Gilbert Strang — Professor of mathematics at MIT and one of the most famous math teachers in the world, whose MIT OpenCourseWare linear algebra lectures (course 18.06) have been viewed millions of times.
The gist
Lex Fridman talks with MIT mathematician Gilbert Strang about linear algebra, teaching, and the impact of MIT OpenCourseWare. Strang explains his beloved four fundamental subspaces, singular value decomposition, and why every matrix can be broken into rotate-stretch-rotate. He argues linear algebra should be prioritized over calculus in education because everything in it is flat and useful for modern data science. The conversation also covers deep learning as piecewise-linear approximation, the role of math in society and politics, and what Strang has learned from decades of teaching.
Big reveals
- Strang recounts how MIT OpenCourseWare began: a committee tasked with monetizing online content instead decided to just give it away for free, approved by President Vest.
- Strang argues linear algebra should be taught before calculus because everything in it is flat and nothing bends.
- He contends education overdoes calculus at the cost of linear algebra, declaring linear algebra the winner.
- Strang frames deep learning as finding rules from data, with linear algebra doing the heavy lifting.
- Strang admits he is 'not really a good teacher' because he dislikes exams and grading.
- He laments that essentially no elected officials in Congress hold engineering or math degrees.
Things worth remembering
- Strang made his famous linear algebra videos back in 2000; they were simply recordings of his actual class.
- Every matrix can be written as a rotation times a stretch (diagonal) times another rotation, the singular value decomposition.
- Eigenvalues only work for square matrices, but real data comes in rectangular matrices, so singular values are needed.
- Deep learning's power comes from a simple piecewise-linear function: two straight lines with a fold, applied a million times.
- The piecewise-flat idea behind neural nets is the same one engineers use in the finite element method to design bridges and airplanes.
- Strang names three major areas math education should balance: calculus, linear algebra, and probability/statistics.
- His favorite matrix is square with 2s down the main diagonal and -1s just above and below, otherwise all zeros.
- The four fundamental subspaces are the column space, row space, and two perpendicular null spaces.
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Introduction to Linear Algebra
Gilbert Strang
“I remember doing the exercises in his book introduction of linear algebra and slowly realizing that the world of matrices” — Lex Fridman 00:00:00Find it on Amazon