A Guide to the Francis L. Miksa Papers,
19291972
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. Selfeducation 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 problemsolving; he
corresponded with other workers and submitted problems and solutions to the
problemsolving 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 (19011975)." Unpublished
typescript, 1979, 3 pp.
Papers contain Miksa's correspondence with problemsolvers, amateur,
and professional mathematicians. Letters may occur in the correspondence files
(19371972; 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 problemsolving. 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.



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 
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 onsite.







Subjects (Persons) 


Benson, William H. 


Candy, Albert L. (Albert Luther),
1857 


Greenwood, R. E. 


Madachy, Joseph S. 


Miksa, Francis L., 19011975 
Archives 


Moser, Leo, 19211970 


Tobin, Cyril 


Trigg, Charles W. 

Subjects 


Combinatorial analysis 


Magic squares 


Mathematical recreations 


Number theory 


Problem solving 
Francis L. Miksa Papers, 19291972, 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.
Detailed Description of the Papers















General correspondence: 
Box 
872/1 


193944 



194445 



1949 



1950 



1951 
Box 
872/2 


195152 



195254 



1955 



1956 



1957 



195961 
Box 
872/3 


196263 



196367 



196872 



Becker, H.W.,
195356 



Conner, Louis; Cummins, D.R. 



Lauthan, C.P. 
Box 
872/4 


Luck, Candy, Antone
(194243) 



Moore, S.A.,
193738 




1937, 194041 




193840 




193940 



O'Keefe, J.J. 



Tobin, C. 
Box 
2010078/1 


Letters to Andrew S. Anema, Sr. [donated by Anema's son, Jay Anema, March 2010] 















Magic squares: 
Box 
872/4 


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 
Box 
872/5 


Studies, List of groups, Letter to Moser (1953), letters
from Anema (19481955), Loomis (n.d.),
19481955 and undated 



Group theory and magic squares (1950s and 60s); Letter to
Struyk (1955),
1950s1960s 



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 
872/6 


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 



5×5 
Box 
872/6 



Spiralbound tables and loose sheets 
Box 
872/7 



Combinations that give the I class squares, and similar
but unlabeled tables 




Carbon copies of basic lattices and squares for the
pandiagonal and halfpandiagonal classes 




Symmetric magic squares (in pencil), sheets
24292772 
Box 
872/8 



Sheets 27733034 
Box 
872/52 



Cards used for symmetric squares 
Box 
872/8 



General, nonsymmetric 




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 
872/9 



Auxiliary squares: A=610, A=11=14 




Auxiliary squares: A=1519, A=2024 
Box 
872/10 



Auxiliary squares: A=2529, A=30=34 




Auxiliary squares: A=3539, A=4044 
Box 
872/11 



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 
Box 
872/12 



Calculations, dittoed drafts for book 
Box 
872/53 



Punch cards 



7×7 
Box 
872/12 



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 
Box 
872/13 



Aframe, Bframe: 





1  7 





8  18 




Frame B, sections 14 




Transforms, transforming diagonals, codes of
lattices 




Work on lattices (largely ms) 
Box 
872/14 



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 
Box 
872/15 



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,
195762 
Box 
872/16 



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 
Box 
872/17 



Panassociated 




Table of combinations 




Original work on the table of all
combinations 
Box 
872/18 



Table of 957 332 combinations 




Symmetric, nonpandiagonal 




Symmetric combinations of 7×7 magic squares of the
irregular type 
Box 
872/19 



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 18 




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 
872/20 



Developing 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 
872/20 



"This is a perfect set…",
dittoed with typed additions 
Box 
872/21 



"This is my own set": vol. 4
& 6 




Vols. 1,2,3 
Box 
872/22 



Vol. 4 (3 slightly differing versions) 




Vol. 5 (2 versions) 




Vol. 6 




Abstract, and notes on organization and
prices 















Dyad squares: 
Box 
872/23 


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 
Box 
872/24 


Master table of all combinations of the 21 dyads taken 3
at a time, with correspondence with O. Gross and H. Lauer,
1962 
Box 
872/57 


Game or puzzle offered to Parker Bros. 



7×7 
Box 
872/24 



Photocopies of ms tables 5  18 




7×7 squares, 11×11 groups 




Correspondence (194263), squares, explanatory texts;
Goofy Baseball Game,
19421963 and undated 




The problem of the 7th order dyad squares 
Box 
872/25 



A study of 7×7 dyad squares 



9×9 
Box 
872/25 



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 
Box 
872/26 



Schedule 




Work on schedules beginning with 11 




Work sheets for schedules, incompatible groups,
1962 




Incompatible groups, master table 
Box 
872/27 



Incompatible 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 
872/28 



Work sheets for schedule #162 
Box 
872/53 



Punch cards 



11×11 
Box 
872/28 



Letters and tables (R.J. Keevers), (196970), Brother U.
Alfred (196162),
19611970 




