OOIR: Observatory of International Research

Papers

(The TQCC of American Mathematical Monthly is 0. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-04-01 to 2025-04-01.)

Article	Citations
Factorization of Perplex Integers	9
Introduction to the Special Issue	8
A Characterization of Rational Functions	8
Convex Bodies with Equipotential Circles	6
Reviews	5
My Friend Abe Shenitzer	5
Polynomial Approximations to Continuous Functions	5
Problems and Solutions	5
The Concentration of the Product of Exponentials Around the Exponential of the Sum	4
A Geometric Summation of the Geometric Series	4
Reviews	4
What Do Networks and Elliptic Curves Have in Common?	4
x + y: A Mathematician’s Manifesto for Rethinking Gender	4
PROBLEMS AND SOLUTIONS	4
On a Classic Problem in the Calculus of Variations: Setting Straight Key Properties of the Catenary	4
The Mathematical Community Working To Create Better (And Free!) Textbooks	3
Editor’s Endnotes	3
Community and Belonging in Mathematics*	3
A Generalization of Schatunowsky’s Theorem	3
Infinitely Many Twin Prime Polynomials of Odd Degree	3
Reviews	3
Letter from the Editor	3
Integration using Schwinger Parametrization	3
Remark on Cauchy–Schwarz Inequality for Differences	2
Gardener’s Hyperbolas and the Dragged-Point Principle	2

Problems and Solutions	2
On Some Localizations and Their Relation to Quotients	2
Ohm My: An Electrifying Method of Summing Arithmetic Sequences	2
Reviews	2
Reviews	2
Metric Spaces where Geodesics are Never Unique	2
100 Years Ago This Month in The American Mathematical Monthly	2
Following in Yiu’s Footsteps but on the Eisenstein Lattice	2
A Statistical Proof of Chebyshev’s Sum Inequality	2
100 Years Ago This Month in The American Mathematical Monthly	2
A Brief Discourse on Hausdorff Dimension and Self-similarity	2
Reviews	2
Reviews	2
Problems and Solutions	2
100 Years Ago This Month in The American Mathematical Monthly	2
Apéry Limits: Experiments and Proofs	1
Cauchy–Schwarz Inequality for Differences Revisited	1
What Is the Shape of a Cupola?	1
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio	1
Tessellations: Mathematics, Art, and Recreation	1
Sharp Effective Finite-Field Nullstellensatz	1
New Primality Criterion Based on Lucas Sequences	1
Which Finite Rings Have the Most or Fewest Units?	1
A Generalization of Bonse’s Inequality	1
The Factor Ring Structure of Quadratic Principal Ideal Domains	1
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics	1
A Short and Elementary Proof of the Central Limit Theorem by Individual Swapping	1
The Altitudes of a Triangle	1
Odd-Period Cycles of the Logistic Map	1
Another Alternating Analogue of Euler’s Constant	1
How Long Can k -Göbel Sequences Remain Integers?	1
A Jeep Crossing a Desert of Unknown Width	1
Reflections on Equidistant Sets	1
100 Years Ago This Month in The American Mathematical Monthly	1
A Note on the Geometry of Figurate Numbers	1
The Theorem of the Primitive Element	1
A Law of Conservation of Symbols	1
Yet Another Proof of the Strong Law of Large Numbers	1
Euclid after Computer Proof-Checking	1
100 Years Ago This Month in The American Mathematical Monthly	1
A Second Look at the Second Ratio Test	1
Moon in a Puddle and the Four-Vertex Theorem	1
A Thābit-like Extension of the Pythagorean Theorem	1
100 Years Ago This Month in The American Mathematical Monthly	1
Polynomially Isometric Matrices in Low Dimensions	1
A Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma	1
The Paul R. Halmos–Lester R. Ford Awards for 2022	1
The Fundamental Theorem of Algebra Via Newton’s Identities	1
Z[−5]: Halfway to Unique Factorization	1
Gaussian Binomial Coefficients in Group Theory, Field Theory, and Topology	1

