Alan J. CainFeb 8

Abū’l-Wafāʾ al-Būzjānī (940–77/8 CE) 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.

For instance, he wrote about a method of constructing a magic square of order 4:

‘It is possible to arrive at the magic arrangement in this square by means of methods without displacement showing regularity and elegance [niẓām wa-tartīb ḥasan نظام وترتيب حسن]’ (trans. Sesiano)

Such a method with ‘regularity and elegance’ was: (1) place the number 1 in a corner, 2 and 3 adjacent to the opposite corner, and 4 diagonally adjacent to 1; (2) place 5 to 8 in reverse order in positions horizontally symmetrically opposite to 1 to 4; (3) place $17 − n$ diagonally two places away from $n$ for $n = 1,\ldots,8$ (see attached image).

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#MagicSquare #HistMath #MathematicalElegance #elegance #aesthetics

Show threadAlan J. CainFeb 1

@marick An exception is perhaps the late Edsger Dijkstra. He wrote often about the important of beauty in programming and computer science generally.

In particular, he noted that beauty and elegance are the greatest virtues that a computer program could have and that

‘when we recognize the battle against chaos, mess, and unmastered complexity as one of computing science's major callings, we must admit that “Beauty is our Business”’,

and

‘in the practice of computing, where we have so much latitude for making a mess of it, mathematical elegance is not a dispensable luxury, but a matter of life and death’.

(He seems not to have distinguished elegance and beauty, and he subsumed the aesthetics of computer science within the aesthetics of mathematics. )

At risk of making this an advertisement, for the citations for these quotations and other sources for Dijkstra's views on beauty, I will point to pp.697–699 of my open-access book ‘Form & Number: A History of Mathematical Beauty’ [https://archive.org/details/cain_formandnumber_ebook_large].

#MathematicalBeauty #MathematicalElegance #aesthetics

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...

Internet Archive
N-gated Hacker NewsJun 9, 2025
🚀🔍 Ah yes, let's gather 'round the campfire and listen to the riveting tale of why an impossibly perfect theory falls apart in the face of real-world #complexities. 🎩💸 Spoiler alert: Reality check—human behavior isn't driven by mathematical elegance. 😅📉
https://jonathanwarden.com/quadratic-funding-is-not-optimal/ #imperfecttheory #realworld #humanbehavior #realitycheck #mathematicalelegance #storytelling #HackerNews #ngated
Eight Reasons Why Quadratic Funding Is Not Optimal

Introduction Quadratic funding has received a lot of attention recently as a mechanism for funding public goods—especially in the cryptocurrency space. QF is appealing because it is theoretically optimal under certain assumptions1.\nThe problem is that these assumptions don’t ever hold in reality.\nThe theory behind QF is sound and elegant, and the authors of the original paper are clear about the assumptions. They don’t claim they are likely to hold in reality, and warn about the consequences when they don’t hold. Unfortunately, practitioners have sometimes been too enthusiastic, implementing QF in settings where theory actually predicts poor results.\n