The nature of intellectual aesthetic experience

I am a painter with a background in mathematics. I paint what has come to be known as ‘math paintings’. It is one of those unfortunate terms that will dog me forever that say so little about my work. But I do paint with mathematics. I spend months developing complex mathematics related to the subject I choose to paint. I get passionately involved with mathematical definitions, theorems, proofs and numbers that I find exciting and beautiful and that describe a certain aspect of my chosen subject matter e.g. beauty if I am painting faces of women. Once I am done with the research, I use the resultant outpouring of mathematics to paint. I literally paint with mathematics. There is often very little on my canvas that is not painstakingly constructed using layered equations, numbers and symbols.

But why do I do this? I have spent years working with mathematics and I am familiar with the excitement that a good piece of mathematics can generate. There are some proofs and theorems and geometrical objects that I find exceptionally beautiful and I have often experienced a racing of pulse when I stumble upon a great mathematical solution. My reaction to my mathematics is often more intellectual than it is emotional. When I call my mathematics beautiful, I have an aesthetic experience which I choose to call an intellectual aesthetic experience (IAE). An intellectual aesthetic experience is intellectual and is elicited by the mind’s experience of an intellectual object. I paint to construct conduits to tap onto this experience. My paintings and everything that goes into making them are special purpose vessels of the IAE. Does that make any sense?

Why mathematics? Scientific theories can be beautiful. Engineering systems are often referred to as aesthetically pleasing. (Much of what you see in Biennales around the world today appeal chiefly to the IAE, in my opinion). Also, mathematics is not a spectator sport and too many people are turned off by it, thanks largely to our education systems.

To answer this question, I want to spend the rest of this article to talk about the special place that mathematics occupies beside aesthetic experience. First, consider the famous question - “…How are synthetic judgments apriori possible?” which begins Kant’s Critique of Pure Reason. Kant proposes that the objective validity of mathematical knowledge rests on the fact that it is based on the apriori forms of our sensibility which condition the possibility of experience. If we have apriori conditions to sensibility, then we have knowledge that is more than just logical. If we say, ‘It is either snowing or not snowing’ we have an analytic proposition. An analytic proposition is about logical relations and not empirical facts. Its truth rests on definition and logic alone. Empirical knowledge on the other hand is synthetic. It tells us more than mere logical relations. For the special case of apriori synthetic knowledge that is independent of experience, we can have knowledge (more than just logic) without experiencing it. Mathematics is this special case of synthetic apriori knowledge. Mathematics, according to Kant is based on the preconditions of experience itself. So, mathematics is closer to the way we experience than we might like to think.


But in the last 200 years, the above apriori synthetic/analytic boundary was challenged by the introduction of non-Euclidean geometry, as well as Turing’s halting and Godel’s incompleteness theorem. With non-Euclidean geometry for instance, apriori synthetic truth is revealed as simply a logical possibility. And if apriori synthetic truths condition the possibility of experience, experience itself becomes malleable. Once we learn the new preconditions, we are free to change the way we experience, altering its very definition. We see here the finitude of Reason, the central theme to Kant’s philosophy. Nature does not speak to Reason. The ‘other’ is mute. Reason is not the mirror reflecting the light of Nature. We know this because it is incompatible with the very essence of empirical science – that we cannot conduct experiments independent of context. The power of human Reason is not in its universality but in articulating its own boundaries against non-Reason. Mathematics is a special form of dialogue between Reason and the ‘other ‘( non-Reason) and Mathematics allows the ‘other’ to reveal its authoring otherness. Mathematics thus becomes a true counterpart to poetry in that both seek ways to transcend the radical finitude of Reason. Aesthetic experience therefore is a constitutive component of human rationality.


I have outlined (too briefly) how mathematics and aesthetic experience might be related. I hope to continue in part II with an in depth discussion on the nature of IAE.