Is beauty mathematical

Math: what makes a formula beautiful?

Abstract aesthetics: Even mathematical laypeople can recognize and evaluate the “beauty” of a mathematical formula, as an experiment reveals. The laypeople were not only largely in agreement on their classification. They also assessed the aesthetics of the equations using the same criteria as the beauty of a painting - elegance, clarity and profundity were particularly important, as the researchers report in the specialist magazine “Cognition”.

Many works of art that are considered beautiful are based on mathematics - for example in the form of the golden ratio. And fine-sounding music and mathematics are also closely linked. Conversely, Albert Einstein is said to have said that a correct equation is usually particularly beautiful and elegant. In fact, there is evidence that a certain mathematical symmetry is more likely to be perceived as correct.

Paintings, music and math formulas in the beauty test

But how objectively can the “beauty” of a mathematical formula be assessed? "Mathematicians often describe equations as 'beautiful' or 'lackluster' and famous scientists claim that mathematical beauty is a guide to the truth," say Samuel Johnson of the University of Bath and his colleagues. “But can laypeople also perceive mathematics as aesthetic?” And are the criteria the same as for the beauty of art or music?

To find out, Johnson and his team asked 300 math laypeople for their assessment. Some of the test subjects were asked to assign four mathematical formulas and four paintings to one another according to aesthetic criteria - the most beautiful picture with the most beautiful equation and so on. The second group received four pieces of classical music for mathematics comparison instead of the paintings.

The third group should describe and classify the four equations and four paintings based on nine criteria. Among them were elegance, novelty, clarity, simplicity, complexity, universality, profundity, seriousness and artistry.

Elegance, clarity and profundity

The surprising result: In fact, the test subjects not only rated the formulas as differently “beautiful” - they also largely agreed on their classification. A striking number of test persons found the same aesthetic similarities in the pictures or pieces of music and the math formulas. “The rankings were consistent between the participants,” report Johnson and his colleagues.

Also interesting: the criteria the participants used to define beauty also agreed in many respects for art, music and mathematics. “When the participants were asked to rate the beauty for works of art and mathematical arguments, the same three criteria were decisive: elegance, clarity and profundity,” report the researchers. In addition, the ratings of this third group matched the rankings of the first group.

Easier access to math?

According to scientists, this shows that even mathematicians have a sense of the “beauty” of abstract equations. In addition, the results demonstrate that similar aesthetic criteria are used here as when evaluating art or music. The qualities that we instinctively perceive as beautiful are therefore relatively universal.

This knowledge could also help to make mathematics easier for people and especially for students. “Understanding what people see as beautiful in math could also provide insights into how they understand and process math,” says Johnson. "This in turn opens up opportunities to make abstract, formal aspects of mathematics more accessible and exciting for students." (Cognition, 2019; doi: 10.1016 / j.cognition.2019.04.008)

Source: Yale University

August 12, 2019

- Nadja Podbregar