@ajcain@mathstodon.xyz

· 1mo ago

Replying to

@drahardja@sfba.social I find useful https://www.europeana.eu/en It searches media from various museums and other cultural institutions across Europe. Some recent items are still in copyright, but most older ones seem to be CC-licensed or public domain. Each item page shows the status/licence.

europeana.eu

7

1

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 2mo ago

Replying to

@nixCraft@mastodon.social I particularly admire the quiet acerbity of this observation: ‘“The fluidity and warmth of human-centered thinking through the use of circles” is perhaps the most elegant way anyone has ever described making a logo that resembles an anus.’

15

0

5

0

Alan J. Cain @ajcain@mathstodon.xyz

· 6mo ago

Just received an email asking me to peer-review a paper, and asking me to decide whether to review it based on an abstract in which every piece of LaTeX code has been replaced with ‘[[EQUATION]]’, so that it reads like:

‘For [[EQUATION]], let [[EQUATION]] be the semigroup of partial bijections on the lattice [[EQUATION]]. For a subset [[EQUATION]] of [[EQUATION]] with size at most [[EQUATION]], we show that [[EQUATION]] and [[EQUATION]] are the unique possible...’

I am not quoting the actual text, but this gives the idea. The email was generated by the publisher's paper management system, so I assume it is to blame, not the editor.

Over the years, I have developed fairly low expectations of academic publishers, but this particular bit of incompetence is new to me.

#academia #AcademicPublishing #AcademicChatter

mathstodon.xyz

21

1

11

0

Alan J. Cain @ajcain@mathstodon.xyz

· 5mo ago

Replying to

@bagder@mastodon.social The best abstract I ever read was "not a typical academic one": https://arxiv.org/abs/2507.03413

arxiv.org

5

1

3

0

Alan J. Cain @ajcain@mathstodon.xyz

· 5mo ago

Replying to

In technical terms, < and > are classified as ‘Bin’ (binary relations) math atoms, while angle brackets are classed as ‘Open’ and ‘Close’ math atoms (opening and closing delimiters). TeX automatically spaces different kinds of math atoms according to their types (see the table in chapter 18 of ‘The TeXbook’). If one really wanted to use symbols identical to < and > as angle brackets, one could redefine the \langle and \rangle commands to (respectively) \mathopen{<} and \mathclose{>}. The \mathopen{...} and \mathclose{...} commands make TeX treat the subformula in the parameter as (respectively) an ‘Open’ and ‘Close’ math atom. 2/2

5

0

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 6mo ago

My new #LuaLaTeX package: lua-simple-wrap

This package allows easy wrapping of text around small figures, pull quotes, etc. (See attached image.)

Unlike (I think) all other LaTeX packages for wrapping text around things, the wrapped object can be specified at its natural place in the text, and the package works out where it should appear. Virtually all the processing happens on the Lua side.

The package is semi-experimental, and definitely requires more work before I submit it to CTAN, but the basic functionality is in place and seems to be working well. In particular, tagging support (for producing accessible PDFs) is already present.

Git repository: https://codeberg.org/ajcain/lua-simple-wrap

Download documentation and built package: https://codeberg.org/ajcain/lua-simple-wrap/releases

If you try it, feedback would be much appreciated!

#TeXLaTeX #typography #Lua #accessibility #TaggedPDF

mathstodon.xyz

Mathstodon

5

0

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

Spencer expressed enthusiasm for mathematics, and was proud enough of a rather slender theorem he proved in 1840 to reprint the paper as an appendix to his autobiography. (The result had actually been known since the mid-18th century.) But his geometrical knowledge was actually quite limited, and the statement he gave of Monge’s theorem was carelessly imprecise. Further, Gaspard Monge’s (1746–1818) original proof is simple and explains the theorem: Imagine the circles are great circles of three spheres. Then there are two planes that are tangent with all three spheres. (See attached image.) These planes are also in contact with the cones defined by each pair of spheres, and the tangent lines are where these cones pass through the original plane. Thus both these planes contain the apices of the three cones, which are the intersections of pairs of the tangents. That is, the intersection points lie in the intersection of the two planes, which is a straight line. 2/3 #SolidGeometry #MathematicalExplanation #simplicity

