TABLE OF CONTENTS
Descriptive Summary
Scope and Contents:
Organization
Restrictions
Index Terms
Related Material
Administrative Information
Description of Series
General correspondence:
Magic squares:
Dyad squares:
Pythagorean triangles:
Number theory:
Eulerian squares:
Problem solving:
Exercises, notes and calculations:
Other mathematical topics:
Unidentified and mixed contents:
Personal:
Works of others:
Separated materials and oversize:
Photographs
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A Guide to the Francis L. Miksa Papers,
1929-1972
Francis Louis Miksa was born in Krakow, Poland, in 1901, emigrating with
his parents to the United States in 1904. He grew up largely in Braidwood,
Illinois, completing the sixth grade before going to work. Self-education and
correspondence school courses led to an interest in mathematics. He married
Frances Barowicz in 1924. From 1930 until his retirement in 1963, Miksa
worked as a switchman for the Illinois Bell Telephone Company. He died in
1975.
Miksa's mathematical work began with problem-solving; he
corresponded with other workers and submitted problems and solutions to the
problem-solving literature. Beginning around 1939, he began work on magic
squares and other areas, including Pythagorean triangles, and several number
theory and combinatoric topics. He also developed dyad squares, his own
invention. He deposited several tables with
Mathematics of Computation, and his table of
Stirling numbers was published by the National Bureau of Standards. His
interest in magic squares led to new algorithms for producing 5×5 and 7×7 magic
squares exhaustively without duplication. This work is embodied in a six volume
dittoed work. Miksa carried on a wide correspondence among recreational and
professional mathematicians. His correspondence with Leo Moser resulted in
collaboration in published work.
Source: Miksa, Francis L., Jr., "Francis Louis Miksa (1901-1975)." Unpublished
typescript, 1979, 3 pp.
Return to the Table of Contents
Papers contain Miksa's correspondence with problem-solvers, amateur,
and professional mathematicians. Letters may occur in the correspondence files
(1937-1972; 19 in.), or with associated mathematical work. The bulk of the
collection consists of calculations and drafts for Miksa's work on magic
squares, Pythagorean triangles, dyad squares, Stirling numbers, various number
theory topics, and problem-solving. The development of his studies of magic and
dyad squares, both involving applications of group theory methods, is well
illustrated in the letters, calculations, and preliminary tables.
Miksa kept his papers largely in looseleaf notebooks, sometimes with more than one
mathematical topic occupying a notebook. These original files have usually been
kept together, necessitating the Unidentified and Mixed Contents series.
Correspondents include W.H. Benson, A.L. Candy, R.E. Greenwood, J.S. Madachy,
S.A. Moore, L. Moser, C. Tobin, and C.W. Trigg.
Forms part of the Archives of American Mathematics.
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Organization |
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Organized into the following 13 series: |
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General Correspondence |
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Magic Squares |
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Dyad Squares |
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Pythagorean Triangles |
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Number Theory |
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Eulerian Squares |
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Problem Solving |
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Exercises, Notes, and Calculations |
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Other Mathematical Topics |
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Unidentified and Mixed Contents |
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Personal |
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Works of Others |
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Photographs |
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Access Restrictions
Unrestricted access
Use Restrictions
These papers are stored remotely at CDL. Advance notice required for retrieval.
Contact repository for retrieval. Photographs are stored on-site.
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Subjects (Persons) |
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Benson, William H. |
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Candy, Albert L. (Albert Luther),
1857- |
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Greenwood, R. E. |
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Madachy, Joseph S. |
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Miksa, Francis L., 1901-1975 --
Archives |
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Moser, Leo, 1921-1970 |
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Tobin, Cyril |
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Trigg, Charles W. |
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Subjects |
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Combinatorial analysis |
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Magic squares |
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Mathematical recreations |
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Number theory |
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Problem solving |
Return to the Table of Contents
Return to the Table of Contents
Francis L. Miksa Papers, 1929-1972, Archives of American Mathematics,
Dolph Briscoe Center for American History, University of Texas at Austin.
This collection was processed by Frederic Burchsted in April 1990.
