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• Infinity, generating galaxies from the top down.
• Miguel Cepero's blog about his as yet unnamed, procedurally generated voxel-based world.
• An interview with the author of Dwarf Fortress, describing how various aspects of the world were modelled (from history to geography to psychology).
• A collection of pages on procedural generation of mazes (graph theory).

• Infinity, generating galaxies from the top down.
• Miguel Cepero's blog about his as yet unnamed, procedurally generated voxel-based world.
• An interview with the author of Dwarf Fortress, describing how various aspects of the world were modelled (from history to geography to psychology).
• A collection of pages on procedural generation of mazes (graph theory).
• A video showing some emerging technologies in the virtual worlds arena.

• Diffusion equations for chemical detection in AI (such as simulating a sense of smell and pulling AI entities along the gradients created by these equations toward their goals)
• Radiosity algorithms using eg. Lambert's equations in realtime raycasting, cellular automata
• Graph theory for generating planar connected world graphs, including such aspects as finding and eliminating Kuratowski subgraphs
• Combinatorics in evaluating corner cases for constructive solid geometry applications
• Statistical modelling and analysis for game rules balancing
• Minkowski sums in opening sufficiently broad paths for navigation during world generation
• Spatial quantisation and subdivision as a general optimisation
• Quaternions to RK4 integration to Delaunay's triangulations in physics and geometry
• Combinatorics, probability theory and general statistics in projecting the emergent outcomes of complex systems
• Probability theory in random number generation eg. Mersenne Twister
• Formal grammars in narrative and physical object construction (eg. Lindemayer systems)
• And more mathematics applicable to broader field of computer programming, such as analysing and reducing computational complexity.

• Infinity, generating galaxies from the top down.
• Miguel Cepero's blog about his as yet unnamed, procedurally generated voxel-based world.
• An interview with the author of Dwarf Fortress, describing how various aspects of the world were modelled (from history to geography to psychology).
• A collection of pages on procedural generation of mazes (graph theory). I would speculate that it is far easier to be a trained mathematician and become a good programmer, than the reverse. In many ways I would rather be in your shoes, reading my post, than vice versa. Of course that's assuming that this is a convincing argument in terms of changing career direction!

• Diffusion equations for chemical detection in AI (such as simulating a sense of smell and pulling AI entities along the gradients created by these equations toward their goals)
• Radiosity algorithms using eg. Lambert's equations in realtime raycasting
• Fluid dynamics using cellular automata
• Graph theory for generating planar connected world graphs, including such aspects as finding and eliminating Kuratowski subgraphs
• Combinatorics in evaluating corner cases for constructive solid geometry applications
• Statistical modelling and analysis for game rules balancing
• Minkowski sums in opening sufficiently broad paths for navigation during world generation
• Spatial quantisation and subdivision as a general optimisation
• Quaternions to RK4 integration to Delaunay's triangulations in physics and geometry
• Combinatorics, probability theory and general statistics in projecting the emergent outcomes of complex systems
• Probability theory in random number generation eg. Mersenne Twister
• Formal grammars in narrative and physical object construction (eg. Lindemayer systems)
• And more mathematics applicable to broader field of computer programming, such as analysing and reducing computational complexity.

• Infinity, generating galaxies from the top down.
• Miguel Cepero's blog about his as yet unnamed, procedurally generated voxel-based world.
• An interview with the author of Dwarf Fortress, describing how various aspects of the world were modelled (from history to geography to psychology).
• A collection of pages on procedural generation of mazes (graph theory).

I would speculate that it is far easier to be a trained mathematician and become a good programmer, than the reverse. In many ways I would rather be in your shoes, reading my post, than vice versa. Of course that's assuming that this is a convincing argument in terms of changing career direction!

If this does interest you even remotely, don't let what they say about games put you off. The line between games, traditional linear narratives, sandboxes for physical and AI experimentation, educational products ("serious games") and so on, is blurring at a rapidly accelerating rate. The vast majority of games, I would say all but less than 1%, are the same old rehashed tripe. But there is enormous potential for creativity, the more so for those with a strong mathematical background, as evidenced by some of the links above.

If this does interest you even remotely, don't let what they say about games put you off. The line between games, traditional linear narratives, sandboxes for physical and AI experimentation, educational products ("serious games") and so on, is blurring at a rapidly accelerating rate. The vast majority of games, I would say all but less than 1%, are the same old rehashed tripe. But there is enormous potential for creativity, the more so for those with a strong mathematical background, as evidenced by some of the links above. I think there is something very positive in giving people new and inspiring spaces in which to play, relax and learn.