1 March 2026
Each day of February 2026, I posted here and on Mastodon a short interesting story/image/fact/anecdote related to the aesthetics of mathematics. This is an index of the posts:
Perfect numbers and aesthetics
February has $28$ days, and $28$ is the second perfect number, so let’s start there.
Apollonius of Perga on beautiful theorems
The Conics of Apollonius of Perga contains the unique instance of an ancient Greek mathematician calling theorems beautiful.
Archimedes on the sphere and cylinder
Max Dehn said that Archimedes’ discovery that the surface area of a sphere was four times its great circle was the one of the most beautiful results of Greek mathematics.
Nicon, the sphere, the cylinder, and the Pantheon
Architecture and Archimedes’ result on the ratio of the volumes of the sphere, cylinder, and cone.
Circular numbers in antiquity and the middle ages
In later antiquity and the middle ages, a ‘circular number’ was one that reappeared in its own powers: $5$ and $6$ were circular numbers since their powers ($25, 125, 625, \ldots$; $36, 216, 1296, \ldots$) always end in $5$ or $6$.
Pythagoras, Thomas Bradwardine, and the beauty of the circle
According to the biography by Diogenes Laertius, Pythagoras ‘held that the most beautiful figure is the sphere among solids, and the circle among plane figures’.
Fibonacci, Archimedes, π, beauty, proof, and misunderstanding
Leonardo Pisano, dubbed ‘Fibonacci’, thought that Archimedes’ calculation of bounds on the value of π was beautiful [pulcra].
Abū’l-Wafāʾ al-Būzjānī and magic squares
Abū’l-Wafāʾ al-Būzjānī wrote one of the earliest extant treatises dedicated to magic squares, focused on constructions. He repeatedly referred to the aesthetic value of the methods of he described.
Al-Kūhī on geometrical constructions and mathematical beauty
Abū Sahl al-Kūhī, regarded by contemporaries as the ‘Master of his age in the art of geometry’, wrote about beauty as a motivation for considering a problem.
Calligraphy and geometry in mediaeval Islamic thought
The scholar Abū Ḥayyān al-Tawḥīdī wrote that ‘handwriting is spiritual geometry by means of a corporeal instrument’.
Islamic geometrical art in theory and practice
Documented connections between the artisans who created Islamic geometrical art and mathematicians.
Luca Pacioli and the ‘divine proportion’
Pacioli’s book Divina proportione is famous in the history of mathematical beauty, but mostly for the wrong reasons.
The discovery and rediscovery of the the polyhedra (other than the five regular solids) all the faces of which are regular polygons and where for each pair of vertices some symmetry transformation carries one vertex to the other.
Cardano and beautiful properties of figures
Book XVI of Girolamo Cardano's De Subtilitate, a compendium of natural philosophy, begins by presenting sixty properties of geometrical figures, ‘outstanding in distinction and beauty and regard’.
Viète and an ‘elegant and very beautiful’ result
Or, how notation can influence aesthetic judgement.
Fermat and the beauty of number theory
Number theory was the one area of mathematics on which Pierre de Fermat worked throughout his life, and he found it ‘very beautiful and very subtle’.
Torricelli's solid, beauty, and sublimity
Infinite length, infinite surface area, finite volume, and aesthetic judgement.
The cycloid, the tautochrone, and the brachistochrone
An enduring locus of mathematical beauty in the seventeenth century concerned curves like the cycloid and the catenary.
‘The beautiful arrangement of their characters’
Observations on beauty in theorems by Leibniz.
For Leonhard Euler, both proven and unproven results could be beautiful.
The idea that the golden ratio has (or should have) an aesthetic role has a relatively short history.
The beginnings of modern aesthetics
When modern aesthetics emerged, many of the early thinkers thought it natural to consider mathematical beauty.
Lagrange and beauty in solid geometry
Examples of mathematical beauty Lagrange saw in solid geometry.
Schiller, Gauss, Archimedes, Goethe, Lagrange
Poetry and the motivation for mathematics.
The mathematical theory of linkages
An area once thought beautiful and now comparatively unknown.
Herbert Spencer and Monge’s theorem
Beauty born of mathematical ignorance?
A typology of beauty by the writer François Le Lionnais.
An exemplar of mathematical beauty in physical law.