MANUSCRIPT COLLECTION


MS 062 – MAHLER, Kurt, FAA (1903-1988)
Mathematician

Kurt Mahler was born on 26 July 1903 at Krefeld am Rhein in Germany; he died in his 85th year on 26 February 1988 in Canberra, Australia.

Mahler left Germany when Hitler came to power in 1933, moving to Manchester and Groningen. In 1941, he was appointed to the Assistant Lectureship at Manchester, and was later promoted to Lecturer (1944), Senior Lecturer (1947) and Reader (1949), and in 1952 the first personal chair in the history of the University was created for him. He became a British subject in 1946 and was elected a Fellow of the Royal Society in 1948. He made his first visit to the United States in 1949, spending most of the time at the Institute for Advanced Study in Princeton.

Mahler moved to Canberra in 1963 to take up a research professorship at the Institute of Advanced Studies at the Australian National University. In 1968, he reached the statutory retiring age for professors, and was forced to retire from the ANU. He then moved to a chair at the Ohio State University. He returned to Canberra in 1972 for his 'final retirement', but continued to publish until his death. He left the bulk of his estate to the Australian Mathematical Society, which has established a lectureship in his memory.

He made major contributions to transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers.

Kurt Mahler never married. He was an excellent photographer, and the study of Chinese remained an important interest and hobby.

Mahler received many distinctions during his lifetime. He was elected a Fellow of the Australian Academy of Science in 1965 and received its Lyle Medal in 1977. The London Mathematical Society awarded him its Senior Berwick Prize in 1950, and its De Morgan medal in 1971. In November 1977, he received a diploma at a special ceremony in Frankfurt to mark the golden jubilee of his doctorate. Het Wiskundig Genootschap (the Dutch Mathematical Society) made him an honorary member in 1957, as did the Australian Mathematical Society in 1986.

Adapted from http://www.science.org.au/fellows/memoirs/mahler.html

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4 working notebooks (undated) 62/2 4 working notebooks (undated)

