Modern mathematics deals with ISA design from the perspective of application: A CPU, an FPGA, and an GPU are all Turing complete substrates, yet they’re useful

Modern mathematics deals with ISA design from the perspective of application: A CPU, an FPGA, and an GPU are all Turing complete substrates, yet they’re useful for wildly different things. Category theory, type theory, and set theory all can embed arbitrary mathematics — but the encodings you get lend themselves to different applications. Eg, category theory is very useful at abstracting structures to check if they’re “the same”.