h a s to copy a chapte r fo r use in teachin g o r research . Permissio n i s grante d t o quot e brie f passage s fro m thi s publicatio n i n reviews, provide d th e customary acknowledgmen t o f the source i s given .

Republication, systemati c copying , o r multiple reproductio n o f any materia l i n this publicatio n is permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Request s fo r suc h permission shoul d b e addressed t o the Acquisitions Department , America n Mathematica l Society , 201 Charle s Street , Providence , Rhod e Islan d 02904-2294 , USA . Requests ca n als o b e mad e b y e-mail t o reprint-permission@ams.org .

© 200 0 by the American Mathematica l Society . Al l rights reserved . Reprinted b y the American Mathematica l Society , 2006 .

The America n Mathematica l Societ y retain s al l right s except thos e grante d t o the United State s Government .

Printed i n the United State s o f America .

@ Th e paper use d i n this boo k i s acid-free an d falls withi n th e guideline s established t o ensure permanenc e an d durability .

The Londo n Mathematica l Societ y i s incorporated unde r Roya l Charte r and i s registered wit h th e Charity Commissioners .

Visit th e AMS hom e pag e a t h t t p : //www. ams. org/

10 9 8 7 6 5 4 3 2 1 1 1 10 09 08 07 06

Contents

Preface i x

Andrei Nikolaevic h Kolmogoro v (Apri l 25 , 190 3 to Octobe r 20 , 1987) . A Biographical Sketc h o f His Life an d Creativ e Path s A. N . SHIRYAE V 1

On A . N . Kolmogoro v V. I . ARNOL' D 8 9

In Memor y o f A . N . Kolmogoro v S. M . NIKOI/SKI I 10 9

Remembrances o f A . N . Kolmogoro v YA. G . SINA I 11 7

The Influenc e o f Andre i Nikolaevic h Kolmogoro v o n M y Lif e P. L . UI/YANO V 12 1

A Few Words on A . N . Kolmogoro v P. S . ALEKSANDRO V 14 1

Memories o f P . S . Aleksandro v A. N . KOLMOGORO V 14 5

Newton an d Contemporar y Mathematica l Though t A. N . KOLMOGORO V 16 3

Bibliography 17 7

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Preface

The Editorial Boar d o f the History of Mathematics serie s has selected for trans -lation a serie s o f writing s fro m th e tw o volume s i n Russian , "Kolmogoro v i n Re -membrance" (A . N . Shiryaev , ed. , "Nauka" , Moscow , 1993 ) an d "Mathematic s and it s Historica l Development " (V . A . Uspenskii , ed. , "Nauka" , Moscow , 1991) . The forme r comprise s article s b y student s an d colleague s o f Andre i Nikolaevic h Kolmogorov o n hi s lif e an d works . Th e piece s i n th e secon d volum e wer e writ -ten durin g Kolmogorov' s lifetime , i n th e earl y t o mi d 1980's . Her e Kolmogorov' s memories o f Aleksandro v wer e irresistible , sketchin g th e earl y year s o f a lifelon g mathematical an d persona l friendship . Share d experience s ar e supplemente d b y quotations fro m letters , a s the y visite d mathematica l center s i n Germany , Pranc e and the United State s in the early 1930's . Thei r comment s on the Western societie s they encountere d ar e fresh , fran k an d charming . Thi s articl e wa s previousl y pub -lished i n "Uspekh i Matematicheskik h Nauk" , an d th e translatio n include d i n th e present volum e wa s made fo r "Russia n Mathematica l Surveys " unde r th e auspice s of th e Londo n Mathematica l Society . Th e secon d o f th e article s b y Kolmogoro v is a 198 2 reissuin g o f a piec e i n a collectio n honorin g th e tricentennia l o f New -ton's birth . H e argue s tha t Newton' s understandin g o f th e fundamenta l concept s of analysi s reall y followe d line s o f thought muc h close r t o thos e o f our tim e tha n i s generally conceded .

In the obituary volume , A. N. Shiryaev present s a quite comprehensive accoun t of Kolmogorov's lif e an d works . Thi s i s a mathematician' s histor y o f mathematics , in tha t h e prefaces man y o f hi s subject' s achievement s wit h a sketc h o f hi s precur -sors' work , the n follow s th e explanatio n o f Kolmogorov' s wor k wit h a n accoun t o f advances mad e b y hi s successors . I n particular , on e may recommen d hi s treatmen t of the tentative s tha t precede d th e famou s "Grundbegriff e de r Wahrscheinlichkeit -srechnung" an d o f th e growt h o f th e subjec t followin g it s publication . Reminis -cences o f V . I . Arnol' d quot e liberall y fro m Kolmogorov' s ow n letter s an d con -versations, displayin g hi s mathematica l taste s an d prejudices . Th e selection s ar e rounded ou t b y accounts o f his activities with student s a t Mosco w State Universit y and o f his continuin g influenc e o n generation s o f Sovie t mathematicians .

Kolmogorov's bibliograph y i s overwhelming, bot h i n it s volum e an d it s range . For th e reade r wh o want s a n overvie w o f tha t range , i t migh t b e a goo d plac e to start , a s woul d th e reprinte d tabl e o f content s fro m hi s three-volum e "Selecte d Works" (Kluwer , 1991-1993) . A n effor t her e t o giv e even a partia l catalogu e o f th e areas o f his contributions woul d b e inadequate .

The Editoria l Boar d wis h t o than k Vladimi r Drobo t wh o hav e advise d o n th e translation, Ha l McFade n wh o translate d mos t o f the article s fo r thi s volume , an d A. N . Shiryae v fo r sendin g additiona l photograph s reproduce d i n th e book .

Editorial Boar d

ix

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