The age of AI requires building capable and more efficient neural networks that are mainly achieved via (I) Developing and manufacturing more capable hardware; (II) Designing smaller and more robust versions of neural networks that realize the same tasks; (III) Reducing the computational complexities of learning algorithms without changing the structures of neural networks or hardware. The approach (I) is an industrial design and manufacturing challenge. The approach (II) is essentially the subject of network pruning. In this talk, we play on mathematicians' strengths and focus on a theoretical approach on (III) based on tropical arithmetics and geometry. I will first describe the setup of machine learning in simple mathematical terms and briefly introduce tropical geometry. After verifying that tropicalization will not affect the classification capacity of deep neural networks, I will discuss a tropical reformulation of backpropagation via tropical linear algebra. This talk assumes no preliminary knowledge of machine learning or tropical geometry, undergraduate-level math, and general curiosity will be sufficient for active participation.