## Introduction

^{iπ}+ 1 = 0) as one of the most beautiful equations (Chatterjee, 2015), a claim beyond the grasp of most laypeople who might not be able to observe the deep conceptual underpinnings of the equation, and thus its meaning. Consistent with this idea, in an experimental study with mathematicians (i.e., domain experts) as participants, Zeki and colleagues (2014) found that beauty ratings correlated negatively with standard deviations in judgments of equations, i.e., there was a greater consensus on beautiful mathematical equations than on not beautiful equations. The authors interpreted this finding to mean that a sense for the beauty of equations is shared and universal, but that it can only be perceived when people understand those equations (or have learned the “language” of mathematics).

## Method

### Participants

^{2}(1, N = 40) = 5.01, p = 0.025. There was no difference in age between the two groups (t[38] = − 1,698, p = n.s.).

### Stimuli

### Procedures

## Results

_{experts}= 38, SD

_{experts}= 3.4; median

_{laypeople}= 39, SD

_{laypeople}= 4.1; Cohen’s d = − 0.180, p = 0.430). This suggests that the two groups did not differ in their general ability to make aesthetic judgments based on the visual stimuli.

^{2}(1, n = 64) = 11.497, p < 0.001.

_{experts}= 21, SD

_{experts}= 9.9; median

_{laypeople}= 12, SD

_{laypeople}= 10.8; Cohen’s d = 0.588, p < 0.05). As for the aesthetics justification, experts stated more often than laypeople that their classification relied on meaning (Chi-squared test: X

^{2}[1, N = 40] = 5.867, p < 0.05). See Table 1 for the other categories.

Familiarity (median number of equations) | Simplicity | Balance | Complexity | Symmetry | Form | Composition | Meaning | |
---|---|---|---|---|---|---|---|---|

Experts | 21 | 17 | 9 | 12 | 8 | 11 | 10 | 14 |

Laypeople | 12 | 16 | 5 | 9 | 8 | 11 | 7 | 7 |

_{experts}= 0.793, p < 0.001), compared to laypeoples’ average aesthetic categorization with number of laypeople familiar with the respective equations (ρ

_{laypeople}= 0.564, p < 0.001, Fisher’s z: p < 0.01) (see Table 2). This means that experts preferred equations that they (as a group) were more familiar with to a higher degree than laypeople preferred equations that they (as a group) were more familiar with. In addition, we calculated the difference in number of experts familiar with each single equation and number of laypeople familiar with the same equation and, again, correlated this value with aesthetic classification by experts and laypeople (ρ

_{experts}= 0.444, p < 0.001; ρ

_{laypeople}= 0.109, p = 0.392, Fisher’s z: p < 0.001) (see Table 2). This means that experts preferred equations that were more familiar to them (as a group)—whereas no such effect was seen for laypeople.

Average (experts) | Average (laypeople) | Fisher’s z | |
---|---|---|---|

Number of participants familiar with this equation | 0.758 | 0.575 | p = 0.032 |

Number of experts familiar with this equation | 0.793 | 0.509 | p = 0.002 |

Number of laypeople familiar with this equation | 0.590 | 0.564 | p = n.s |

Difference between number of experts and number of laypeople familiar with this equation | 0.444 | 0.109 | p < 0.001 |

Experts | Laypeople | Fisher’s z | |
---|---|---|---|

Numbers | − 0.197 | − 0.071 | p = n.s |

Latin letters | − 0.485 | − 0.009 | p < 0.001 |

Greek letters | 0.017 | 0.020 | p = n.s |

Signs | − 0.507 | − 0.244 | p = n.s |

Sum of all elements | − 0.540 | − 0.133 | p < 0.001 |