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The Sublime is sometime used as a synonym for subtle or sophisticated but with aesthetic overtones. In the original setting for this aesthetic notion it was a combination of Beauty & Greatness, and it evolved to also include Awe & Terror & Horror. For example Kant held that

the sublime was of three kinds: the noble, the splendid, and the terrifying.

Mathematics is commonly held (by mathematicians and others - for example Rexroth a poet, and Pasternak a novelist and poet) to have Beauty; can it also be sublime in all of Kants sense?

Sublime in the 16th century was generally understood to mean as:

"expressing lofty ideas in an elevated manner," from Middle French sublime (15c.), or directly from Latin sublimis "uplifted, high, borne aloft, lofty, exalted, eminent, distinguished," possibly originally "sloping up to the lintel," from sub "up to" + limen "lintel, threshold, sill".

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I think you can argue that mathematics can be sublime based on how mathematics is able to invoke emotions and inspire even those who aren't directly involved with solving the equations.

To give a few examples, I would argue that Conway's game of life as a mathematical topic is able to demonstrate how complex patterns can develop out of simple rules.

Similarly the Mandelbrot Set shows us an abstract and beautiful pattern resulting from the continous application of a simple rule, which I at least for my own part find inspiring similarly to a work of art in it's reflection on how complex patterns in the world around me may arise from simple things.

In the realm of number theory, primes and pi have inspired people for centuries, not just because of their mathematical properties but also by virtue of an unpredictable behaviour (pi is irrational, primes are hard to predict) emerging from a deterministic system. Classically this unpredictable behaviour was so frightening to the Pythagoreans that they supposedly resorted to drowing Hippasus when he proved the irrationality of sqrt(2) although this is probably not entirely based on reality.

Whether these examples are enought to justify mathematics as sublime is up to you to decide, but I think it's fair to conclude that mathematics is able to both inspire, frighten, and amaze.

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Mathematics is the fundamental programming code of reality. It is without doubt that reality is both grotesque and exquisite. It therefore reasons that mathematics is sublime,in essence reality is sublime.

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