MathOverflow

What are some of the "advantages", as it were, of set theory compared to type theory when it comes to mathematical research?
Many papers tell of the potential advantages of type theory over set theory (e.g. dependent type theory in proof assistants). I am not speaking about polemical writings but instead where a type-theorist is giving justification for their research project...

I have been considering whether the distribution of prime numbers can be viewed as a structured phenomenon driven by wave-like or energy-based behavior, rather than being purely random.
My intuition is that there may be an underlying pattern that could be interpreted in terms of oscillatory or wave interactions....

Suppose there are two classes of morphisms $w_1, w_2$ in $C$ and twotwo reflective localizations $L_1: C \overset{\rightarrow}{\hookleftarrow} C^\text{$w_1$-local}: i_1$ and $L_2: C \overset{\rightarrow}{\hookleftarrow} C^\text{$w_2$-local}: i_2$. I...

Let $H$ be a Reproducing Kernel Hilbert Space with elements $f:X\rightarrow \mathbb{C}$, with kernel $K(x, y)$. My question is whether, for some choice of $x_i\in X$, it is the case that $u_i:=K(x_i, \cdot)$ is a basis for $H$. What additional conditions...