THE SQUARE ROOT OF NEGATIVE ONE IS IMAGINARY

I focus on specific practices in twentieth- and twenty-first-century mathematics of articulating, barring, taming, and operating with what mathematicians widely call mathematical monsters. I describe how over centuries the quotidian procedures of the epitome of rational practice – mathematics – have produced beings outside the extant purified categories understood by theorems and proofs, despite, and sometimes as a consequence of, ever greater...