Is there any gamified software for learning advanced mathematics? I have been thinking for a while that new ed-tech software, such as Babbel, could be applied to higher level mathematics.
Although visualisations of mathematical forms, akin to diagrams, are often seen in for example Wikipedia pages, it does not seem that highly interactive software has been designed to the potential that it can be imagined.
For example, imagine an animated, interactive simulation designed to make intuitive the principles of special relativity. I haven't worked out the details, but, you might imagine that you can control the velocity at which some object travels, play with different parameters like the speed of light (slowing it down), and observe in an intuitive way some of the known effects, i.e., time dilation, length contraction, etc, in relation to other on-screen objects, almost like a pleasant video game.
Or, imagine making interactive animations of algebraic structures. A group could be an actual on-screen object. Clicking on two of the elements, the object that is their composition lights up and makes a sound. Or, for a category, for each pair of objects is associated a set of arrows - one could click on each pair, and see a little window opening with those arrows. There are many courses called "Visual Group Theory" making group theory very accessible - could not these ideas could be applied one step further, in interactive, highly visual programs?
One could imagine Euclid's Elements being turned into software. One could devise a way of clicking on two line segments or filling in some key information on a diagram that the software accepts as a valid step in the proof, almost like filling in a Sudoku. Slowly working through each proof would be like solving a little puzzle in The Legend of Zelda.
Or even merely taking a book like Tristan Needham's Visual Complex Analysis, but "gamifying" it - the Table of Contents are modules - you get a little green "completion" check when you finish one - it displays the text one sentence or paragraph at a time, you proceed by clicking "next" - and the exercises give immediate feedback, flashing red if the wrong answer is given, green if correct.
Does anything remotely similar to this exist?
Thank you.
 A: I don't know of any, and I'm not at all sure there will ever be any.  I see two obstacles, based on what you write:

*

*The simulations you describe work for getting across single ideas, or simple linked ideas that resolve into a single theme.  A simulation where you can change the value of the gravitational constant, for example, or the speed of light, shows you results but doesn't tell you how you get there.  You don't gain understanding, though you might gain intuition, without doing the actual study of the theory behind it.  So the simulation can provide nice examples... but so can a textbook.  And with the textbook and the theory you can work out your own examples, for the areas that interest you, so there's greater value.


*Gamification is all about keeping a player's interest when there's competition for it.  For higher-level studies the interest has to be there in the beginning and be maintained by the thrill of understanding and discovery, because the effort required to keep going keeps increasing.  For gamification to work here, it would have to reward smaller and smaller improvements (or the rewards wouldn't come fast enough)... and if you're studying the Feit-Thompson theorem, a gamification reward is pretty meaningless.
Gamification does work at lower levels and maths educators have been looking at ways to implement it for years -- from handing out gold stars for work well done, to assigning students to teams to build cubes from cardboard nets and measure surface areas and volumes and draw conclusions, to modern computer games aimed at getting kids to do maths without actually calling it that.
