Borges may have studied mathematics, but I posit that he was simply a well educated man of the time. Its not unreasonable to assume that he would have read ancient Greek thinking, grounding him in logic and paradoxes, for example, or looked at Pascal and Descartes for their philosophy and picked up mathematics on the way. I see evidence of a well educated and supremely well read humanist rather than someone quietly studying Cauchy and Legendre on the down low.