Dear Dr. Alyssa Adams,
Thank you for your kind feedback!
I am in agreements. While in the essay I did not reflect on the ontological status of mathematics, merely that we cannot reason scientifically without the usage of mathematics, I believe that math while deeply linked to our psychology is at the same time independent of it.
Alien species aside, we can also readily use computers to do mathematics, and I think that is a good argument that mathematics indeed is independent of the human mind.
An interesting experiment is to ask complete novices in computer science and mathematics to code some basic arithmetic. For instance, raising a number by an exponent. Many people don't know that any number raised to zero is one, and indeed would be surprised that their correct code automatically gives the right response. If mathematics was purely psychological, then there was no way they could have given a code that produced a counter-intuitive but correct ans. Or at least this is how I would interpret this situation.
Again, thanks for your feedback here!
Best Wishes,
Raiyan Reza