62/3

  1. Manuscript of Cambridge tract,'Introduction to p-adic numbers and their functions'
  2. Photocopies of paper,'On the generating functions of integers with a missing digit, in Chinese and English translation versions, with accompanying Chinese tables and a glossary of Chinese symbols'
  3. Chapters 1-8 of Mahler's book,'Introduction to p-adic numbers and their functions'. 2nd edition
  4. 'Lectures on transcendental numbers', by Mahler. Published version
  5. 'Lectures on transcendental numbers', by Mahler. Photocopy of typed manuscript version, with some additional typed pages
  6. Various handwritten and typed notes and some manuscript pages connected with Mahler's book,'Lectures on transcendental numbers'
  7. 'Lectures on transcendental numbers', by Mahler. Draft version of chapters 1-6
  8. 'Lectures on transcendental numbers', by Mahler. Draft versions of chapter 7
  9. 'Lectures on transcendental numbers', by Mahler. Various draft versions of chapter 8
  10. Lecture notes on selected topics in the theory of transcendental numbers - lectures given at the University of Colorado in the summer of 1965
  11. Lecture notes on transcendental numbers given at the University of Arizona, September 1967- January 1968
  12. 'Transcendental numbers'. Various lecture notes, largely handwritten
  13. Introductory lecture on transcendental numbers
  14. 'The census taker problem', by Leroy F Meyers and Richard See. Various lecture notes, mostly handwritten, including those for a seminar on algebraic numbers
  15. 'Further results on the values of analytic functions' (handwritten)
  16. 'On a false proof' (handwritten)
  17. 'The modular figure' (handwritten lecture notes)
  18. 'Algebraic functions and their integrals' (handwritten lecture notes)
  19. Lecture notes on algebraic and Abelian functions
62/4
  1. Number theory: lecture notes (most handwritten)
  2. Modular functions: lecture notes (handwritten)
  3. Manuscripts of published papers
  4. Three photographs (1 coloured); certificate and newspaper clipping of honorary doctorate from Johann Wolfgang Goethe-Universität
  5. Old miscellaneous notes (2 folders)
  6. Letters received, 1912 - 1949. Includes references and some school reports
  7. Letters received, 1950-62
  8. Letters received, 1963-64
  9. Letters received, 1965-66
  10. Letters received, 1967
  11. Letters received, 1968
  12. Letters received, 1969
  13. Letters received, 1970
  14. Letters received, 1971
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  1. Letters received, 1972 (3 large envelopes, each containing about 120 items)
  2. Letters received, 1973 (3 large envelopes, each containing about 120 items)
  3. Letters received, 1974, part 1 (1 large envelope, containing about 120 items)
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  1. Letters received, 1974, part 2 (1 large envelope, containing about 120 items)
  2. Letters received, 1975 (2 large envelopes, each containing about 120 items)
  3. Letters received, 1976 (2 large envelopes, each containing about 120 items)
  4. Letters received, 1977 (1 large envelope, containing about 120 items, and 1 medium envelope, containing about 100 items)
  5. 18 coloured slides, apparently of a function in the grounds of University House, 1979. (Possibly garden party as part of the Australian Academy of Science's silver jubilee celebrations)
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  1. Letters received, 1978 (1 medium envelope)
  2. Letters received, 1979 (1 medium envelope)
  3. Letters received, 1980 (1 medium envelope)
  4. Letters received, 1981 (1 large envelope)
  5. Letters received, 1982 (1 large envelope)
  6. Letters received, 1983 (1 large envelope)
  7. Letters received, 1984 (1 large envelope)
  8. Letters received, 1985 (1 large envelope)
  9. Letters received, 1986 (1 large envelope)
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  1. Letters received, 1987 (2 medium envelopes)
  2. Letters received, 1988 (1 medium envelope, containing 6 items)
  3. Folder of letters, cards, etc, sent to Mahler on his 80th birthday, 26 July 1983
  4. Obituary of Hua Luogeng, 1983
  5. Typescript of Mahler's book, Lectures on transcendental numbers, 1976
  6. Material on transcendental numbers by Mahler (typescript and handwritten). In German
  7. Fragments of material by Mahler (typescript, with corrections). Some in English, some in German
  8. Australian Mathematical Society. Proceedings of the 1975 Summer Research Institute, University of New South Wales, 13 January -14 February 1975. [Contains abstract of paper by Mahler]

    9-11. MSc theses acknowledging Mahler's supervision or assistance, 1960-66

  9. Cohen, Alan Max'Problems in the geometry of numbers'. University of Manchester, 1960
  10. Gaudry, Patricia Jacqueline'Two problems in the geometry of numbers'. ANU, 1966
  11. Nguyen Huu Bong'On approximations over ideal bases in quadratic number fields'. ANU, 1966

    12-15. PhD theses acknowledging Mahler's supervision or assistance, 1952-69

  12. Cohen, Alan Max'Problems in the theory of numbers'. University of Manchester, 1963
  13. Aitcheson, P W'Some characterisations of the ellipsoid and the Minkowski theory of reduction'. ANU, 1968
  14. Nicholson, Arthur Richard'Some results on transcendency'. Victoria University of Manchester, 1952
  15. McFeat, Richard B'Geometry of numbers in Adele spaces'. University of Adelaide, 1969
62/9
    1-10. Theses and other publications citing Mahler, 1964-87

