When one looks at a title “Beauty: a Mathematical Aesthetics” one never 
expects to get into a discussion at the beauty parlor level.  Near IADE 
there is a school of aesthetics “Escola Internacional de Est?tica” EIT, 
where people learn about creams and powders, maquillage, what so ever… I 
some times nag one of our colleagues that teach aesthetics submerged in 
Tarkovski, Deleuze, Plato, Kant and other ugly guys that she should go there 
(to the EIT) and learn something about real aesthetics.

I guess Pythagoras is one of the first guys that reflected upon mathematics 
and Aesthetics. ( I must stress this, like Ranulph did: Aesthetics deals 
with sensible perception in which beauty MAY be encompassed. Aesthetics is 
not about deciding what is Beautiful or Ugly, like Ethics is not about 
deciding what is Good or Evil.

Well, back to Pythagoras, by associating dimensions, numbers and aesthetical 
appreciation in dividing cords in proportionate intervals, the Greek 
footballer established a relation between geometric, numeric, and aesthetic 
entities. The proportioned subdivision of the cords conducted to agreeable 
chords. Other subdivisions not according to that subdivision of cords 
produced not agreeable chords.

This would make guys like Alban Berg, Arnold Schonberg, even the final Aaron 
Copeland, Luciano Berio and so forth laugh to the tears, not because they 
had not found the validity of the Greek proportions but because their 
musical aesthetics was being really aesthetical by manipulating the human 
capacity of sensible perception in all possible directions.

Well, the title conjures a different question by making Beauty = to 
Mathematical Aesthetics or Beauty =» Mathematical Aesthetics or probably 
Mathematical Aesthetics «=» Beauty. In any case one must know what a 
Mathematical Aesthetics is.

By replacing Aesthetics by sensible perception we get: Mathematical sensible 
perception. By replacing sensible by “through sentiments” and perception by 
“immediate apprehension” we get: Mathematical immediate apprehension through 
sentiments. Now let’s replace Mathematical. Not that easy, but we would risk 
to say that all mathematics lies on abstract reasoning so we will have: 
“abstract reasoning immediate apprehension through sentiments” = 
Mathematical Aesthetics. This sounds very much like an oxymoron… Let’s move 
through another path: Mathematical Aesthetics is the set of theories that 
study the qualification of mathematical expressions by its aesthetical 
value, say by categories long established resulting from sensible 
perception: beautiful, gorgeous, attractive, repulsive, nauseous, ugly, 
perfect, unperfected, imperfect, ooohhh, ghghgghh, elegant, etc, etc. This 
make sense, we hear a lot of times, “well done that’s a beautiful solution, 
that’s an elegant formulation" or “your calculus seem a bit chubby”.

Well, both paths are far from establishing the expression “Beauty: A 
Mathematical Aesthetics” as a valid matter illustrated by good looking girls 
becoming even more good looking and not so good looking guys staying not so 
good looking.

There is still another path to move through: Aesthetics with a capital A 
turn out to be in the last two centuries the Academic discipline that 
studies Art in the sense that Art Objects are made specially FOR sensible 
perception (and social acclamation as superlative we might add). In that 
sense none of the examples of face lifting and notions of average beauty are 
of any interest since they are not Art although there is a mathematical 
study of Art and even mathematical production of art as we have seen since 
Pythagoras. The conspicuous relations between Mathematics and Music and 
Mathematics and Architecture  (and consequently with Design) are too 
fastidious, but are all that matters when we use the word “Aesthetics”.

Well, it’s a great thread like Ido said,



Cheers everyone,



Eduardo