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General correspondence: |
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1939-44 |
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1944-45 |
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1949 |
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1950 |
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1951 |
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1951-52 |
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1952-54 |
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1955 |
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1956 |
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1957 |
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1959-61 |
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1962-63 |
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1963-67 |
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1968-72 |
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Becker, H.W.,
1953-56 |
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Conner, Louis; Cummins, D.R. |
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Lauthan, C.P. |
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Luck, Candy, Antone
(1942-43) |
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Moore, S.A.,
1937-38 |
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1937, 1940-41 |
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1938-40 |
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1939-40 |
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O'Keefe, J.J. |
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Tobin, C. |
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Letters to Andrew S. Anema, Sr. [donated by Anema's son, Jay Anema, March 2010] |
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Magic squares: |
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| 87-2/4 |
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Lattices, schedules, tables, working out of codes, letter
to Loomis |
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Tables of all combinations (4×4, 5×5, 6×6), including
Candy's 5×5 |
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Studies, List of groups, Letter to Moser (1953), letters
from Anema (1948-1955), Loomis (n.d.),
1948-1955 and undated |
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Group theory and magic squares (1950s and 60s); Letter to
Struyk (1955),
1950s-1960s |
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Candy's pandiagonal squares of type II, A table of all
valid column permutations, Letter to Struyk,
1955 |
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Stewart's equations; Anema, Complex rotating 9th order
magic squares; Letter from Anema,
1955 |
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Table of all possible 880 squares, by F.W. Haunnum, with
letter,
1969 |
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Table of 880 squares (Stewart's method), with letters from
Stewart,
1962 |
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Explanations and combinations (4×4, 6×6) |
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A collection of transparent ozalid masters (5×5, 7×7),
with letter to Stewart,
1962 |
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5×5 |
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Spiral-bound tables and loose sheets |
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Combinations that give the I class squares, and similar
but unlabeled tables |
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Carbon copies of basic lattices and squares for the
pandiagonal and half-pandiagonal classes |
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Symmetric magic squares (in pencil), sheets
2429-2772 |
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Sheets 2773-3034 |
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Cards used for symmetric squares |
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General, non-symmetric |
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Magic combinations and auxiliary squares |
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5th order of auxiliary squares; Vol. 4 material:
"The tranforms and their
patterns"; Schedule no. 5, cyclic, etc. |
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All symmetric squares, pandiagonal and half pandiagonal,
under G58
transforms |
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Auxiliary squares: A=6-10, A=11=14 |
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Auxiliary squares: A=15-19, A=20-24 |
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Auxiliary squares: A=25-29, A=30=34 |
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Auxiliary squares: A=35-39, A=40-44 |
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Dittoed book plus ms and ts material |
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Ms figuring sheets |
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Working out of the auxiliary squares of the horizontal
sides of combinations |
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Pandiagonal, 72 basic and 72 permuted |
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| 87-2/12 |
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Calculations, dittoed drafts for book |
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| 87-2/53 |
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Punch cards |
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7×7 |
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| 87-2/12 |
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Plastic ring binder with letters from N. Stewart
1963) |
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Ms squares and diagrams on graph paper |
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Arranged by classes, also some of Anema's
results |
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Work on 7×7 squares, ms and ts |
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Notes, tables, and dittoed drafts |
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| 87-2/13 |
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A-frame, B-frame: |
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1 - 7 |
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8 - 18 |
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Frame B, sections 1-4 |
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Transforms, transforming diagonals, codes of
lattices |
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Work on lattices (largely ms) |
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| 87-2/14 |
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The 3456 magic square lattices, eDE, with letter to
Struyk,
1955 |
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Magic combinations and auxiliary squares, vol.
