University of Texas, Dolph Briscoe Center for American History

A Guide to the Francis L. Miksa Papers, 1929-1972

Descriptive Summary

Creator Miksa, Francis L., 1901-1975
Title: Francis L. Miksa Papers,
Dates: 1929-1972
Accession No.: 87-2; 1991; 2010-078
OCLC Number 19401161
Extent: 40 ft. 2 in.
Language Materials are written in English.
Repository: Dolph Briscoe Center for American History, The University of Texas at Austin

Biographical Note

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 Unpublished typescript, 1979, 3 pp.

Scope and 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.



Organized into the following 13 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
Works of Others


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.

Index Terms

Subjects (Persons)
Benson, William H.
Candy, Albert L. (Albert Luther), 1857-
Greenwood, R. E.
Madachy, Joseph S.
Miksa, Francis L., 1901-1975 -- Archives
Moser, Leo, 1921-1970
Tobin, Cyril
Trigg, Charles W.
Combinatorial analysis
Magic squares
Mathematical recreations
Number theory
Problem solving

Related Material

Letters to R.E. Greenwood are located in the GREENWOOD (ROBERT E.) PAPERS.

Administrative Information

Preferred Citation

Francis L. Miksa Papers, 1929-1972, Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin.

Processing Information

This collection was processed by Frederic Burchsted in April 1990.

Detailed Description of the Papers


General correspondence:

87-2/1 1939-44
87-2/2 1951-52
87-2/3 1962-63
Becker, H.W., 1953-56
Conner, Louis; Cummins, D.R.
Lauthan, C.P.
87-2/4 Luck, Candy, Antone (1942-43)
Moore, S.A., 1937-38
1937, 1940-41
O'Keefe, J.J.
Tobin, C.
2010-078/1 Letters to Andrew S. Anema, Sr. [donated by Anema's son, Jay Anema, March 2010]


Magic squares:

87-2/4 Lattices, schedules, tables, working out of codes, letter to Loomis
Tables of all combinations (4×4, 5×5, 6×6), including Candy's 5×5
87-2/5 Studies, List of groups, Letter to Moser (1953), letters from Anema (1948-1955), Loomis (n.d.), 1948-1955 and undated
Group theory and magic squares (1950s and 60s); Letter to Struyk (1955), 1950s-1960s
Candy's pandiagonal squares of type II, A table of all valid column permutations, Letter to Struyk, 1955
Stewart's equations; Anema, Complex rotating 9th order magic squares; Letter from Anema, 1955
Table of all possible 880 squares, by F.W. Haunnum, with letter, 1969
87-2/6 Table of 880 squares (Stewart's method), with letters from Stewart, 1962
Explanations and combinations (4×4, 6×6)
A collection of transparent ozalid masters (5×5, 7×7), with letter to Stewart, 1962
87-2/6 Spiral-bound tables and loose sheets
87-2/7 Combinations that give the I class squares, and similar but unlabeled tables
Carbon copies of basic lattices and squares for the pandiagonal and half-pandiagonal classes
Symmetric magic squares (in pencil), sheets 2429-2772
87-2/8 Sheets 2773-3034
87-2/52 Cards used for symmetric squares
87-2/8 General, non-symmetric
Magic combinations and auxiliary squares
5th order of auxiliary squares; Vol. 4 material: "The tranforms and their patterns"; Schedule no. 5, cyclic, etc.
All symmetric squares, pandiagonal and half pandiagonal, under G58 transforms
87-2/9 Auxiliary squares: A=6-10, A=11=14
Auxiliary squares: A=15-19, A=20-24
87-2/10 Auxiliary squares: A=25-29, A=30=34
Auxiliary squares: A=35-39, A=40-44
87-2/11 Dittoed book plus ms and ts material
Ms figuring sheets
Working out of the auxiliary squares of the horizontal sides of combinations
Pandiagonal, 72 basic and 72 permuted
87-2/12 Calculations, dittoed drafts for book
87-2/53 Punch cards
87-2/12 Plastic ring binder with letters from N. Stewart 1963)
Ms squares and diagrams on graph paper
Arranged by classes, also some of Anema's results
Work on 7×7 squares, ms and ts
Notes, tables, and dittoed drafts
87-2/13 A-frame, B-frame:
1 - 7
8 - 18
Frame B, sections 1-4
Transforms, transforming diagonals, codes of lattices
Work on lattices (largely ms)
87-2/14 The 3456 magic square lattices, eDE, with letter to Struyk, 1955
Magic combinations and auxiliary squares, vol. 1
vol. 2
vol. 3
Aux. [X & Y], Frame -V-; Aux. [Y], Frame -H-
Working out of auxiliary squares, columns 1 - 5
87-2/15 Table of partitions of 175, with letter to Moser, 1962
Table of partitions of 175 of 7×7 magic combinations (regular type)
Table of partitions, old copy pages
Table of partitions of 175, final corrected copy
Explanations of substitution group method, with resulting squares; correspondence with Stewart and A. Struyk, 1957-62
87-2/16 On the construction of the 7×7 pandiagonal magic squares by substitution methods
Lattices, pandiagonal, associated
Pandiagonal, associated
Associated pandiagonal, misc. results
The 3456 pandiagonal associated magic squares…arranged in ascending order according to the first row
87-2/17 Pan-associated
Table of combinations
Original work on the table of all combinations
87-2/18 Table of 957 332 combinations
Symmetric, non-pandiagonal
Symmetric combinations of 7×7 magic squares of the irregular type
87-2/19 Special symmetric magic squares
Letter to Moser (1962); Corrections to 7×7 combination tables; Symmetric group 5040 transformations, 1962 and undated
Transformations and codes, copies of works of others
Codes 1-8
Table of all codes for 85 basic lattices
Codes for 85 squares and basic lattices
Basic 1C1 lattice and developing the rest of 120 .D. squares
87-2/20 Developing E.D. lattices and squares by symmetric G75040 permutations
Work done on the essential substitutions for the G742 inv. substitution group
87-2/20 "This is a perfect set…", dittoed with typed additions
87-2/21 "This is my own set": vol. 4 & 6
Vols. 1,2,3
87-2/22 Vol. 4 (3 slightly differing versions)
Vol. 5 (2 versions)
Vol. 6
Abstract, and notes on organization and prices


