Artificial intelligence represents a major expansion of applied mathematics. Autoencoders, autoregression, Gaussian mixture models, independent component analysis, learned noise bases, and modern optimization recover structure directly from measured data.
Brian Greenforest argues that students should learn this mathematical toolkit alongside classical calculus, differential equations, and finite-element methods.
Recover the Hidden Structure of Phenomena
Sensors provide observations, while statistical learning estimates latent variables, masses, modes, sources, and relationships that a hand-written low-dimensional model may miss.
Autoencoders compress structure, autoregressive models track dynamics, mixture models separate regimes, and ICA searches for independent generating factors. Together they provide new ways to formulate physics and engineering questions.
Teach the Mathematics Behind the Interface
A chatbot interface can distract from the algebra, probability, optimization, and representation learning that make the system work. Education should reveal those mechanisms and connect them to measurement and control.
Schools, universities, and makerspaces can update the curriculum now. Teach learners to derive, implement, inspect, and challenge the models that increasingly shape the physical world.
Run AI Is Mathematics in a Four-Layer Transformer
The complete training run connects this mathematical argument to executable code, data flow, and a working small model.
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AI is not a tool. AI is mathematics. A much better math, than we had a century ago. Do not try to understand how to use GPT-4. It's not a tool. Teach kids UPDATED math at school instead of the ancient obsolete manual methods. Autoencoders, autoregression, gaussian mixture models, noise eigenbases, ICA were around for a while now, but our classical cources on physics and engineering use ancient FEM (finite element analysis) at best, or few variables estimates in ODE/PDE, and teach nothing how to automatically recover masses and internal structures of measured phenomena using only sensors and MODERN mathematics. Then comes control theory, and deep reinforcement learning is an overhyped hack IMO. Teach kids math, not HYPES.