1 |
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vol. 2 |
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vol. 3 |
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Aux. [X & Y], Frame -V-; Aux. [Y], Frame
-H- |
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Working out of auxiliary squares, columns 1 -
5 |
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| 87-2/15 |
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Table of partitions of 175, with letter to Moser,
1962 |
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Table of partitions of 175 of 7×7 magic combinations
(regular type) |
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Table of partitions, old copy pages |
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Table of partitions of 175, final corrected
copy |
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Explanations of substitution group method, with
resulting squares; correspondence with Stewart and A. Struyk,
1957-62 |
| Box |
| 87-2/16 |
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On the construction of the 7×7 pandiagonal magic squares
by substitution methods |
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Lattices, pandiagonal, associated |
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Pandiagonal, associated |
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Associated pandiagonal, misc. results |
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The 3456 pandiagonal associated magic squares…arranged
in ascending order according to the first row |
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| 87-2/17 |
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Pan-associated |
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Table of combinations |
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Original work on the table of all
combinations |
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Table of 957 332 combinations |
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Symmetric, non-pandiagonal |
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Symmetric combinations of 7×7 magic squares of the
irregular type |
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| 87-2/19 |
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Special symmetric magic squares |
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Letter to Moser (1962); Corrections to 7×7 combination
tables; Symmetric group 5040 transformations,
1962 and undated |
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Transformations and codes, copies of works of
others |
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Codes 1-8 |
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Table of all codes for 85 basic lattices |
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Codes for 85 squares and basic lattices |
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Basic 1C1 lattice and developing the rest of 120 .D.
squares |
| Box |
| 87-2/20 |
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Developing E.D. lattices and squares by symmetric G75040 permutations |
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Work done on the essential substitutions for the G742 inv. substitution
group |
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Book |
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| 87-2/20 |
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"This is a perfect set…",
dittoed with typed additions |
| Box |
| 87-2/21 |
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"This is my own set": vol. 4
& 6 |
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Vols. 1,2,3 |
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Vol. 4 (3 slightly differing versions) |
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Vol. 5 (2 versions) |
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Vol. 6 |
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Abstract, and notes on organization and
prices |
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Dyad squares: |
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| 87-2/23 |
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Vol. 1 |
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Vol. 2 |
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Vol. 3 |
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Candy's 15 arrays |
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Tobin's schedule |
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Problem of the 7th order dyad squares, Problem of the
"Baseball Schedules," Two
combinatorial problems, Master table of all combinations of 4 dyads…, A study
of 7×7 dyad squares |
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Tables, work on compatible groups |
| Box |
| 87-2/24 |
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Master table of all combinations of the 21 dyads taken 3
at a time, with correspondence with O. Gross and H. Lauer,
1962 |
| Box |
| 87-2/57 |
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Game or puzzle offered to Parker Bros. |
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7×7 |
| Box |
| 87-2/24 |
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Photocopies of ms tables 5 - 18 |
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7×7 squares, 11×11 groups |
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Correspondence (1942-63), squares, explanatory texts;
Goofy Baseball Game,
1942-1963 and undated |
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The problem of the 7th order dyad squares |
| Box |
| 87-2/25 |
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A study of 7×7 dyad squares |
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9×9 |
| Box |
| 87-2/25 |
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Ts legal sheets, Ms corrections |
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Ms tables (unlabeled) |
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Paper ruled for 9×9 squares, some sheets with
squares |
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Work sheets |
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Notebook with dyad square work |
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400 perfect squares arranged in standard
form |
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| 87-2/26 |
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Schedule |
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Work on schedules beginning with 1-1 |
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Work sheets for schedules, incompatible groups,
1962 |
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Incompatible groups, master table |
| Box |
| 87-2/27 |
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Incompatible groups to be used to develop 9×9 dyad
squares |
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Incompatible groups |
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Master table of all combinations of the (92) dyads |
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Variations and solutions of schedule #162; Attempt to
find all dyad squares, perfect and imperfect, by incompatible
groups |
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Use of schedule #162 |
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Work sheets of the new method of finding perfect squares
from schedule #162 |
| Box |
| 87-2/28 |
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Work sheets for schedule #162 |
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| 87-2/53 |
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Punch cards |
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11×11 |
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| 87-2/28 |
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Letters and tables (R.J. Keevers), (1969-70), Brother U.