Dyad squares:

87-2/23 Vol. 1
Vol. 2
Vol. 3
Candy's 15 arrays
Tobin's schedule
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
Tables, work on compatible groups
87-2/24 Master table of all combinations of the 21 dyads taken 3 at a time, with correspondence with O. Gross and H. Lauer, 1962
87-2/57 Game or puzzle offered to Parker Bros.
87-2/24 Photocopies of ms tables 5 - 18
7×7 squares, 11×11 groups
Correspondence (1942-63), squares, explanatory texts; Goofy Baseball Game, 1942-1963 and undated
The problem of the 7th order dyad squares
87-2/25 A study of 7×7 dyad squares
87-2/25 Ts legal sheets, Ms corrections
Ms tables (unlabeled)
Paper ruled for 9×9 squares, some sheets with squares
Work sheets
Notebook with dyad square work
400 perfect squares arranged in standard form
87-2/26 Schedule
Work on schedules beginning with 1-1
Work sheets for schedules, incompatible groups, 1962
Incompatible groups, master table
87-2/27 Incompatible groups to be used to develop 9×9 dyad squares
Incompatible groups
Master table of all combinations of the (92) dyads
Variations and solutions of schedule #162; Attempt to find all dyad squares, perfect and imperfect, by incompatible groups
Use of schedule #162
Work sheets of the new method of finding perfect squares from schedule #162
87-2/28 Work sheets for schedule #162
87-2/53 Punch cards
87-2/28 Letters and tables (R.J. Keevers), (1969-70), Brother U. Alfred (1961-62), 1961-1970
Original manuscript (1962), Table of all combinations, 1962 and undated
Typed tables
Efforts to make
Ms calculations and tables


Pythagorean triangles:

