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University of Texas, Center for American History

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


Descriptive Summary

CreatorMiksa, Francis L., 1901-1975
Title:Francis L. Miksa Papers,
Dates:1929-1972
OCLC Number19401161
Extent:40 ft. 2 in.
LanguageMaterials are written in English.
RepositoryArchives of American Mathematics, 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, Mr. Miksa worked as a switchman for the Illinois Bell Telephone Company. He died in 1975.

Mr. 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. Mr. Miksa carried on a wide correspondence among recreational and professional mathematicians. His correspondence with Leo Moser resulted in collaboration in published work.

Scope and Contents:

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

 

Organization
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
Personal
Works of Others
Photographs

Restrictions

Access Restrictions

Unrestricted access

Use Restrictions

The majority of this collection is stored off-site at the Collections Deposit Library. Please contact reference staff for retrieval.

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.
Subjects
Combinatorial analysis
Magic squares
Mathematical recreations
Number theory
Problem solving

Administrative Information

Preferred Citation

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

Processing Information

This collection was processed by Frederic Burchsted in April 1990.

Source:

Miksa, Francis L., Jr., "Francis Louis Miksa (1901-1975)." Unpublished typescript, 1979, 3 pp.

Detailed Description of the Papers

 

General correspondence:

Box
16.6/87-2/1 1939-44
1944-45
1949
1950
1951
Box
16.6/87-2/2 1951-52
1952-54
1955
1956
1957
1959-61
Box
16.6/87-2/3 1962-63
1963-67
1968-72
Becker, H.W., 1953-56
Conner, Louis; Cummins, D.R.
Lauthan, C.P.
Box
16.6/87-2/4Luck, Candy, Antone (1942-43)
Moore, S.A., 1937-38
1937, 1940-41
1938-40
1939-40
O'Keefe, J.J.
Tobin, C.


 

Magic squares:

Box
16.6/87-2/4Lattices, schedules, tables, working out of codes, letter to Loomis
Tables of all combinations (4×4, 5×5, 6×6), including Candy's 5×5
Box
16.6/87-2/5Studies, 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
Box
16.6/87-2/6Table 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
5×5
Box
16.6/87-2/6Spiral-bound tables and loose sheets
Box
16.6/87-2/7Combinations 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
Box
16.6/87-2/8Sheets 2773-3034
Box
16.7/87-2/52Cards used for symmetric squares
Box
16.6/87-2/8General, 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 G5 8 transforms
Box
16.6/87-2/9Auxiliary squares: A=6-10, A=11=14
Auxiliary squares: A=15-19, A=20-24
Box
16.6/87-2/10Auxiliary squares: A=25-29, A=30=34
Auxiliary squares: A=35-39, A=40-44
Box
16.6/87-2/11Dittoed 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
Box
16.6/87-2/12Calculations, dittoed drafts for book
Box
16.7/87-2/53Punch cards
7×7
Box
16.6/87-2/12Plastic 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
Box
16.6/87-2/13A-frame, B-frame:
1 - 7
8 - 18
Frame B, sections 1-4
Transforms, transforming diagonals, codes of lattices
Work on lattices (largely ms)
Box
16.6/87-2/14The 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
Box
16.6/87-2/15Table 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
Box
16.6/87-2/16On 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
Box
16.6/87-2/17Pan-associated
Table of combinations
Original work on the table of all combinations
Box
16.6/87-2/18Table of 957 332 combinations
Symmetric, non-pandiagonal
Symmetric combinations of 7×7 magic squares of the irregular type
Box
16.6/87-2/19Special 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
Box
16.6/87-2/20Developing E.D. lattices and squares by symmetric G7 5040 permutations
Work done on the essential substitutions for the G7 42 inv. substitution group
Book
Box
16.6/87-2/20"This is a perfect set…", dittoed with typed additions
Box
16.6/87-2/21"This is my own set": vol. 4 & 6
Vols. 1,2,3
Box
16.6/87-2/22Vol. 4 (3 slightly differing versions)
Vol. 5 (2 versions)
Vol. 6
Abstract, and notes on organization and prices


 

Dyad squares:

Box
16.6/87-2/23Vol. 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
Box
16.6/87-2/24Master table of all combinations of the 21 dyads taken 3 at a time, with correspondence with O. Gross and H. Lauer, 1962
Box
16.6/87-2/57Game or puzzle offered to Parker Bros.
7×7
Box
16.6/87-2/24Photocopies 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
Box
16.6/87-2/25A study of 7×7 dyad squares
9×9
Box
16.6/87-2/25Ts 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
Box
16.6/87-2/26Schedule
Work on schedules beginning with 1-1
Work sheets for schedules, incompatible groups, 1962
Incompatible groups, master table
Box
16.6/87-2/27Incompatible groups to be used to develop 9×9 dyad squares
Incompatible groups
Master table of all combinations of the (9 2) 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
Box
16.6/87-2/28Work sheets for schedule #162
Box
16.7/87-2/53Punch cards
11×11
Box
16.6/87-2/28Letters 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:

Box
16.6/87-2/28Studies, tables, counts (dittoed copies)
Box
16.6/87-2/29Isoperimetric 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
Box
16.6/87-2/54Tapes
Box
16.7/87-2/54Clear cards for marking Pythagorean triangles, also 1 set already marked and paper cards
Box
16.7/87-2/55Clear cards for marking Pythagorean triangles, also 1 set already marked and paper cards
Box
16.7/87-2/56Cards for areas of10 × 106 to 15 × 106 (Special problem)
Box
16.6/87-2/29Table of primitive Pythagorean triangles (carbon)
Primitive Pythagorean triangles and formulas, letters and calculations, 1952, 1969
Box
16.6/87-2/30Primitive 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:
Box
16.6/87-2/30vol. 1
vol. 2
Box
16.6/87-2/31vol. 3
vol. 5
vol. 6
Vol. 1, with letters from A. Anema, 1954
Primitive, according to increasing areas, Generators ABC, Area, S
Box
16.6/87-2/32Primitive, 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
Box
16.6/87-2/33Table 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:

Box
16.6/87-2/33Table of quadratic partitions, x2 + y2 = N
Results on cards
Box
16.6/87-2/34Additional 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
Box
16.6/87-2/35Table 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
Box
16.6/87-2/36Problems 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:

Box
16.6/87-2/37All possible Tobin's squares made by the strip method
Candy's 15 schedules, Tobin's method
Candy's schedules
Codes 4 - 6
Box
16.7/87-2/57Collection of results on Tobin's 7×7 squares
Box
16.6/87-2/37Tobin's codes
Tobin's method (letters), 1943
Box
16.6/87-2/38Tobin's method, permutation groups, Tobin's schedules
Tobin's method, with papers on group theory Ga b a=1 − a=8


 

Problem solving:

Box
16.6/87-2/38Problems, 1936-39
Late 1930s
1938
1937-38, 1950-53
1940-41
1945-47
1948
Box
16.6/87-2/39Problems 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
Box
16.6/87-2/40Probleme des menages
Point inside a triangle
Solution of a problem by V. Thebault
Firing ship and misc. problems, late 1930s
Box
16.6/87-2/41Elliptical 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
Box
16.6/87-2/42Logic 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
Box
16.7/87-2/43Inscribed 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:

Box
16.7/87-2/43Area of paraboloid and others
8 notebooks
Box
16.7/87-2/44Calculus, 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


 

Other mathematical topics:

Box
16.7/87-2/44[Diagram of contiguous colored shapes]
Latin Squares
Box
16.7/87-2/45Moser'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:

Box
16.7/87-2/45Date 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
16.7/87-2/57Large sheets with calculations, including geometrical problems and dyad squares
Box
16.7/87-2/45Magic 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
Box
16.7/87-2/46Notes (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


 

Personal:

Box
16.7/87-2/47Papers by Francis L. Miksa
Library of Francis L. Miksa: Catalog; Bookplate
Electrical correspondence school, 1929 and undated
Electrical problems at night school I
Box
16.7/87-2/48Electrical problems at night school II
Magazine list and letters concerning sale
Medical information


 

Works of others:

Box
16.7/87-2/57Anema, A.S., Thalesian 17th order magic square, 1945
Box
16.7/87-2/48Benson, 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
Box
16.7/87-2/49The 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.
Box
16.7/87-2/50Moser, L. Introduction to the Theory of Numbers, (Items sent by L. Moser) 1957
Pamphlets, including calculator manuals
RAND Corporation Approximations in Numerical Analysis, 1950
Reprints
Box
16.7/87-2/51Robinson, 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
box
16.7/87-2/51Math, science, and technology book catalogs:
1930-1937
box
16.7/87-2/58 1937-1947 and undated
International Correspondence Schools, "Manual of Information for Students," 1922
Illinois Bell Telephone Company, "Annual Report," 1946


 

Separated materials and oversize:

Box
16.7/87-2/52Cards used for symmetric squares
Box
16.7/87-2/53 Punch cards for 5×5 magic squares; Punch cards for 9×9 dyad squares
Box
16.7/87-2/54Tapes
Clear cards for marking Pythagorean triangles, also 1 set already marked, and paper cards
Box
16.7/87-2/55Clear cards for marking Pythagorean triangles, also 1 set already marked, and paper cards
Box
16.7/87-2/56Cards for areas of10 × 106 to 15 × 106 (Special problem)
Box
16.7/87-2/57Oversize
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


 

At Sid Richardson Hall:

box
4RM51Photographs (donated by Mr. Miksa's family in 1991), 1953