Alfred (1961-62),
1961-1970 |
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Original manuscript (1962), Table of all combinations,
1962 and undated |
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Typed tables |
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Efforts to make |
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Ms calculations and tables |
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Pythagorean triangles: |
| Box |
| 87-2/28 |
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Studies, tables, counts (dittoed copies) |
| Box |
| 87-2/29 |
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Isoperimetric with Moser; Some work per Moser |
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Work sheets on multiple primitive Pythagorean triangles
having the same perimeter |
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Count for my part of the tables and related
matters |
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x2 + y2 = N |
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Tapes |
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Clear cards for marking Pythagorean triangles, also 1 set
already marked and paper cards |
| Box |
| 87-2/55 |
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Clear cards for marking Pythagorean triangles, also 1 set
already marked and paper cards |
| Box |
| 87-2/56 |
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Cards for areas of10 × 106 to
15 × 106 (Special problem) |
| Box |
| 87-2/29 |
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Table of primitive Pythagorean triangles
(carbon) |
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Primitive Pythagorean triangles and formulas, letters and
calculations,
1952, 1969 |
| Box |
| 87-2/30 |
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Primitive Pythagorean triangles and formulas, primes and
factors; Count of all primitive Pythagorean triangles whose areas are below one
billion; Table of primitive equiareal Pythagorean triangles below 10 billion in
area |
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Primitive Pythagorean right triangles, developed by
generators [m,n], and of A,B,C and their areas |
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Equal area Pythagorean triangles; by formulas 1, 2, and 3
by Abel Jordan; Primes and factors - letters, tables, calculations |
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Pythagorean triangles by areas: |
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vol. 1 |
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vol. 2 |
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vol. 3 |
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vol. 5 |
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vol. 6 |
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Vol. 1, with letters from A. Anema,
1954 |
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Primitive, according to increasing areas, Generators ABC,
Area, S |
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| 87-2/32 |
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Primitive, according to increasing areas: defective
scattered sheets, with ms pages |
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Table of primitive Pythagorean triangles, arranged
according to increasing perimeters, part 1 |
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Part 2, plus, Study of primitive, isoperimetric
Pythagorean triangles |
| Box |
| 87-2/33 |
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Table of primitive Pythagorean triangles, arranged
according to increasing perimeters, part 1 - Sheets with
corrections |
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Isoperimetric triangles whose perimeters differ by
2 |
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Centroid and incircle problems |
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Number theory: |
| Box |
| 87-2/33 |
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Table of quadratic partitions, x2 + y2 = N |
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Results on cards |
| Box |
| 87-2/34 |
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Additional quadratic partitions, 100 009 to 149
993 |
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Solutions of x2 + y2 + z2 + w2 = R2 |
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A2 + B2 + C2 = R2 |
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Table of binomial coefficients |
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Original computations of the binomial coefficients in the
expansion of (1 + 1)n,
1954 |
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Study of Bernoulli's polynomials, with letters,
1947 |
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Cunningham's binary canon; Exercises in Cunningham's
binary canon |
| Box |
| 87-2/35 |
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Table of indices and residues for different primes (to be
used with Cunningham's binary canon) |
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Residues and indices |
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Power residues modulo P |
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Odd-abundant numbers; Fermat's theorem, Work with L.
Moser |
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Table of least primitive roots, Table of linear forms,
Methods of factoring |
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Algebraic forms (#13), also geometry |
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Solution of ax ± by = c; Moore's series for Pell equations
(#16),
1938? |
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Pell's equation; Krishnaswami conjecture; Power
sums |
| Box |
| 87-2/36 |
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Problems and solutions, with letters,
1944-46 |
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Table of prime numbers,
1938 |
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Integral means and other problems, with letters,
late 1940's |
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Formulas (#9) |
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Congruences of the form 10n =
mod P; Some solutions of the forms aabbcc = o mod P |
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Work sheets on solutions to x2
-Dy2 = -1; Solution to form ababbbcc = N2 |
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Quadratic reciprocity |
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Moser's recursion formula |
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Linear quadratic forms; Quadratic linear forms |
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Eulerian squares: |
| Box |
| 87-2/37 |
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All possible Tobin's squares made by the strip
method |
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Candy's 15 schedules, Tobin's method |
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Candy's schedules |
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Codes 4 - 6 |
| Box |
| 87-2/57 |
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Collection of results on Tobin's 7×7 squares |
| Box |
| 87-2/37 |
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Tobin's codes |
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Tobin's method (letters),
1943 |
| Box |
| 87-2/38 |
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Tobin's method, permutation groups, Tobin's
schedules |
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Tobin's method, with papers on group theory Gab a=1 − a=8 |
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Problem solving: |
| Box |
| 87-2/38 |
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Problems,
1936-39 |
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Late 1930s |
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1938 |
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1937-38, 1950-53 |
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1940-41 |
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1945-47 |
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1948 |
| Box |
| 87-2/39 |
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Problems and correspondence,
1940s |
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Tables, calculations, problems, letters,
1952-53 |
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Problems, calculations, letters (Moser and others),
1949 |
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Misc. problems, spiral notebook |
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Problem of Arbelos and others, with letters,
1942 |
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Problems of inscribed circles by S.A.M. and A.L.M.; Curve
of pursuit,
1938 |
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Match problem, Gamma function, with letters,
1946-48 |
| Box |
| 87-2/40 |
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Probleme des menages |
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Point inside a triangle |
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Solution of a problem by V. Thebault |
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|
Firing ship and misc. problems,
late 1930s |
| Box |
| 87-2/41 |
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Elliptical egg in a cone and other problems,
1939 |
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|
Pile of four spheres, weight of, and letters (Johnson),
1947 |
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Geometry problems,
1942 |
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Bored cube problem and others,
1946-48 |
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Problem of Easter, and others,
1943 |
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|
Will problem and others, 1937-40
(letters, C. Tobin, 1951)
1937-1951 |
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Mechanics problems,
1937 |
| Box |
| 87-2/42 |
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Logic problems and others, early
1940s |
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|
Snow problem and others, early 1940s(?) (letter, A.L.
