The weierstrass function is one of famous examples of pathological function. The property of that function is continuous for all real numbers, but not differentiable everywhere.
Before discovering the pathological function, every continuous function was considered to be differentiable.
I do not understand the thought that The continuous functions are differentiable. So,I do not know why the weierstrass function is pathological. Also,I would like to gain views of the weierstrass function from present mathematics.
I wish you answer this question.