Original manuscript (1962), Table of all combinations,
1962 and undated 




Typed tables 




Efforts to make 




Ms calculations and tables 















Pythagorean triangles: 
Box 
872/28 


Studies, tables, counts (dittoed copies) 
Box 
872/29 


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 
Box 
872/54 


Tapes 



Clear cards for marking Pythagorean triangles, also 1 set
already marked and paper cards 
Box 
872/55 


Clear cards for marking Pythagorean triangles, also 1 set
already marked and paper cards 
Box 
872/56 


Cards for areas of10 × 106 to
15 × 106 (Special problem) 
Box 
872/29 


Table of primitive Pythagorean triangles
(carbon) 



Primitive Pythagorean triangles and formulas, letters and
calculations,
1952, 1969 
Box 
872/30 


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: 
Box 
872/30 



vol. 1 




vol. 2 
Box 
872/31 



vol. 3 




vol. 5 




vol. 6 



Vol. 1, with letters from A. Anema,
1954 



Primitive, according to increasing areas, Generators ABC,
Area, S 
Box 
872/32 


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 
Box 
872/33 


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: 
Box 
872/33 


Table of quadratic partitions, x2 + y2 = N 




Results on cards 
Box 
872/34 


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 
Box 
872/35 


Table of indices and residues for different primes (to be
used with Cunningham's binary canon) 



Residues and indices 



Power residues modulo P 



Oddabundant 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 
872/36 


Problems and solutions, with letters,
194446 



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 
872/37 


All possible Tobin's squares made by the strip
method 



Candy's 15 schedules, Tobin's method 



Candy's schedules 



Codes 4  6 
Box 
872/57 


Collection of results on Tobin's 7×7 squares 
Box 
872/37 


Tobin's codes 



Tobin's method (letters),
1943 
Box 
872/38 


Tobin's method, permutation groups, Tobin's
schedules 



Tobin's method, with papers on group theory Ga_{b} a=1 − a=8 















Problem solving: 
Box 
872/38 


Problems,
193639 




Late 1930s 




1938 




193738, 195053 




194041 




194547 




1948 
Box 
872/39 


Problems and correspondence,
1940s 



Tables, calculations, problems, letters,
195253 



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,
194648 
Box 
872/40 


Probleme des menages 



Point inside a triangle 



Solution of a problem by V. Thebault 



Firing ship and misc. problems,
late 1930s 
Box 
872/41 


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,
194648 



Problem of Easter, and others,
1943 



Will problem and others, 193740
(letters, C. Tobin, 1951)
19371951 



Mechanics problems,
1937 
Box 
872/42 


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 
Box 
872/43 


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,
193941 



SAM's parabola 



School Science and Math, with S.A.
Moore letters,
194041 















Exercises, notes and calculations: 
Box 
872/43 


Area of paraboloid and others 



8 notebooks 
Box 
872/44 


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 
Box 
2010078/1 


"Misc."  problems, notes [donated by Jay Anema, March 2010] 















Other mathematical topics: 
Box 
872/44 


[Diagram of contiguous colored shapes] 



Latin Squares 
Box 
872/45 


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: 
Box 
872/45 


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 
872/57 


Large sheets with calculations, including geometrical
problems and dyad squares 
Box 
872/45 


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 
Box 
872/46 


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 19.0.A. 



Unidentified tapes 















Personal: 
Box 
872/47 


Papers by Francis L. Miksa 



Library of Francis L. Miksa: Catalog;
Bookplate 



Electrical correspondence school,
1929 and undated 



Electrical problems at night school I 
Box 
872/48 


Electrical problems at night school II 



Magazine list and letters concerning sale 



Medical information 















Works of others: 
Box 
872/57 


Anema, A.S., Thalesian 17th order magic square,
1945 
Box 
872/48 


Benson, W.H., The World of Magic Squares, with letter,
1964 



Magical Magic Squares (1949); TriMagic Squares,
1949 and undated 



British Association Mathematical Tables V  Factor tables
with insertions 



Brousseau, Brother A., Number Theory Tables,
1973 
Box 
872/49 


The Dial,
195157 



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,
19581959 



Gruenberger's list of primes, Computing News 



Magic squares, etc. 
Box 
872/50 


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 



Reprints 
Box 
872/51 


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 
box 
872/51 


Math, science, and technology book catalogs: 




19301937 
box 
872/58 



19371947 and undated 



International Correspondence Schools, "Manual of
Information for Students,"
1922 



Illinois Bell Telephone Company, "Annual Report,"
1946 















Separated materials and oversize: 
Box 
872/52 


Cards used for symmetric squares 
Box 
872/53 


Punch cards for 5×5 magic squares; Punch cards for 9×9
dyad squares 
Box 
872/54 


Tapes 



Clear cards for marking Pythagorean triangles, also 1 set
already marked, and paper cards 
Box 
872/55 


Clear cards for marking Pythagorean triangles, also 1 set
already marked, and paper cards 
Box 
872/56 


Cards for areas of10 × 106 to
15 × 106 (Special problem) 
Box 
872/57 


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 















Photographs 
Box 
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 