  1. Amice, Yvette'Interpolation p-adique'.'Propositions données par la faculté'. Doctoral theses, University of Paris, ca 1965
  2. Syllabus Seminarium'Getal en Kans' 1967-68 (2 vols)
  3. van Rooij, A C M'Non-Archimedean functional analysis'. Department of Mathematics, Catholic University, Nijmegen, The Netherlands, 1973
  4. Mignotte, Maurice'Quelques problèmes d'effectivité en théorie des nombres'.'Proposition donnée par la faculté'. Doctoral theses, University of Paris, 1975
  5. Book in Chinese. 1975
  6. Book in Chinese. 1978
  7. Geijsel, J M'Transcendence in fields of positive characteristic'. Doctoral thesis, University of Amsterdam, 1978
  8. Bertrand, Daniel and Waldschmidt, Michel'Publications mathematiques de l'Université Pierre et Marie Curie'. Pierre and Marie Curie University, 1982
  9. Buchmann, Johannes'Zahlengeometrische Kettenbruchalgorithmen zur Einheitenberechnung'. Doctoral thesis, University of Cologne, 1982
  10. Evertse, J H et al'S-unit equations and their applications'. Mathematical Institute, University of Leiden, The Netherlands, 1987
  11. Journal of number theory editorial newsletter, no 1 (July 1982) - no 38 (February 1986). No 4 missing
62/10
    1-22. Publications sent to Mahler, but not referring to him

  1. Alladi, Krishnaswami.'Contributions to number theory' (revised and enlarged). The Institute of Mathematical Sciences, Madras, 1974
  2. American Mathematical Society. Lecture notes prepared in connection with the Summer Institute on Number theory ..., held at State University of New York at Stony Brook, 7 July to 1 August, 1969
  3. Australian Mathematical Society Gazette, vol 14, no 1, February 1987
  4. Bertrand, Daniel. Doctoral theses presented to Pierre and Marie Curie University, Paris, 1977.'Approximations diophantiennes p-adiques et courbes elliptiques'.'Propositions données par l'université'
  5. Brentjes, A J'Multi-dimensional continued fraction algorithms'. Doctoral thesis, University of Leiden, 1981
  6. Caldwell, Roderick'Numerical studies on recent improvements of the Minkowski-Hlawka theorem'. US Office of Naval Research, 1962
  7. Davy, J L'Generalized differential equations satisfying Carathéodory type conditions'. PhD Thesis, ANU, 1974
  8. De Bruin, Marcelis'Generalized C-fractions and a multidimensional Padé table'. Doctoral thesis, University of Amsterdam, 1974
  9. DeFrancis, John'Chinese-English glossary of the mathematical sciences'. American Mathematical Society, 1964
  10. Katchalski, Meir'Dimensions of intersections of convex sets'. PhD thesis, Hebrew University, Jerusalem, 1974
  11. Laurent, Michel.'Indépendance algébrique de nombres de Liouville à des puissances algébriques'. Doctoral thesis, Pierre and Marie Curie University, 1977
  12. Lesca, Jacques'Sur les approximations diophantiennes à une dimension'.'Propositions données par la Faculté'. Doctoral theses, University of Grenoble, 1968
  13. Marcus, Leo'On minimal models'. PhD thesis, Hebrew University, Jerusalem, 1974
  14. Philippon, Patrice'Pour une theorie de l'indépendance algébrique'.'Propositions données par l'université'. Doctoral theses, South Paris University, 1983
  15. Philippon, Patrice'Critères pour l'indépendance algébrique'. Publications Mathématiques, 1987
  16. Richert, Norman'Diophantine approximation of complex numbers' PhD thesis, Claremont Graduate School, 1980
  17. Tijdeman, Robert'On the distribution of the values of certain functions'. Doctoral thesis, University of Amsterdam, 1969
  18. Van Rooij, A'Notes of p-adic Banach spaces'. Mathematics Institute, Catholic University, Nijmegen, The Netherlands, 1976
  19. Van Rooij, A'Non-Archimedean representations of compact groups'. Mathematics Institute, Catholic University, Nijmegen, The Netherlands, 1977
  20. Wang, Chu-Chi et al.'English-Chinese dictionary of mathematical terms'. Hongkong, 1961
  21. Weinstein, Lenard. Several papers on the Hyper-Kloosterman of Deligne'. ca 1978
  22. Publication in Chinese. 1979
  23. Research proposals for 1982 submitted to National Science Foundation and sent to Mahler for review, because they build on his work
  24. Expenses book for trip to USA, 7 September 1968 to 2 December 1969
  25. Miscellaneous correspondence (mainly business) and addresses 1963-79 (mainly 1978-79)
  26. Correspondence from Cambridge University Press 1980
  27. Information on the Einstein Institute of Mathematics and Computer Science at The Hebrew University of Jerusalem 1987 (this institution is assisted by The Kurt Mahler Fund for Research in Mathematics)
62/11
    1-5 Typescripts and drafts of papers

