Software development is interesting in that it borrows for a vast range of other disciplines depending on what you're building. Very commonly, that's maths. You're not going to get very far manipulating matrices for 3D geometry without a bit of maths understanding. But, similarly, you're not going to get very far into developing a knitting pattern generator without understanding knitting - but that doesn't mean you can't be a developer unless you can knit. That'd be crazy.

If you develop applications that aren't reliant on maths then sure, you don't need to understand maths. On a day to day basis I write web apps that take strings from users, store them in a database, and display them in a different way later. No maths at all. Conversely, I've once wrote an image manipulation library based around convolution filters that used lots of maths.

As with most things, there's no single black and white rule. It's all shades of grey.