Modern video games are one of the most stunning applications of algebra in the world. It's the code behind the magic.

1. Physics Engines: When your character jumps, the perfect arc of that jump is calculated by a quadratic equation in real-time.

2. 3D Graphics: Every object is a set of points (vertices). Linear algebra (matrices) is used to rotate, scale, and move them around the world.

3. Collision Detection: The game is constantly using algebraic inequalities to see if the 'hitbox' of your character is overlapping with a wall or enemy.

4. AI Behavior: An enemy deciding to attack might use an equation based on variables like your distance, health, and its own 'aggro' level.

5. Damage Formulas: 'Your attack (A) minus enemy defense (D) equals damage.' This is a core algebraic expression in every RPG.

6. Procedural Generation: 'Infinite' worlds are not designed by hand. They are created by complex algebraic algorithms that generate terrain and place objects.

7. Lighting and Shaders: The way light reflects off a surface is modeled by complex algebraic equations.

Game designers are not just artists; they are masters of applied algebra.

The next time you play a game, remember that you are running through a beautiful, interactive world made entirely of math.