Why do many experienced programmers have a Maths or Physics background?

If you have a mathematics or physics background you can pick up programming in your spare time and on the job. Frankly, if you can do physics or mathematics it's not very hard to get started in programming, though obviously programming can get as deep and as hard as you want. As a mathematician I got my first job in programming by posting an algorithm on the web (here it is: https://groups.google.com/forum/?fromgroups=#!topic/comp.graphics.algorithms/9tzu-_bJgOg) and getting noticed by a game developer. The algorithm was really just pure mathematics but it partially solved what was a challenging problem at the time. (I came up with a better algorithm 6 months later.) I taught myself x86 assembly language to code it up really fast and that got my foot in the door. When I started the job I learnt tons of programming by talking with my coworkers and I've bluffed my way ever since.

In the rear view mirror, computer science emerged from somewhere between mathematics and electrical engineering not so long ago, so by the mere passage of time, anyone who's still hanging around it from then is going to be pretty experienced. I don't suppose that's exactly what the question is about, though, so I'll try another take as well. One central question when you are completing the construction of a mathematical model is does it cover all the corner cases? If a program is going to be any good, it faces the exact same question, and requires a similar kind of systematic examination in order to get it right. Answering it is a little harder in the sense that the kind of enormous outcome spaces of a program makes it hard to analyze everything, but it's a little easier in the sense that you have a machine that can test parts of it quicker than you can think. The fundamental part of getting it right is the eternal thought experiment to play the devil's advocate to your own logic. Every mathematician and physicist I know are extremely good at that, it's what they do. Modern math and physics curricula expose mathematicians and physicists to at least a modest amount of programming, for visualization purposes, simulation, etc. This computer capability of testing your ideas faster than you can think is very appealing to some of them, so when it also makes a lucrative way to earn a living, you have the makings of what catapults them into programming, I believe. Just a guess, though, I don't have this background myself.

They could have started their academic career in Maths or Physics, and learned programming while studying their field. Then they learned that programming could earn them much more than working in science. And startups - even more.

There are 3 major components in programming 1) Understanding the Question 2) Making or designing the algorithm for solving the problem 3) Converting the logic to machine language/code The toughest part is obviously understanding the question, if you fail at that then basically you fail at what you were asked to design The next toughest part is designing the algorithm. Here will come all the logic which is required. Since maths and physics are more logical they give a programmer a kind of logical approach over the years. This in-turn helps him think creatively and think new for a program The easiest part is converting it into code because you have already understood WHAT needs to be done and HOW it needs to be done. And regarding your question they are catapulted by their sheer interest in computers and yes they do well because they understand how computers work, because computer is also a mathematical algorithm after all. Hope this helped you.

Because computer science is in a  large part math. But, unless you gets really great research position, programming pays better then math or physics.

Well programming and physics/math aren't much interrelated. However since programming is strongly based on logic and creativity, maths and physics background might help them to expand them, in their own fields. This opens many doors for that person. Also the programming part helps them to get more and quick results.