There are three mental modes in which human minds interface with mathematics.
- Wrinkly virgin beta brain: Speaks only in formal statements. Visible confusion when you omit a technical hypothesis. Prefers multi-page align environments and custom tikzcd arrows to plain english words.
- Smooth concave tripping-balls brain: Communicates only in metaphors and similes that strip away all literal mathematical content in favor of pure vibes.
- Chad alpha physicist brain: Comprehends the conceptual heart of all matters, reduces complex statements to crystalline nuggets of clarity. Respects rigor, but never pays it unwavering deference.
The first mode is incapable of eye contact but can write referee-validated proofs. The second mode can inspire and conjecture but can’t compute anything. The third mode can make real progress on uncharted problems but approaches technical lemmas like a politician approaches alegations of sexual misconduct – by denying and ignoring. An effective mathematician must command all three unified under a common will.
This is not a Goldilocks situation: unlike the three bears, there is no mode which is “just right”, all three are mission critical. Nor is this a Holy Trinity type deal – while Abraham’s god was obviously autistic and Jesus definitely knew to pass left, no one would ever describe any manifestation of the Christian god as a “Chad”.
*Category theorists have no access to mode 3. They flit rapidly between 1 and 2, with no apparent sense of irony.