87-2/28 Studies, tables, counts (dittoed copies)
87-2/29 Isoperimetric with Moser; Some work per Moser
Work sheets on multiple primitive Pythagorean triangles having the same perimeter
Count for my part of the tables and related matters
x2 + y2 = N
87-2/54 Tapes
Clear cards for marking Pythagorean triangles, also 1 set already marked and paper cards
87-2/55 Clear cards for marking Pythagorean triangles, also 1 set already marked and paper cards
87-2/56 Cards for areas of10 × 106 to 15 × 106 (Special problem)
87-2/29 Table of primitive Pythagorean triangles (carbon)
Primitive Pythagorean triangles and formulas, letters and calculations, 1952, 1969
87-2/30 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
Primitive Pythagorean right triangles, developed by generators [m,n], and of A,B,C and their areas
Equal area Pythagorean triangles; by formulas 1, 2, and 3 by Abel Jordan; Primes and factors - letters, tables, calculations
Pythagorean triangles by areas:
87-2/30 vol. 1
vol. 2
87-2/31 vol. 3
vol. 5
vol. 6
Vol. 1, with letters from A. Anema, 1954
Primitive, according to increasing areas, Generators ABC, Area, S
87-2/32 Primitive, according to increasing areas: defective scattered sheets, with ms pages
Table of primitive Pythagorean triangles, arranged according to increasing perimeters, part 1
Part 2, plus, Study of primitive, isoperimetric Pythagorean triangles
87-2/33 Table of primitive Pythagorean triangles, arranged according to increasing perimeters, part 1 - Sheets with corrections
Isoperimetric triangles whose perimeters differ by 2
Centroid and incircle problems


Number theory:

87-2/33 Table of quadratic partitions, x2 + y2 = N
Results on cards
87-2/34 Additional quadratic partitions, 100 009 to 149 993
Solutions of x2 + y2 + z2 + w2 = R2
A2 + B2 + C2 = R2
Table of binomial coefficients
Original computations of the binomial coefficients in the expansion of (1 + 1)n, 1954
Study of Bernoulli's polynomials, with letters, 1947
Cunningham's binary canon; Exercises in Cunningham's binary canon
87-2/35 Table of indices and residues for different primes (to be used with Cunningham's binary canon)
Residues and indices
Power residues modulo P
Odd-abundant numbers; Fermat's theorem, Work with L. Moser
Table of least primitive roots, Table of linear forms, Methods of factoring
Algebraic forms (#13), also geometry
Solution of ax ± by = c; Moore's series for Pell equations (#16), 1938?
Pell's equation; Krishnaswami conjecture; Power sums
87-2/36 Problems and solutions, with letters, 1944-46
Table of prime numbers, 1938
Integral means and other problems, with letters, late 1940's
Formulas (#9)
Congruences of the form 10n = mod P; Some solutions of the forms aabbcc = o mod P
Work sheets on solutions to x2 -Dy2 = -1; Solution to form ababbbcc = N2
Quadratic reciprocity
Moser's recursion formula
Linear quadratic forms; Quadratic linear forms


Eulerian squares:

87-2/37 All possible Tobin's squares made by the strip method
Candy's 15 schedules, Tobin's method
Candy's schedules
Codes 4 - 6
87-2/57 Collection of results on Tobin's 7×7 squares
87-2/37 Tobin's codes
Tobin's method (letters), 1943
87-2/38 Tobin's method, permutation groups, Tobin's schedules
Tobin's method, with papers on group theory Gab a=1 − a=8


Problem solving:

87-2/38 Problems, 1936-39
Late 1930s
1937-38, 1950-53
87-2/39 Problems and correspondence, 1940s
Tables, calculations, problems, letters, 1952-53
Problems, calculations, letters (Moser and others), 1949
Misc. problems, spiral notebook
Problem of Arbelos and others, with letters, 1942
Problems of inscribed circles by S.A.M. and A.L.M.; Curve of pursuit, 1938
Match problem, Gamma function, with letters, 1946-48
87-2/40 Probleme des menages
Point inside a triangle
Solution of a problem by V. Thebault
Firing ship and misc. problems, late 1930s
87-2/41 Elliptical egg in a cone and other problems, 1939
Pile of four spheres, weight of, and letters (Johnson), 1947
Geometry problems, 1942
Bored cube problem and others, 1946-48
Problem of Easter, and others, 1943
Will problem and others, 1937-40 (letters, C. Tobin, 1951) 1937-1951
Mechanics problems, 1937
87-2/42 Logic problems and others, early 1940s
Snow problem and others, early 1940s(?) (letter, A.L. Candy, 1943), 1940s
Electrical problems
Early 1930's
Lyons and other electrical problems
Johnson's problem; Moore's problem of Joe, Jack and Bill generalized, 1940
Centroid and incircle problems
87-2/43 Inscribed circles; #2110; Triangle; Crossing the river
McCankey's problem; Sphere resting in water; Ladder problem; Rational right triangles; Cow and goat; Sphere volumes
Equations of lines and parabolas, with letters, 1939-41
SAM's parabola
School Science and Math, with S.A. Moore letters, 1940-41