Water-Based Proof of Jensen’s Inequality	1
A Friendly Introduction to Path Algebras and Quiver Representations	1
Editor’s Endnotes	1
100 Years Ago This Month in The American Mathematical Monthly	1
100 Years Ago This Month in The American Mathematical Monthly	1
A Combinatorial Proof of a Symmetric Group Character Involution	1
Bijective Proofs of Proper Coloring Theorems	1
A Plethora of Polynomials: A Toolbox for Counting Problems	1
169 and Sums of Positive Squares	1
Minimax Theorem Revisited	1
On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement	1
Monthly Referees for 2023	1
How (Not) to Cut Your Cheese	1
A Dynamic Kelly Criterion for Games with a Maximum Payout	1
Stickelberger’s Discriminant Theorem for Algebras	1
Regular Patterns of Quadratic Residues	1
Commutators in the Rubik’s Cube Group	1
100 Years Ago This Month in The American Mathematical Monthly	1
Extremal Values of Pi	1
Five or Ten New Proofs of the Pythagorean Theorem	1
Problems and Solutions	1
The Distribution of Fibonacci Numbers Modulo Primes	1
Six Houses and Three Utilities on A Coffee Mug	1
In Search of Comrade Agronomof: Some Tribonacci History	1
On the Tower Factorization of Integers	0
Using Ultrafilters to Prove Ramsey-type Theorems	0
A Pigeon Hole Proof of the Infinitude of Primes	0
The Basel Problem and the Fundamental Theorem of Calculus	0
A Model for Birdwatching and other Chronological Sampling Activities	0
100 Years Ago This Month in The American Mathematical Monthly	0
Ghostly Irrational Numbers	0
Counting Zeros of Random Functions	0
Reviews Graph Theory in America: The First Hundred Years . By Robin Wilson, John J. Watkins, and David J. Parks, Princeton University Press, 2023. 320 pp., ISBN 978-0691	0
Problems and Solutions	0
Odometers, Backward Continued Fractions, and Counting Rationals	0
Gambling Under Unknown Probabilities as Proxy for Real World Decisions Under Uncertainty	0
A Shortcut to the Cauchy Integral Theorem	0
An Equilateral Triangle of Side > n Cannot be Covered by n ² + 1 Unit Equilateral Triangles Homothetic to it	0
A Prime Primitive Root p of 2 p + 1 is a Sophie Germain Prime	0
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers	0
Sum of a Geometric Series Via the Integral	0
The Eighty-Fourth William Lowell Putnam Mathematical Competition	0
Newton’s Method Without Division	0
Legendre–Teege Quadratic Reciprocity	0
Faculty Seminar	0
On a Uniqueness Problem in Discrete Tomography	0
A Tale of Two by Two Matrices	0
A Second Raabe’s Test and Other Series Tests	0
Invariance of the Area and Volume of Cycloid Surfaces and Trochoid Surfaces	0
Construction of an Iterated Function System on ℝ ² whose Attractor is a QR Code	0
A Special Form of Slower Divergent Series	0
There are 2^c Quasicontinuous Non-Lebesgue Measurable Functions	0
Freely Independent Coin Tosses, Standard Young Tableaux, and the Kesten–McKay Law	0
Launching a Data Analytics Major: How Collaboration and Agility Built a Successful Program	0
Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions	0
Problems and Solutions	0
Problems and Solutions	0
Reconstructing Signals from Aperture-Filtered Samples	0
Yet Another Integral Representation of Catalan’s Constant	0
100 Years Ago This Month in The American Mathematical Monthly	0
Problems and Solutions	0
Pythagorean Boxes and Quotients of Gaussian Integers	0
Pollock’s Generalized Tetrahedral Numbers Conjecture	0
Celebrating Herbert Slaught’s “Romance of Mathematics”	0
The Fundamental Theorem of Algebra via Real Polynomials	0
Problems and Solutions	0
Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model	0
Jordan’s Inequality — as Sharp as You Please	0
On Erdős’s Method for Bounding the Partition Function	0
Topology Meets Number Theory	0
A Sufficient Condition for a Prime to be a Sophie Germain Prime	0
The Determinant Mod p of a Circulant Matrix of Order p ^m	0
A Prime Testing Algorithm from Leonhard Euler	0
Generalized Rental Harmony	0
The Inverse of a Bad Primitive Root is Not Bad	0
A Derivation of the Infinitude of Primes	0
Correction	0
100 Years Ago This Month in The American Mathematical Monthly	0
Can One Visualize a Continuous Nowhere Differentiable Function?	0
Polynomials Consisting of Quadratic Factors with Roots Modulo Any Positive Integer	0