5

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 8mo ago

Replying to

References • Qāḍī Aḥmad. ‘Calligraphers and Painters’. Freer Gallery of Art Occasional Papers, no.3.2. Washington: Smithsonian Institution, 1959. URL: https://archive.org/details/calligrapherspa321959ahma p. 52. • A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large pp.220–1 • F. Rosenthal. 'Abū Ḥaiyān al-Tawḥīdī on Penmanship'. In: Ars Islamica. 13 (1948), pp.1-30. DOI: 10.2307/4515645 pp.6, 15. • S.H. Nasr. ‘Islamic Art and Spirituality’. State University of New York Press, 1987. ISBN: 978-0-88706-174-5 URL: https://archive.org/details/islamicartspirit0000nasr • M.A.J. Yaghan. 'Mathematical concepts in Arabic calligraphy: The proportions of the ʾAlif'. In: PLoS ONE. 15, no.5 (2020). DOI: 10.1371/journal.pone.0232641 • Y. Tabbaa. ‘The Transformation of Islamic Art During the Sunni Revival’. Publications on the Near East. Seattle & London: University of Washington Press, 2001. ISBN: 978-0-295-98125-3 p. 37 Images from ‘Form & Number’, figure 7.2. 2/2

archive.org

5

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Each day of February I posted a fact/image/anecdote about the aesthetics of mathematics, which seemed to provoke a certain amount of interest.

The posts are all collected on my personal website, with minor fixes and improvements (including vector versions of diagrams).

The index is here: https://ajcain.codeberg.page/posts/2026-03-01-aesthetics-of-mathematics.html

#aesthetics #MathematicalBeauty #HistMath #elegance #beauty

ajcain.codeberg.page

4

0

7

0

Alan J. Cain @ajcain@mathstodon.xyz

· 5mo ago

Replying to

The ‘Mathematics Magazine’ review said I was ‘very particular to consult original sources to verify quotations and claims’. I suspect there might have been a temptation to use the adjective ‘pedantic’ rather than ‘particular’. :-)

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

Romantic beauty could arise from unexpectedness, such as the formulae for the volumes and surface areas of $n$-dimensional unit spheres reaching their maximums at non-integer values (see 1st attached image). The tractroid pseudosphere (see 2nd attached image) also had romantic beauty, for it was in some ways close to the sphere, having constant Gaussian curvature (negative, while the sphere's is positive), and the same surface area as the sphere, and finite volume (equal to half of the sphere), but was in other respects wild, having infinite extent. The cycloid had both classical beauty – in its simple definition — and romantic beauty — in its unexpected appearance as the solutions to the tautochrone and brachistochrone problems, contrary to intuition. 2/3

3

1

0

Alan J. Cain @ajcain@mathstodon.xyz

· 12mo ago

Replying to

@Doveux@meow.social "Yes, doctor. As soon as I see \documentclass my nose starts running. By the time I reach \begin{document} I develop this itchy rash..." :-)

5

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

But Maxwell wrote: ‘I always regarded mathematics as the method of obtaining the *best* shapes and dimensions of things; and this meant not only the most useful and economical, but chiefly the most harmonious and the most beautiful.’ This does not point to using beauty *in* mathematics: the mathematics was a means to a beautiful end. Beauty in mathematics is never mentioned in Maxwell’s ‘Treatise on Electricity and Magnetism’ (1873). Elegance is mentioned precisely once. And Maxwell did not use the concise modern notation, and did not group the four equations together. It was Oliver Heaviside (1850–1925) who put the equations into their modern form, which brought out their symmetry. As Heaviside’s contemporary George Francis FitzGerald (1851–1901) put it: ‘Every mathematician can appreciate the value and beauty of this.’ 2/3

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 14mo ago

I have uploaded a new version of my book ‘Form & Number: A History of Mathematical Beauty’ [https://archive.org/details/cain_formandnumber_ebook_large] to archive.org.