Candy, 1943),
1940s |
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Electrical problems |
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Early 1930's |
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Lyons and other electrical problems |
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Johnson's problem; Moore's problem of Joe, Jack and Bill
generalized,
1940 |
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Centroid and incircle problems |
| Box |
| 87-2/43 |
|
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Inscribed circles; #2110; Triangle; Crossing the
river |
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McCankey's problem; Sphere resting in water; Ladder
problem; Rational right triangles; Cow and goat; Sphere volumes |
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|
Equations of lines and parabolas, with letters,
1939-41 |
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|
SAM's parabola |
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|
School Science and Math, with S.A.
Moore letters,
1940-41 |
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Exercises, notes and calculations: |
| Box |
| 87-2/43 |
|
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Area of paraboloid and others |
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|
8 notebooks |
| Box |
| 87-2/44 |
|
|
Calculus, determinants, geometry |
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|
|
Friden's and Marchant's calculator methods, with
calculations |
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|
Geometry and trigonometry; Some multiplications on adding
machine |
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|
Program: Canula electronic calculator, with calculations;
printed matter |
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|
Trigonometry; Formulas for analytic geometry connected
with parabola |
| Box |
| 2010-078/1 |
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"Misc." - problems, notes [donated by Jay Anema, March 2010] |
Return to the Table of Contents
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Other mathematical topics: |
| Box |
| 87-2/44 |
|
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[Diagram of contiguous colored shapes] |
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Latin Squares |
| Box |
| 87-2/45 |
|
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Moser's problem on power sum (letters),
1951 |
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|
|
Table of Stirling numbers of the second kind and of
exponential numbers; Table of Stirling numbers of the first kind |
|
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|
Original manuscripts: Stirling numbers of the first
kind |
Return to the Table of Contents
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| |
Unidentified and mixed contents: |
| Box |
| 87-2/45 |
|
|
Date problems, Quadratic linear forms, Candy's
transformation #1, Tablesof squares, Pythagorean triangles. |
|
|
|
Factoring exercises, Triangles with integral sides and
medians, codes 3 & 4 |
|
|
|
King's tour on chessboard; Unidentified
calculations |
| Box |
| 87-2/57 |
|
|
Large sheets with calculations, including geometrical
problems and dyad squares |
| Box |
| 87-2/45 |
|
|
Magic squares (notes on methods), calculator programs,
Unidentified tables |
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|
|
Ms tables |
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|
Moron's dissection, x2 +
y2 + z2 + w2 = R2 |
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|
Notebook containing largely number theory and Pythagorean
triangles |
| Box |
| 87-2/46 |
|
|
Notes (alphabetical card file);
"Materials found among School Science
and Mathematics magazine" |
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|
Sets of four squares with reversed digits, x2 + y2 + z2 + w2 = r2, Pythagorean triangles, Unidentified |
|
|
|
Unidentified tables |
|
|
|
Unidentified tables 1-9.0.A. |
|
|
|
Unidentified tapes |
Return to the Table of Contents
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| |
Personal: |
| Box |
| 87-2/47 |
|
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Papers by Francis L. Miksa |
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|