Reciprocal Sums and Counting Functions	0
A Determinantal Identity for the Permanent of a Rank 2 Matrix	0
Invariance of the Cauchy Family Under Linear Fractional Transformations	0
New Elementary Derivation of Fresnel Integrals	0
100 Years Ago This Month in The American Mathematical Monthly	0
Polynomials and Integration in Finite Terms	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Probabilistic Pigeonhole Principle	0
From Abel’s Binomial Theorem to Cayley’s Tree Formula	0
Simpson’s Paradox, Visual Displays, and Causal Diagrams	0
When I Knew Math Was Mine	0
Analytic Continuations of Character and Alternating Tornheim Zeta Functions	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Eighty-Third William Lowell Putnam Mathematical Competition	0
100 Years Ago This Month in The American Mathematical Monthly	0
Odds Inversion Problem With Replacement	0
The Pentagonal Pizza Conjecture	0
Computing Moore–Penrose Inverses with Polynomials in Matrices	0
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2022 to Barbara Faires for Distinguished Service to Mathematics	0
What Newton Might Have Known: Experimental Mathematics in the Classroom	0
A Quick Route to Unique Factorization in Quadratic Orders	0
The Area Under the Witch of Agnesi	0
The Lavrentiev Phenomenon	0
A Third Real Solution to x=x⁻¹, Not Really	0
The Eighty-First William Lowell Putnam Mathematical Competition	0
Grades Are Not Money	0
Reviews	0
New Properties of Triangular Orbits in Elliptic Billiards	0
Problems and Solutions	0
a ² =b ² +cd , an Extended Pythagorean Formula	0
Some Inequalities for Power Means; a Problem from “The Logarithmic Mean Revisited”	0
Deranged Matchings: Proofs and Conjectures	0
Finite Abelian Groups via Congruences	0
Problems and Solutions	0
N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium	0
Integers as Sums of Four Tetrahedral Numbers and Eight Pentatope Numbers in One Identity	0
Reviews	0
A Generalization of Euler’s Limit	0
What Type of Apollonian Circle Packing Will Appear?	0
Sums of Generalized Tetrahedral Numbers	0
The Powers of Certain Number-Theoretic Matrices	0
Polynomials Whose Zeros Are Powers of a Given Polynomial’s Zeros	0
Problems and Solutions	0
Classifying Groups With a Small Number of Subgroups	0
What Can You Draw?	0
An Exact Bound for the Inner Product of Vectors in ℂ ⁿ	0
Remark on Jensen’s Inequality	0
Reviews	0
i nd uct ion!	0
An Upper Bound on the Size of Sidon Sets	0
Non-Archimedean Views on Gershgorin’s Theorem and Diagonal Dominance	0
Elementary Derivations of the Euclidean Hurwitz Algebras Adapted from Gadi Moran’s last paper	0
Monthly Referees for 2022	0
On Experimental Mathematics and Mathematics Education	0
Extension of the Fundamental Theorem of Algebra for Polynomial Matrix Equations with Circulant Matrices	0
Lagrange Inversion Formula by Induction	0
Vieta’s Formula, the Fabius Function and the Partition Function	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reciprocity via Reciprocants	0
The Simplest Unlimited-Player Game of Skill	0
Problems and Solutions	0
100 Years Ago This Month in The American Mathematical Monthly	0
Biology in Time and Space: A Partial Differential Equation Modeling Approach. James Keener, American Mathematical Society, 2021. 308 pp., ISBN 978-1-4704-5428-9, $99.00.	0
On Random Walks with Geometric Lifetimes	0
Sums of Finite Sets of Integers, II	0
Reviews	0
A Quixotic Proof of Fermat’s Two Squares Theorem for Prime Numbers	0
Flip a Coin, Get an Annular Function?	0
On Nonnegativity of the Generalized Discriminants of Quadratics	0
The Green-Tao Theorem and the Infinitude of Primes in Domains	0
The Digital Rubáiyát	0
Using a SAT Solver to Find Interesting Sets of Nonstandard Dice	0
Problems and Solutions	0
An Extension of Ceva’s Theorem to n-Simplices	0
Problems and Solutions	0
Problems and Solutions	0
March Madness Magic: Constructing a Tournament with a Magic Cube	0
The Matrix Equation X ³ + Y ³ = 2 Z ³	0
Generalized Repeated Integration by Parts	0
Problems and Solutions	0
The Paul R. Halmos–Lester R. Ford Awards for 2020	0
Inellipses of Convex Polygons, Brianchon’s Theorem, and Bradley’s Theorem	0
Problems and Solutions	0
Integral Recurrences from A to Z	0
Sós Permutations	0
When Does F(α^d) = F(α)?	0
Sum of an Alternating Geometric Series Via Self-Similarity	0
An Inequality of a Matrix with a Unit Vector	0
Reviews	0
A New Perspective on Impartial and Unbiased Apportionment	0
Frobenius Integrability, Automotive Blind Spots, Non-reversing Mirrors, and Panoramic Mirrors	0
On Parking Functions and The Tower of Hanoi	0
Regular Polygons and Central Moments	0
Uncovering the Euclidean Geometry of Data	0
Correction	0