Exercises, notes and calculations:

87-2/43 Area of paraboloid and others
8 notebooks
87-2/44 Calculus, determinants, geometry
Friden's and Marchant's calculator methods, with calculations
Geometry and trigonometry; Some multiplications on adding machine
Program: Canula electronic calculator, with calculations; printed matter
Trigonometry; Formulas for analytic geometry connected with parabola
2010-078/1 "Misc." - problems, notes [donated by Jay Anema, March 2010]


Other mathematical topics:

87-2/44 [Diagram of contiguous colored shapes]
Latin Squares
87-2/45 Moser's problem on power sum (letters), 1951
Table of Stirling numbers of the second kind and of exponential numbers; Table of Stirling numbers of the first kind
Original manuscripts: Stirling numbers of the first kind


Unidentified and mixed contents:

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
87-2/57 Large sheets with calculations, including geometrical problems and dyad squares
87-2/45 Magic squares (notes on methods), calculator programs, Unidentified tables
Ms tables
Moron's dissection, x2 + y2 + z2 + w2 = R2
Notebook containing largely number theory and Pythagorean triangles
87-2/46 Notes (alphabetical card file); "Materials found among School Science and Mathematics magazine"
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



87-2/47 Papers by Francis L. Miksa
Library of Francis L. Miksa: Catalog; Bookplate
Electrical correspondence school, 1929 and undated
Electrical problems at night school I
87-2/48 Electrical problems at night school II
Magazine list and letters concerning sale
Medical information


Works of others:

87-2/57 Anema, A.S., Thalesian 17th order magic square, 1945
87-2/48 Benson, W.H., The World of Magic Squares, with letter, 1964
Magical Magic Squares (1949); Tri-Magic Squares, 1949 and undated
British Association Mathematical Tables V - Factor tables with insertions
Brousseau, Brother A., Number Theory Tables, 1973
87-2/49 The Dial, 1951-57
The Graphic Work of M.C. Escher, 1960
Finite sums and groups of substitutions, ms copies
Glaischer, J.W.L., General Summation Formulae in Finite Differences
Gould, H.W., Combinatorial Identities, 1959; Anon., Approximate Values of Stirling Numbers of the Second Kind, 1958, 1958-1959
Gruenberger's list of primes, Computing News
Magic squares, etc.
87-2/50 Moser, L. Introduction to the Theory of Numbers, (Items sent by L. Moser) 1957
Pamphlets, including calculator manuals
RAND Corporation Approximations in Numerical Analysis, 1950
87-2/51 Robinson, R.M., Stencils for solving x2 = a(mod m), 1940
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
87-2/51 Math, science, and technology book catalogs:
87-2/58 1937-1947 and undated
International Correspondence Schools, "Manual of Information for Students," 1922
Illinois Bell Telephone Company, "Annual Report," 1946


Separated materials and oversize:

87-2/52 Cards used for symmetric squares
87-2/53 Punch cards for 5×5 magic squares; Punch cards for 9×9 dyad squares
87-2/54 Tapes
Clear cards for marking Pythagorean triangles, also 1 set already marked, and paper cards
87-2/55 Clear cards for marking Pythagorean triangles, also 1 set already marked, and paper cards
87-2/56 Cards for areas of10 × 106 to 15 × 106 (Special problem)
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



4RM203c Personal photographs [donated by Mr. Miksa's family in 1991], November 1953
Francis Miksa, Andrew Anema [donated by Jay Anema, March 2010], 1946, 1953, undated