  1. Box of near-final typescripts for published papers: 'On some special decimal fractions;' 'Applications of a theorem by A.B. Shidlovski;' 'On Algebraic differential equations satisfied by automorphic functions;' 'Remarks on a paper by W. Schwarz;' 'An arithmetic remark on entire periodic functions;' 'Baker's Theorems;' 'A remark on the computation of the Fourier coefficients of the modular function;' 'On the order function of a transcendental number;' 'The representation of squares to the base 3;' (manuscript), 'The Interpolation Series for a continuous p-adic function of two variables;' 'On a paper by A. Baker on the approximation of rational powers of e;' 'Functions on quadratic extensions of Qp;' 'On a class of functions on finite algebraic extensions of the p-adic field;' 'On a special function;' 'On a lemma by P. Turán on Diophantine approximation;' 'On a special approximation problem;' 'Some results on decimal fractions;' 'On a theorem in the geometry of numbers in a space of Laurent Series;' 'Algebraic approximations of a special number;' 'Chapter 1: Estimates for |F(x,y)|;' 'On a problem in Diophantine Approximations;' 'A short treatment of the Reimann Integral;' 'The ┌-function' University of Manchester; 'On the Staudt-Clauseu theorem' (photocopy of manuscript); 'Chapter 3. Discriminants and Resultants' (typescript with handwritten corrections); 'An elementary existence theorem for entire functions;' 'Arithmetic properties of lacunary power series with integral coefficients;' 'A remark on recursive sequences;' 'On a lemma by A.B. Shidlovski;' 'An unsolved problem on the powers of 3/2;' 'Behrend's papers on number theory;' 'On the approximation of real numbers by roots of integers;' 'Perfect systems' and 'Vollkommene Systeme' (German version)
  2. Manuscript in German; duplicated typescript in German
  3. Lecture notes and drafts on work by A. Baker, including: 'A lecture on a Theorem of A. Baker' 10th S.R.I. January 1970, Hobart; 'Baker's trancendency theorems' 'Manuscript by K. Mahler : Notes to A. Baker: Spriudzuk's Theorem, Real case;' 'On a theorem by A. Baker' (photocopy with corrections, heading amended to 'Chapter 8 A. Baker's theorem on logarithms of algebraic numbers')
  4. Assorted mostly untitled typescripts and drafts
  5. Assorted untitled typescripts and drafts
62/12
    1-6 Drafts for books

  1. Folder labelled 'Red p-adic (Mahler's book)' with some duplicated draft chapters
  2. Red springback folder with photocopy of manuscript for Introduction to p-adic numbers and their functions (second edition) with corrections and some correspondence with the publisher
  3. Proofs for Introduction to p-adic numbers and their functions (first edition, 1973)
  4. Duplicated typescript of a book (to do with Minkowski, 16 Chapters, 204 pages plus index) with some handwritten corrections
  5. Typescript with corrections, Chapter 1 ('Arithmetical lemmas')-8
  6. Manuscript 'The Theorem of Schneider' (in envelope labelled 'Notes for Book')

    7-9 Lecture notes

  7. Notes for R.G. Brett Memorial Lecture, Hobart 1976: 'On the decimal fraction 0.123…1001…' (manuscript)
  8. Copies of 1964 lectures: 'General Theorems on Lattice Points: Two lectures given by Professor K. Mahler, F.R.S., at University of Melbourne on 12th and 14th May 1964;''Periodic Algorithms for Algebraic Number Fields: Lectures given at the Fourth Summer Research Institute of the Australian Mathematical Society held in the University of Sydney, January, 1964'
  9. 'Lectures on Geometric Number Theory ex Kurt Mahler Notre Dame. Notes by Paul A. Viebrock Summer Session 1962' (duplicated typescript)

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    1-12 Lecture notes (cont)

