I've kind of asked this before but I don't think I asked it properly, so I'm changing it up and hopefully I should get better responses.
I'd like to change the nature of my day job, Rails, with something that requires more thinking, something that requires math hopefully. I'd really like for the change to be gradual. That would help my resume look more coherent when I say that I did 3 years of Rails plus something else for 1 year that was still related to the web.
In the last version of this question, I got a few replies that really didn't take this into account. Remember, that my target job market will probably be a niche corner of my current job market. I'm not in the position to break into something entirely new without some amount of prior experience.
Also, in contrast to the previous question, I'm changing the format so a broader audience can see where I'm going here, and could potentially respond. Here's a few possible paths I could take. Please try and consider these three points with your answer.
Computer Graphics Algorithms
Where is the math? Computer graphics is well known for having some very math-oriented problems. I'm not against doing eye-candy but doing eye-candy that a requires little if any technical understanding doesn't sound fun to me.
How is it related to the web? While not immediately obvious, computer graphics comes up during web development in the form of data visualization and fancy marketing animations. Also, Flash makes it easy to demo such a project on the web.
How would I promote myself? I'd probably have to implement some specialized open source graphics algorithms for Flash. Fisix comes to mind as an obvious example. Alot of the info-aesthetics work is good (but some of it is also too simple). Not a lot of employers would look for the level of sophistication I would bring, but that's okay since, if I did this correctly, I could potentially move into game dev, where such skills are obviously in demand.
Statistics and Machine Learning
Where is the math? Statistics is a branch of math I'm not entirely familiar with, but that's okay, I'm a fairly quick learner. Machine learning requires a fair bit of calculus and linear algebra, both of which I'm comfortable.
How is it related to the web? The most obvious application of machine learning to the web would be recommendation algorithms, although statistics could be useful for understanding user patterns or other data that is collected by many sites.
How would I promote myself? One possible way would be to set up a dummy e-commerce site with products, wish lists, consumer data, etc., it could be dumbed down enough that managers could understand why I'm important. The same idea would probably work for statistical analysis provided it included fancy looking charts.
Performance Intensive Web Services
Where is the math? Performance circles around data structures and their algorithms, which is at the core of real computer science.
How is it related to the web? High traffic sites need services that are fast and reliable, thus the motivation.
How would I promote myself? This would be the most difficult path since I assume these employers would want proven experience in a real work environment, but I could potentially break in with my current experience and the right connections.
Can you think of any others? If you'd like to bring up your own example, try to fit the format. Also, if you're a person who has made this transition and can share about how you did it, you're a likely candidate for being the chosen answer.