The game of roulette is not beatable. It is strictly a game of chance, with the odds against you. You can not gain an advantage by playing roulette. What you can beat is the the wheel, the table, the ball, etc. You are not playing to beat the game, you are playing to beat the physical conditions of that particular table/wheel that the game of roulette is being played on in a land casino.
Each table is different, each wheel is different, albeit very slightly as they are meant to be standard. If you study one table for hours, days, weeks, and record the thousands of results, input it into a computer program that will appropriately analyze the data, you will see that some wheels favour certain number/sections more frequently. This is due to physical flaws in the table or wheel. Obviously you will need a large amount of data to see if there are such patterns and this is quite time consuming so not very plausable to the vast majority, although it has been done. It was done by an Italian family 10 years ago, if anyone is interested I will look up the name of the family. Long story short, the guy gathered information about a particular wheel, computer predicted certain numbers/sections to be favoured, computer was right, family made just over $1,000,000 USD then stopped because the father had some health issues.
Another method that has been tried at a casino is bringing the computer into the casino with you and you feed it information through a toe switch. Yes, that has been done unsuccessfully. The people that tried this had too many computer errors and the group fell apart. Could it possibly be done successfully? Sure, why not, people could be doing it now, and some probably are.
Those two methods are aided with computers. Theoretically, a person could beat the table/wheel themselves if they can perform the complex calculations. It is not as if they have to do some insane calculation right then and there before the betting period is taken away. They can gather the results, bring them home, and figure out if the ball is will be more likely to land on certain numbers/sections more than others. It seems people are confusing this idea of beating the wheel with predicting where the ball will land in each spin. Do you see the difference? One way is figuring out if the ball will land on certain numbers/sections more often in the long run than others, where the other is trying to calculate the speed of the ball, the speed of the wheel, keeping in mind the weight of the ball, gravity, et cetera and trying to figure out approximately where it will land spin after spin, with all different data for each spin. Both are theoretically possible, I think it would take an extraordinary individual to be able to do the necessary calculations of the latter method in such a short period of time.
Bottom line is that it is possible to beat the wheel/table, not the game. You can do it without any mathematical forte, just a lot of spare time. There are people that have and are putting the edge in their favour through minor defects in the table and the wheel in casinos all over the world.