  1. Lecture notes (numbered 1-9 in Chinese) 'Algebraic functions and their Integrals' (photocopies of manuscript)
  2. Lecture notes: 'Geometry of Numbers'(manuscript); 'Theta Functions' (manuscript); 'The Riemann Theta Function' (manuscript); 'Schneider's Theorem' (photocopy of manuscript, numbered 'V'); 'The Congruence Subgroup' (photocopy of manuscript, numbered 'II'); SSTP Special Lecture 'On the Zeros of the Polynomials ~' (photocopy of typescript); photocopy of untitled manuscript (3pp)
  3. 'A property of sets of positive integers closed under addition' 1974 (photocopy); 'Lecture to the Australian Academy of Science' (typescript); 'The Decimal Expansion of an Irrational Number' (manuscript); 'Functions on J' (manuscript); 'Powers' (manuscript)
  4. 'Lectures on selected questions in Number Theory' Canberra, ANU, 1974 (manuscript)
  5. Canberra Lectures on p-adic functions, Spring 1972 (manuscript)
  6. Lectures on geometric methods in Number Theory (manuscript)
  7. 'The Group-theoretical Theorem of Hajós' (manuscript)
  8. 'Lectures on Turán's Method' (manuscript)
  9. 'An introduction to the Calculus of Variations' (manuscript)
  10. 'The Fatoli Theta Functions OSU Fall 1970' (manuscript)
  11. 'Lectures on Transcendental Numbers given at Stony Brook, L.I. July 1969' (manuscript)
  12. 'Applications of the modular and Picard groups to problems of Diophantine Approximations (Fall 1969)' (manuscript)
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    1-2 Manuscript lecture notes and further notes

  1. Box of manuscript lecture notes, mostly on transcendental numbers and modular functions, photocopied set of manuscript I-V beginning 'On the modular function j(w);' also 'Local and Global theory of Algebraic Numbers;' 'Continuous Functions (cont.)' and others
  2. Box of miscellaneous notes (manuscript and some typescript papers, notes and calculations)
62/15
    1-3 Notes and Papers

  1. Box labelled 'Mixed Notes:' assorted notes, calculations and diagrams, some in German; mostly manuscript
  2. Lists of publications from other researchers: J.W.S. Cassels, A. Baker, B.J. Birch, J.E. Clunie, A. Erdélyi, Harish-Chandra, R. Penrose, R. Rado, S.J. Taylor; bibliography (alphabetically by author) contributed by L. Mirsky 1950;
  3. Offprints, copies and drafts of papers by other mathematiciansincluding: five microfiche of papers by Dieudonné, Schöbe and Néron; R.J. McIntosh 'Recurrences for Alternating Sums of Powers of Binomial Coefficients' 1993; S.P. Norton; Gramain, Mignotte and Waldschmidt; chapters of a book in Chinese; A. Brace (in Chinese); G. Szekeres; J.H. Loxton and A.J. van der Poorten; Noriko Yui; A. Khintchine; N. Tschebortarëw (translation); L.J. Mordell; T.W. Cusick 'Dirichlet's Diophantine Approximation Theorem' AMS 1976; J.W.S. Cassels; I.W.L. Cassels; H. Gericke; D.B. Sawyer; article in Acta Mathematica Sinica (in Chinese) on a theorem by Mahler; parts of articles in German
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    1-8 Biographical materials, photographs and miscellaneous materials

