How important is it for a mathematician to be able to be able to visualize some given curve or object in their minds. I ask because, while I like to think I’m a pretty good at purely analytical reasoning, my capacity for visualizing curves and geometries in my head is not that great. I had lots of issues with this in multivariable calc . Are there branches of math where the ability to do this kinda visualization is not so important? How much does each realm of mathematics make use of this?
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