"Algebra is concerned with manipulation in time and geometry is concerned with space. These are two orthogonal aspects of the world, and they represent two different points of view in mathematics."
"Our brains have been constructed in such a way that they are extremely concerned with vision. [...] Therefore, spatial intuition or spatial perception is an enormously powerful tool, and that is why geometry is actually such a powerful part of mathematics. [...] Seeing is synonymous with understanding, and we use the word ‘perception’ to mean both things as well."
"One way to put the dichotomy in a more philosophical or literary framework is to say that algebra is to the geometer what you might call the ‘Faustian offer’. As you know, Faust in Goethe’s story was offered whatever he wanted (in his case the love of a beautiful woman), by the devil, in return for selling his soul. Algebra is the offer made by the devil to the mathematician. The devil says: ‘I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine."
Mathematics in the 20th Century - Michael Atiyah
Bull. London Math. Soc. 34 (2002) 1–15
https://marktomforde.com/academic/miscellaneous/images/atiyah20thcentury.pdf