  1. Curriculum Vitae 1962 (2-page autobiographical), autobiographical notes 'After I retired;' letters of reference (1930s); London Mathematical Society List of Members 1st December 1972 (Mahler listed as member, Berwick prizewinner 1950, De Morgan medallist 1971); Certificate from Johann Wolfgang Goethe Universität, Frankfurt 1977 (honorary doctorate?); flyers for colloquia given by Mahler 1977; 'Report of the Sixteenth Summer Research Institute of the Australian Mathematical Society' Adelaide 1976; Second Australian Number Theory Conference 1979 program; Canberra Mathematical Association Newsletter October 1964; press clippings; photographs including SSTP-Math Ohio State University Group Photograph 1971, with list of names; birthday cards c.1984
  2. Lists of Mahler's publications and some annual report summaries; notes from a seminar; ANU RSPS dept of Mathematics Annual Report 1973; copy out of 1975 issue
  3. Photographs in folder labelled 'Not pertaining to University House,' of Mahler and others, very few labelled; envelope of negatives (mostly of people); box of 4x5 inch colour sheet film negatives
  4. Selected photographs by Mahler: black and white photos of University House, ANU and Lake Burley-Griffin including panorama series; prints from 4x5 inch colour sheet film; nature prints from 120 film; box of colour slides of Ohio and Canberra
  5. Reviews and book notices of p-adic Numbers and their Functions 1st and 2nd editions
  6. Correspondence received, mostly on mathematical topics, some with papers, proofs and data printouts enclosed, including correspondence from and copies of papers by G.E. Wall 1979
  7. Chinese language aids and notes for mathematical purposes; hand-drawn cardboard go board
  8. Miscellaneous items including: notes for a book review (Nature c.1953); photocopy of a letter to 'Ernst' with mathematical proof 15 July 1972; notes on English style and mathematical usage (author unknown); mathematical poem by A.D. Hope

62/17

    1-10 Manuscript notes and calculations

  1. Notes and calculations in envelope labelled 'From May 1981 for Nov, 1981'
  2. Calculations
  3. Calculations
  4. Notes and calculations
  5. Notes and calculations including on Cantor's Set
  6. Notes and calculations
  7. Calculations and computer printout
  8. Calculations and notes including 'A problem in the Geometry of Numbers;' 'The Elements of p-adic Calculus'
  9. Calculations on polynomials
  10. Assorted notes and calculations including on Baker's second theorem; p-adic functions; 'p-adic numbers' typescript by Dieudonné

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    1-13 Calculations and notes

  1. Hand-drawn diagrams inscribed 'K. Mahler 1940 Drawn in Internment! Approximation of complex numbers'
  2. Program record for computation
  3. Notes, tables and calculations on Modular Functions; copies of articles by H. Rademacher and D.H. Lehmer on the coefficients of modular invariants; untitled typescript
  4. Three notebooks of calculations, one labelled 'Programs for SR52;' mathematical table booklet in German; printed prime number list; two lists of problems for further work; folder labelled 'Calculations'
  5. Hand-drawn charts and diagrams
  6. Tables
  7. Calculations, tables and diagrams
  8. Folder of calculations, tables and diagrams labelled 'Undigested writings'
  9. Untitled typescript with tables and notes
  10. Untitled typescripts and notes
  11. Assorted partial typescripts
  12. Unsorted notes for 'My work with p-adic numbers;' Draft of 'The Dieudonné integral' and some notes; 'Chapter: Polynomial Lattices;' untitled typescripts
  13. Notes and calculations

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    1-11 Calculations and computer printout

  1. Calculations labelled 'Calculations for Paper #221 (Check though)'
  2. Calculations with two papers by A.J. van der Poorten from Macquarie Mathematics Reports 1987
  3. Calculations and tables
  4. Calculations
  5. Notes, tables and calculations
  6. Notes, tables and calculations
  7. Notes, computer calculations, tables and (partial) draft typescript for 'On a Special Integral'
  8. Calculations and computer data printouts
  9. Calculations, tables and computer data printouts
  10. Notes and calculations
  11. Notes, calculations and computer printout

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    1-14 Calculations and computer printout (cont)

  1. Computer printout, notes on Mahler Chains
  2. Calculations and computer printout
  3. Calculations and computer printout
  4. Calculations and notes
  5. Computer printout
  6. Computer printout and tables
  7. Calculations, tables and notes
  8. Calculations and computer printout
  9. Calculations
  10. Computer printout
  11. Computer printout labelled 'Further Tables to Brown and Mahler, A Generalisation of Farey functions'
  12. Calculations and computer printout
  13. Computer printout and notes
  14. Computer printout

442 cm