the apps you can build without mathematics are limited to crappy Facebook clones.
Most business software doesn't require more than basic algebra. As long as you know how to read math formulas and implement them in code, you can just look up most of the stuff on wikipedia.
For example, I worked on a monthly payment calculator for loans. All I needed to do was spend an hour reading http://en.wikipedia.org/wiki/Annuity_(finance_theory)#Proof and playing with the forumla on paper.
Create a function to wrap the algorithm and test the inputs and outputs. Then you spend 2 days writing code and tests for the web interface around the function. In my job most programming is plumbing with infrequent math problems that only need to be solved once in a generic fashion. Heck, if there's complex math, there's an open source library for that. (Or a contractor! Or a web service. Or a contractor writing a custom accounting system that does the heavy lifting.)
Unless you're going to be specializing heavily on a specific problems, you don't need college level math, you just need your basic high school education and access to the internet.\
Note: My high school education included a semester of statistics. I would add my discrete mathematics classes in college have been useful but not strictly necessary.
It's not that people don't like math. People are inherently lazy and acquiring logical skills requires work.
* implementing the accounting formulas
* Chrome interpreted your HTML code and calculated the layout for your website
* your ISP knew to attach your URL with your IP address and serves it to your users
* even the development process itself is iterative; building on previous changes
Algorithms were present in all these steps. Once you have users, you will need to keep track of them. Probably you will use an array, tree or other data structure.
As long as you feel comfortable outsourcing the hard stuff, you can put together simple projects like these.
The second point isn't mathematics; it's arithmetic.
The third and fourth points are really statements that are as too broad as the statement that "math is not necessary for software development". In particular, were were to employ your use of the word "algorithm" it would apply to literally any activity that can be described as a series of instructional steps. Consequently "how to make a peanut butter and jelly sandwich" becomes an exercise in mathematics, for example.
As a person who comes from an academic field in science that is rich in applied (and some theoretical) mathematics, my observation is that there exists very few cases where a person writing software at almost any level actually needs to have a deep mathematical/theoretical understanding of the data structures and algorithms he employs. And I mean "deep" in the sense that he even has to understand that a mathematically-backed theory is what he's employing. This is as true for computer science graduates having a prolonged bout of anxiety and envy of mathematicians and scientists as it is for the "lowly" CRUD App Developer. At the deepest, one needs to be able to employ arithmetic to compute a rough "Big O" estimate. That's "doing math" I guess, in the strictest sense, but only in the same sense as a child "does number theory" when he writes, e.g. "10" in the blank for "9+1 = ___".