Does a programmer need to know complex math in order to write efficient algorithms?

Depends on what the algorithm is for. Here, in pseudocode form, is an extremely efficient algorithm to print all the positive integers between 1 and N: x := 1 while x <= N:     print x     x := x + 1 Not much mathematical heavy lifting there, and you won't be able to improve much on that solution no matter how much of a math whiz you are. Many common, useful algorithms are closer in mathematical complexity to the above than to, say, Diffie-Hellman.

Not at all.  You could just be lucky.  But you may need complex math to prove that your algorithm is efficient.  But no one forces you to do that.

There are two sides for this story: 1. Implementing an already existing algorithm using your favorite language. This is where computer organization, and a good grasp of the environment where your code is going to run is fundamental. 2. Designing an algorithm from scratch (i.e coming up with a pseudocode) This field requires a decent amount of math. Especially if you are expected to prove that your algorithm is correct and to provide a given performance measure (i.e. time complexity or space requirements).

According to Webster, an algorithm is "a step-by-step procedure for solving a problem or accomplishing some end especially by a computer". So ANY step-by-step procedure you program is an algorithm! It doesn't have to be complicated. http://www.merriam-webster.com/dictionary/algorithm

It depends on the nature of problem you are trying to solve. In most of the cases basic mathematic skills are enough. Even if the problem requires complex calculations, you can always find third party APIs that will do all the heavy duty work for you.

The most "complex" math I ever used in 40 years of software development was high school algebra.  (I had to learn accounting to write an accounting program, but that's arithmetic.)If you develop scientific software that uses complex math you have 2 options.  You can learn the math (which can take years) or you can have someone you're developing the program for write the equations for you, and plug them into the program.  (I did that with a program dealing with optics - instead of learning optics, I had a technician write out the formulas I needed.)

Mathematics helps you rigorously prove your algorithm and it can also help you reason your way quickly towards the correct solution. Basically math is to software development what science is to other engineering disciplines.

I don't think Big O notation http://en.wikipedia.org/wiki/Big_O_notation requires "complex math"