The PDF of the new version is available immediately, and archive.org will re-generate the pages for the in-browser reader over the next few hours.

Changes:

• Improvements to several figures.
• Various small improvements to the text.
• Several minor corrections, including a number of reader-submitted ones.
• All end-of-line word hyphenations now follow the Oxford University Press standard. (The TeX/LaTeX #hyphenation algorithm does a good job, but is not perfect.)
• Many previously-bad page breaks have been adjusted.

#MathHist #MathematicalBeauty #aesthetics #typography

Internet Archive

Form & Number: A History of Mathematical Beauty (Ebook, large format) : Alan J. Cain : Free Download, Borrow, and Streaming : Internet Archive

This book offers a history of beauty in mathematics and of the study of beauty in mathematics. Its intention is to examine the historical development of the...

7

6

8

0

Alan J. Cain @ajcain@mathstodon.xyz

· 6mo ago

Yves-Marie André's (1675–1764) [https://en.wikipedia.org/wiki/Yves_Marie_André] ‘Essay on Beauty’ (‘Essai sur le beau’, 1741) was an important work of 18th-century aesthetics. In the article on beauty in the 2nd volume (1752) of the ‘Encylopédie’, Denis Diderot praised André's system as the best he knew, elevating it above the work of Plato, Augustine, Wolff, Crousaz, Shaftesbury.

In 2010, I released a #CreativeCommons-licensed annotated English translation [https://archive.org/details/EssayOnBeauty]. I have just made an update: the PDF is now an accessible #TaggedPDF.

(The LaTeX tagging system is still under development [https://latex3.github.io/tagging-project/], but I have been adapting my LaTeX styles to be tagging-compatible.)

Although I was a much less practised typographer 16 years ago, I have left the overall design of ‘Essay on Beauty’ unchanged, contenting myself with minor improvements offered by an updated version of the Baskervald font, ensuring that line-end hyphenations follow the OUP standard, and a few other localized improvements.

#accessibility #OpenAccess #aesthetics #HistPhil

en.wikipedia.org

1

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

References • A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large pp.671–7. • F. Le Lionnais. ‘La Beauté en Mathématiques’. In: F. Le Lionnais, ed. ‘Les Grands Courants de la Pensée Mathématique’. L'Humanisme Scientifique de Demain. Cahiers du Sud, 1948. • F. Le Lionnais. ‘Beauty in Mathematics’. In: F. Le Lionnais, ed. ‘Great Currents in Mathematical Thought’, vol.2. New York: Dover, 1971. ISBN: 978-0-486-62724-3. URL: https://archive.org/details/greatcurrentsofm0000leli/page/121 (Note: translation is sometimes very free, and some quotations have been distorted by being translated from English to French and back.) Images from ‘Form & Number’, figures 19.3, 19.4, 19.5, and 19.6. 3/3

Internet Archive

Form & Number: A History of Mathematical Beauty (Ebook, large format) : Alan J. Cain : Free Download, Borrow, and Streaming : Internet Archive

This book offers a history of beauty in mathematics and of the study of beauty in mathematics. Its intention is to examine the historical development of the...

1

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

@cstross @overeducatedredneck @tilton @a_cubed I seem to remember some supermarkets selling milk in plastic bottles in multiples of 568ml. Did that stop? I left the UK almost 20 years ago.

1

3

0

Alan J. Cain @ajcain@mathstodon.xyz

· 8mo ago

Replying to

@arensb @onpaperwings 1969 is too early to look for a mention of Knuth — he only started working on TeX in 1977 because he saw a decrease in typesetting quality in the 2nd edition of ‘The Art of Computer Programming’ (set electronically in 1977) compared to the 1st edition (set using Linotype in 1968). I think the best resource for how/when Knuth worked on typography is his collection of papers on ‘Digital Typography’, which you can read on the Internet Archive: https://archive.org/details/digitaltypograph0000knut

Internet Archive

Digital typography : Knuth, Donald Ervin, 1938- : Free Download, Borrow, and Streaming : Internet Archive

xv, 685 p. : 24 cm

1

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 14mo ago

Replying to

@the_roamer@mastodonapp.uk Thank you! ‘Form & Number’ is still a ‘beta version’ and the content is still being polished, so comments and corrections are very welcome!

