# Mathematical Beauty, Understanding, and Discovery

@article{Cellucci2015MathematicalBU, title={Mathematical Beauty, Understanding, and Discovery}, author={Carlo Cellucci}, journal={Foundations of Science}, year={2015}, volume={20}, pages={339-355} }

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can…

## 21 Citations

### The Importance of Surprise in Mathematical Beauty

- Education
- 2016

Synopsis Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity,…

### Aesthetic Preferences in Mathematics: A Case Study

- Art, Philosophy
- 2018

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them?…

### Artistic Proofs: A Kantian Approach to Aesthetics in Mathematics

- Art, PhilosophyEstetika: The European Journal of Aesthetics
- 2019

This paper explores the nature of mathematical beauty from a Kantian perspective. According to Kant’s Critique of the Power of Judgment, satisfaction in beauty is subjective and non-conceptual, yet a…

### What is a Beautiful Experiment ? ( forthcoming in Erkenntnis )

- Art
- 2021

This article starts an engagement on the aesthetics of experiments and offers an account for analysing how aesthetics features in the design, evaluation and reception of experiments. I identify two…

### What is a Beautiful Experiment?

- ArtErkenntnis
- 2022

This article starts an engagement on the aesthetics of experiments and offers an account for analysing how aesthetics features in the design, evaluation and reception of experiments. I identify two…

### Beauty in Motion Through the Lens of Doppler’s Formula

- Physics
- 2020

Many founding fathers of science have underscored the importance of beauty in mathematical representations of natural phenomena and their connection with the beauty of the objects they represent.…

### Aesthetic values in science

- Philosophy
- 2017

Scientists often use aesthetic values in the evaluation and choice of theories. Aesthetic values are not only regarded as leading to practically more useful theories but are often taken to stand in a…

### MOTIVATED PROOFS: WHAT THEY ARE, WHY THEY MATTER AND HOW TO WRITE THEM

- PhilosophyThe Review of Symbolic Logic
- 2020

It is argued that motivated proofs promote understanding, convey new mathematical resources and stimulate new discoveries, thus have significant epistemic benefits and directly contribute to the efficient dissemination and advancement of mathematical knowledge.

### Philosophy of mathematical practice: a primer for mathematics educators

- Philosophy
- 2020

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we…

## References

SHOWING 1-10 OF 50 REFERENCES

### Mathematical Beauty and Perceptual Presence

- Philosophy, Art
- 2011

This paper discusses the viability of claims of mathematical beauty, asking whether mathematical beauty, if indeed there is such a thing, should be conceived of as a sub-variety of the more…

### THE PHENOMENOLOGY OF MATHEMATICAL BEAUTY

- ArtSynthese
- 2004

The purpose of the present paper is to try to uncover the sense of the term “beauty” as it is currently used by mathematicians.

### Mathematical Beauty and the Evolution of the Standards of Mathematical Proof

- Philosophy, Art
- 2005

an important part in the subjective experience and enjoyment of doing mathematics. Some mathematicians claim also that beauty acts as a guide in making mathematical discoveries and that beauty is an…

### The Roles of the Aesthetic in Mathematical Inquiry

- Art
- 2004

Mathematicians have long claimed that the aesthetic plays a fundamental role in the development and appreciation of mathematical knowledge. To date, however, it has been unclear how the aesthetic…

### Beauty in Proofs: Kant on Aesthetics in Mathematics

- Philosophy, Art
- 2015

It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems,…

### The Omniscienter: Beauty and scientific understanding

- Philosophy, Education
- 2002

Science has more to offer than just knowledge of nature; it can give us understanding of nature as well. Epistemology of science is usually focused on knowledge and the criteria of justification,…

### Aesthetic Considerations in Mathematics

- Art
- 2011

Drawing on some of the principles of humanistic mathematics rst outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics…

### V—Aesthetics in Science: a Kantian Proposal

- Philosophy, Art
- 2013

Can aesthetic judgements legitimately be linked to the success of scientific theories? I suggest that a satisfactory answer to this question should account for the persistent attraction that…

### Are these the most beautiful?

- Psychology
- 1990

In the Fall 1988 Mathematical Intelligencer (vol. 10, no. 4) (11) readers were asked to evaluate 24 theorems, on a scale from 0 to 10, for beauty. I received 76 completed ques(12) tionnaires,…

### The experience of mathematical beauty and its neural correlates

- PsychologyFront. Hum. Neurosci.
- 2014

Functional magnetic resonance imaging (fMRI) was used to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly, and showed that the experience of mathematical beauty correlates parametrically withActivity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as theExperience of beauty derived from other sources.