Library of Francis L. Miksa: Catalog;
Bookplate |
|
|
|
Electrical correspondence school,
1929 and undated |
|
|
|
Electrical problems at night school I |
| Box |
| 87-2/48 |
|
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Electrical problems at night school II |
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|
|
Magazine list and letters concerning sale |
|
|
|
Medical information |
Return to the Table of Contents
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| |
Works of others: |
| Box |
| 87-2/57 |
|
|
Anema, A.S., Thalesian 17th order magic square,
1945 |
| Box |
| 87-2/48 |
|
|
Benson, W.H., The World of Magic Squares, with letter,
1964 |
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|
|
Magical Magic Squares (1949); Tri-Magic Squares,
1949 and undated |
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|
|
British Association Mathematical Tables V - Factor tables
with insertions |
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|
|
Brousseau, Brother A., Number Theory Tables,
1973 |
| Box |
| 87-2/49 |
|
|
The Dial,
1951-57 |
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|
The Graphic Work of M.C. Escher,
1960 |
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|
Finite sums and groups of substitutions, ms
copies |
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|
|
Glaischer, J.W.L., General Summation Formulae in Finite
Differences |
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|
Gould, H.W., Combinatorial Identities, 1959; Anon.,
Approximate Values of Stirling Numbers of the Second Kind, 1958,
1958-1959 |
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|
Gruenberger's list of primes, Computing News |
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|
|
Magic squares, etc. |
| Box |
| 87-2/50 |
|
|
Moser, L. Introduction to the Theory of Numbers, (Items
sent by L. Moser)
1957 |
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|
|
Pamphlets, including calculator manuals |
|
|
|
RAND Corporation Approximations in Numerical Analysis,
1950 |
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|
|
Reprints |
| Box |
| 87-2/51 |
|
|
Robinson, R.M., Stencils for solving x2 = a(mod m),
1940 |
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|
|
Stewart, J., 880 Magic Squares of the Fourth Order;
Lehmer, List of prime numbers; Special paper grid for 5×5 and 7×7 magic squares
(Oversize box) |
|
|
|
Negative glass plate of the 880 4th order magic
squares |
|
|
|
Table of the First Ten Powers of the Integers from 1 to
1000, Work Program, WPA,
1939 |
| box |
| 87-2/51 |
|
|
Math, science, and technology book catalogs: |
|
|
|
|
1930-1937 |
| box |
| 87-2/58 |
|
|
|
1937-1947 and undated |
|
|
|
International Correspondence Schools, "Manual of
Information for Students,"
1922 |
|
|
|
Illinois Bell Telephone Company, "Annual Report,"
1946 |
Return to the Table of Contents
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| |
Separated materials and oversize: |
| Box |
| 87-2/52 |
|
|
Cards used for symmetric squares |
| Box |
| 87-2/53 |
|
|
Punch cards for 5×5 magic squares; Punch cards for 9×9
dyad squares |
| Box |
| 87-2/54 |
|
|
Tapes |
|
|
|
Clear cards for marking Pythagorean triangles, also 1 set
already marked, and paper cards |
| Box |
| 87-2/55 |
|
|
Clear cards for marking Pythagorean triangles, also 1 set
already marked, and paper cards |
| Box |
| 87-2/56 |
|
|
Cards for areas of10 × 106 to
15 × 106 (Special problem) |
| Box |
| 87-2/57 |
|
|
Oversize |
|
|
|
|
Game or puzzle offered to Parker Bros. |
|
|
|
|
Collection of results on Tobin's 7×7 squares |
|
|
|
|
Large sheets with calculations, including geometrical
problems and dyad squares |
|
|
|
|
Anema, A.S., Thalesian 17th order magic square,
1945 |
|
|
|
|
Stewart, J., 880 Magic Squares of the Fourth Order;
Lehmer, List of prime numbers; Special paper grid for 5×5 and 7×7 magic
squares |
Return to the Table of Contents
|
|
|
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|
| |
Photographs |
| box |
| 4RM51 |
|
|
Photographs (donated by Mr. Miksa's family in
1991), 1953 |
| Box |
| 4RM203c |
|
|
Photographs of Miksa and Andrew S. Anema, Sr. [donated by Anema's son, Jay Anema, March 2010] |
Return to the Table of Contents
|
