Why Every ML Engineer Eventually Has to Learn Linear Algebra Properly (quantumformalism.substack.com)

Quantum Formalism ran its first live Book Review session on the opening chapter about vector spaces, sparking a robust debate about how math should be taught to ML practitioners. Attendees praised the book’s motivation—clearly arguing why math matters beyond coding—but flagged several practical and technical issues: poor digital typography, notation like ℝ⁴ appearing before key definitions, and vector diagrams that fail to build clear geometric intuition (especially for vector addition). More substantive critiques noted an overloaded but informal definition of a vector space and the omission of a fundamental scalar-multiplication axiom—(a + b)x = ax + bx—as well as the lack of brief definitions for fields and groups that would clarify what “scalars” and algebraic structure mean for readers. For the AI/ML community the debate matters because rigorous yet accessible linear algebra underpins almost every model and algorithm. Missing or informal definitions can leave practitioners with shaky foundations, leading to misunderstandings in areas like feature representations, optimization geometry, and numerical stability. The session encapsulated the trade-off between abstraction (starting from groups/fields) and readability for applied learners, concluding that the book succeeds at motivation but must better balance precision and accessibility. QF also promoted their Abstract Maths 101 bootcamp and upcoming review session for those wanting to deepen their foundations.