Solar2D (successor of Corona SDK)is a free and open-source game engine for Windows, Mac and Linux platforms, originated from the popular and widely utilized Corona SDK game engine, which is no longer receiving commercial support. It utilizes the Lua programming language, and is designed to prioritize simplicity and efficiency in the game development process.

001 Game Creator is a graphically assisted scripting game engine for both beginners and advanced users, developed by SoftWeir from Canada. With its help, game developers can quickly prototype ideas, test complex systems, and build single-player or online/local multi-player (up to 4 players) and split-screen games for Windows, Steam, HTML5 web browsers, and Android/iOS, no coding required.

Clickteam Fusion (formerly called Multimedia Fusion Developer) is a classic, powerful and extensible 2D/3D game making engine, developed by Clickteam from France in 1995. It is easy to understand and use, allowing developers to create all kinds of cross-platform games without writing any code.

3D mathematics is a subject related to computational geometry. 3D math is the technical basis of computer graphics and computer 3D game development, while computational geometry is a subject that studies how to solve geometric problems with numerical methods. Both 3D math and computational geometry are widely used in fields that use computers to simulate the 3D world, such as graphics, games, simulations, robotics, virtual reality, animation design, and more.

To learn 3D game development with limited pockets, I guess you've tried many classic, free, open-source game development engines like TV3D (Truevision3D), OGRE and Irrlicht Engine. By contrast, the pros of TV3D are easy to learn and get started with; its cons are that it was built based on the ActiveX control and requires the RunTime DLL to be registered before running; OGRE is better than Irrlicht in that it has a capable and vigorous engine framework, and supports for extending new functionality in the form of plug-ins (this is better than Irrlicht); but its downside is that it's not easy to get started with.