1

0

Alan J. Cain @ajcain@mathstodon.xyz

· 14mo ago

Replying to

@alexanderdyas@mindly.social Sorry, there is no official print version of ‘Form & Number’. But you are welcome to print it yourself. There is a variant PDF with a two-sided layout and hidden hyperlinks for printing [https://archive.org/details/cain_formandnumber_print]

archive.org

1

2

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

References • A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large pp.882–3. • H. Poincaré. ‘Analysis and Physics’. In: ‘The Value of Science’. In: ‘The Value of Science: Essential Writings of Henri Poincaré’. Modern Library Science Series. Modern Library, 2001. ISBN: 978-0-307-82406-6. § II. • Maxwell, quot. in F. Galton. ‘English Men of Science: Their Nature and Nurture’. London: Macmillan & Co., 1874. URL: https://archive.org/details/cu31924031010535 p.155–6. • J.C. Maxwell. ‘A Treatise on Electricity and Magnetism’. 3rd edition. Oxford: The Clarendon Press, 1892. URLs: https://archive.org/details/treatiseonelectr01maxw_0 https://archive.org/details/treatiseonelectr02maxw esp. vol. I, p. 281. • G.F. FitzGerald. ‘Heaviside's Electrical Papers’. In: ‘Scientific Writings’. Ed. by J. Larmor. Dublin: Hodges, Figgis & Co., 1902. URL: https://archive.org/details/scientificwriti00fitzgoog/page/292 3/3

Internet Archive

Form & Number: A History of Mathematical Beauty (Ebook, large format) : Alan J. Cain : Free Download, Borrow, and Streaming : Internet Archive

This book offers a history of beauty in mathematics and of the study of beauty in mathematics. Its intention is to examine the historical development of the...

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

References • A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large pp.574–5. • J.S. Mackay. ‘Herbert Spencer and Mathematics’. In: Proceedings of the Edinburgh Mathematical Society. 25 (February 1906), pp.95-106. DOI: 10.1017/S0013091500033629. • G. Monge. ‘Géométrie Descriptive: Leçons Données aux Écoles Normales, l'An 3 de la République’. Paris: Baudouin, 1798. URL: https://archive.org/details/bub_gb_Tg-L1dslDaUC • H. Spencer. ‘An Autobiography’. New York: D. Appleton and Company, 1904. vol.1 URL: https://archive.org/details/cu31924031008885 p.187. 3/3

Internet Archive

Form & Number: A History of Mathematical Beauty (Ebook, large format) : Alan J. Cain : Free Download, Borrow, and Streaming : Internet Archive

This book offers a history of beauty in mathematics and of the study of beauty in mathematics. Its intention is to examine the historical development of the...

0

Alan J. Cain @ajcain@mathstodon.xyz

· 7mo ago

Replying to

@Virginicus I completely agree that physics has different standards of beauty from mathematics per se. In physics, the beauty can involve not just the mathematical formulation, but also considerations like visualizability, conceptual commitments (what is posited to exist, etc.), and, as you say, how well it works (empirical adequacy, ease of use, stability under changing theoretical underpinnings). That said, there are quite a few instances of physicists asserting that mathematical beauty can be a guide to correctness in physics. Dirac is probably the most famous example, although his open proselytizing for mathematical beauty came *after* his own most productive period. In my work on the history of mathematical beauty, when I looked at physics, I specifically focused only on *mathematical* beauty. A general study of the role of beauty in physics (or the physical sciences more broadly) would be another book.

0

1

0