If you’re reading this post it’s likely that you already fully comprehend that beauty by it’s very nature is subjective (i.e. beauty is in the eye of the beholder). A consequence of that is there are many individuals who will not be able to experience the true beauty of mathematics, just as I may never be able to experience the true beauty of poetry (although I do believe everyone is able to have basic aesthetic responses). Every aesthetic response is uniquely individual, and of course dependent on the knowledge, understanding, experience and motivation of each person. Having said that, what we can do is use evidence to convince anyone that mathematics is inherently beautiful, even if all people can not experience all of that beauty laid bare.
Given that beauty is subjective, you could easily argue that anything has inherent beauty, and it depends on the individual as to whether the aesthetic response is negative or positive. I do not dispute that point. I simply enjoyed finding evidence on why mathematics is inherently beautiful from a number of different perspectives.
This is based on an argument I made in a previous post about the nature and pursuit of mathematics as finding, analysing and understanding pattern (Link to that post).
Mathematical Beauty Pre-Pillar:
The study of mathematics, which fundamentally seeks to find, analyse and understand patterns, provides aesthetic experiences of beauty from the perspectives of neuroscience, psychology and evolutionary biology.
Psychology: According to Dietrich Dorner’s PSI-theory, beauty is based on a need for reducing uncertainty. Human beings crave explanations of our surroundings, and when we are able to discern order from something that may initially appear disorderly, we satisfy a basic need for reducing chaos. Once uncertainty diminishes we open the door to feeling pleasure, and this is precisely the point at which we access aesthetic appreciation (cited in Delle-Donne, 2010). Hence, given that a fundamental aim of mathematics is to reduce uncertainty by seeking, analysing and understanding pattern, there becomes little to dispute from a psychological perspective that mathematics is inherently beautiful.
Evolutionary Biology: Anjan Chatterjee, Professor of Neurology at the University of Pennsylvania, wrote a supremely detailed account of aesthetics in his book, ‘The Aesthetic Brain’, in which there are numerous references to the integral connection between pleasure and beauty – he understandably referred to the work of Edmund Burke who may have popularised this idea. Chatterjee provides an evolutionary biological interpretation of why human beings have a need to reduce chaos. He draws on research which shows that people prefer landscapes and scenes which predict safety and nourishment due to their relative uniformity. Human beings were more likely to survive if they could see patterns in landscapes amenable to survival. This idea is elaborated on in Denis Dutton’s TED Talk, “A Darwinian Theory of Beauty,” and also in the idea of patternicity put forth by Michael Shermer, which is the phenomenon in which human beings have a predisposition through the process of evolution to search for patterns in anything, even in meaningless noise (Shermer, 2008).
Of course, one might say that the leap between drawing on visual patterns amendable to survival – to abstract pattern recognition in mathematics – is a leap too far. However, as Mattson (2014) argues, the increased size of our cerebral cortex dramatically increased our superior pattern processing (SPP), which he argues is the “fundamental basis of, if not all, unique features of the human brain including intelligence, language, imagination and invention.”
Neuroscience: Scientists in the UK recently conducted an experiment in which fifteen mathematicians were asked to rate sixty equations on an aesthetic scale of -5 to 5 (ugly to beautiful). MRI scans showed that the region of the brain which connects sensory experience, emotions and decision making, was highly active when the mathematicians saw equations that they considered to be beautiful. It happens that the same region of the brain is similarly active when we look at art of listen to music that is perceived as beautiful. So, if anyone is to claim that particular pieces of music or art are beautiful, neuroscientists would also claim that particular parts of mathematics are perceived in a similar way (Newman, 2014). In addition, one of the reasons we enjoy music is based precisely on pattern recognition and prediction. As Salimpoor et al (2013) found, when we listen to an unfamiliar piece of music, our brains predict how the music is likely to develop, and we get a sense of reward from that. You might be forgiven for thinking that reward is purely sensory, but the researchers found that this reward is a direct intellectual one also, which is what we could reasonably expect from pattern searching and recognition in mathematics.
Chaterjee, A. (2014). The Aesthetic Brain: How we Evolved to Desire Beauty and Enjoy Art. UK: Oxford University Press.
Delle-Donne, V. (2010). How can we explain Beauty? A Psychological Answer to a Philosophical Question. Proceedings of the European Society for Aesthetics, vol 2.
Mattson, M. (2014). Superior pattern processing is the essence of the evolved human brain. Retrieved from: https://www.frontiersin.org/articles/10.3389/fnins.2014.00265/full
Newman, S. (2014). Beauty in Math and Art Activate the Same Brain Area. Retreived from https://www.scientificamerican.com/article/beauty-in-math-and-art-activate-same-brain-area/
Samimpoor, V. N., Van den Bosch, I., Kovacevic, N., McIntosh, A. R., Dagher, A., & Zatorre R.J. (2013). Interactions between the nucleus accumbens and auditory cortices predict music reward value. Science, 320(6129), p. 216-219.
Shermer, M. (2008). Patternicity: Finding Meaningful Patterns in Meaningless Noise. Scientific American. Retreived from https://www.scientificamerican.com/article/patternicity-finding-meaningful-patterns/