Question 2: If “the mathematician’s patterns, like the painter’s and the poet’s, must be beautiful” (G.H. Hardy), how might this impact the production of knowledge? Discuss with reference to mathematics and the arts.
Guiding Questions
What does beauty mean?
In math - Simplicity? How succinct it is? Symmetry? Ease?
In art - Evokes emotion? Aesthetically pleasing to the viewer (what makes it aesthetic)?
Do we seek to make art only for the purpose of making it beautiful?
What other reasons might we have to create art? Could beauty or lack thereof play a more profound role?
Do we happen to find beauty in math, or is it because of a mathematician’s desire for simplicity, that one is drawn towards the most “beautiful” math?
This question might not be the most relevant in writing the essay. Still, it does help to frame any arguments regarding the production of mathematical knowledge and beauty being coincidental or purposeful.
Is there math that might not be beautiful?
What is the link, if any, between function and beauty?
Question Analysis
For this question, you can come up with your definition of beauty in both mathematics and the arts. Perhaps for mathematics, beauty could be seen in the simplicity of an equation (taking something complicated and creating an easy way to solve or simplifying the process). It could also refer to the cyclical nature of some mathematical concepts (e.g. trigonometry, certain functions) or even symmetry within mathematics (numerically or geometrically). For the arts, beauty could refer to how it is seen to be aesthetically pleasing by viewers, its ability to evoke emotion and make you feel a certain way.
The statement in this question comes in with the assumption that mathematical patterns must be beautiful. What you might want to consider is whether this is even true and then how that will impact knowledge production. Perhaps, you think that it is not the case, but rather we seek simplicity and as a result, mathematics tends to be beautiful. So, while these two points are similar, the original intent is different. Both lead to the outcome of beautiful mathematics, but one stems from intentionally searching for beauty, while the other just seeks to solve problems quickly and the knowledge just so happens to be beautiful in the process.
The other assumption of this question is that art has to be beautiful and once again you can consider whether the only purpose for creating art is for beauty. Could there be other reasons for the creation of art (e.g. political motivations, personal agenda)? If you find other reasons, then you can also look into how beauty or the lack thereof might play a more profound role than simply aesthetics. Maybe the art has an implicit purpose and the beauty of it helps to draw more viewers in.
For both of these AOKs, something that might be helpful to consider is also whether there are any links between form and function. Perhaps mathematics and art that is more beautiful are better able to convey a message and solve a problem. On the other hand, it might just be that we as humans find beauty in things that are functional. Of course, the line between the two might not even be so clear so as you traverse this blurry boundary, you can also find ways to answer the original statement.
AOKs: must be mathematics and art