Through my colleague, Prof. Andrew Ranicki, I came upon this interesting interview with another distinguished colleague, Sir Michael Atiyah: https://www.quantamagazine.org/20160303-michael-atiyahs-mathematical-dreams/. The interview contains interesting reflection upon many things including the notion of beauty in mathematics. Indeed, Atiyah has co-authored a paper based on a very interesting neuroscience study on neural correlates of beauty: http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068.
The key conclusion of this paper is that,
… the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.
This in itself is cool, but it made me wonder – if we have a parametric signal in our brains, after a certain level of expertise has already been acquired, which correlates with how ‘beautiful’ something is, then is this useful as a heuristic in the search for new such objects? One of the limitations of most computational intelligent systems is precisely that they perform so poorly when it comes to exploratory search in open ended domains. Does this signal then help us prune search in our heads, a bit along the lines of José Raúl Capablanca’s famous, “I see only one move ahead, but it is always the correct one”?