The philosophy has an impact in the mental model and the learnability of the mathematical theories. Technically you could learn and use the mathematics without

The philosophy has an impact in the mental model and the learnability of the mathematical theories. Technically you could learn and use the mathematics without knowing the philosophy behind it but in practice almost nobody does that. It's like knowing design patterns in OO: it's ultimately all software right? But software exists first in the mind of the programmer, and what's written in the IDE is just a shadow of what the programmer imagined. This makes one appreciate the point that there are things in software that exists entirely inside our heads