Alex Smith (@ninja

Alex Smith

2,645 posts

Alex Smith

@ninja_maths

Chief content architect @_MathAcademy_ | Math PhD | AKA MathNinja. Developing (possibly) the world's largest online math curriculum.

Joined October 2010

Pinned
Alex Smith
@ninja_maths
Mar 1
For anyone wondering how a third-grader can complete six years' worth of math in a single year. This knowledge graph spans 3,000 math topics, from 4th grade to the university level, providing the perfect basis for mastery learning. Students can go as fast or far as they want!
Nadja
@unrealNadja
Feb 28
Today feels big. My third grader earned another stripe on his BJJ belt and then casually finished the last lesson of his Calc BC course. This kid, who just over a year ago claimed he hated math, fell in love with the subject when he started @_MathAcademy_. He became thirsty for
2.5M
Alex Smith
@ninja_maths
Aug 16, 2024
The four fundamental subspaces of a matrix.
221K
Alex Smith
@ninja_maths
Aug 19, 2024
I’ve spent the past seven years mapping out a significant chunk of the math genome. The mathematical hierarchy is a vast and profoundly interconnected web of topics, where advanced topics depend intricately on more basic ones, which in turn rest on even more fundamental ideas.
191K
Alex Smith
@ninja_maths
Sep 25, 2025
Green's theorem is probably the most important result that multivariable calculus students need to grasp. A very solid understanding of Green's theorem makes its higher-dimensional counterparts (the divergence theorem, Stokes' theorem) feel almost trivial.
Alex Smith
@ninja_maths
Aug 17, 2024
Replying to @ZahlenRMD
Green's Theorem. The sum of the microscopic scalar curls equals the circulation (macroscopic curl).
72K
Alex Smith
@ninja_maths
Nov 7, 2025
Love this image!
Alex Smith
@ninja_maths
Aug 16, 2024
The four fundamental subspaces of a matrix.
103K
Alex Smith
@ninja_maths
Sep 12, 2024
I designed the Mathematical Foundations Series to help adults efficiently master all the middle and high school material (including calculus) necessary for university-level math. It starts with fractions and goes as far as calculus, basic linear algebra, & random variables.
165K
Alex Smith
@ninja_maths
Dec 16, 2024
Great news. @_MathAcademy_'s Probability and Statistics course will be launched in time for Christmas. The final list of topics is attached. Just call me Santa Claus. 🎅
63K
Alex Smith
@ninja_maths
Sep 9, 2025
Beware the "curse of knowledge". The curse of knowledge is a cognitive bias where instructors who are highly knowledgeable in a domain forget the steps they took to acquire the knowledge and can't understand why novices just don't "get it." Taken from "How Learning Happens."
Alex Smith
@ninja_maths
Mar 10, 2025
This is an excellent book. I encourage all those interested in the science of learning to grab a copy. Sections: * Memory & cognition * How the brain works * Prerequisites for learning * How learning can be supported * Teacher activities * Learning in context * Cautionary tales
71K
Alex Smith
@ninja_maths
Mar 10, 2025
This is an excellent book. I encourage all those interested in the science of learning to grab a copy. Sections: * Memory & cognition * How the brain works * Prerequisites for learning * How learning can be supported * Teacher activities * Learning in context * Cautionary tales
124K
Alex Smith
@ninja_maths
Nov 7, 2025
On the subject of Laplace Transforms, our Differential Equations course is well underway. I'm excited about this one. Here's a sneak peek.
00:00
148K
Alex Smith
@ninja_maths
Jul 29, 2024
The First Isomorphism Theorem.
87K
Alex Smith
@ninja_maths
Nov 6, 2025
I love @3blue1brown. However, the biggest beneficiaries are those who already have solid fundamentals. Take the recent excellent video on Laplace Transforms. I wouldn't recommend starting there if you've no idea what a Laplace Transform is! Build the fundamental skills first.
116K
Alex Smith
@ninja_maths
Oct 13, 2024
I've been brushing up on Machine Learning algorithms this weekend to prepare for our upcoming ML course, which we plan to release sometime in 2025 (basically, ASAP). @justinskycak and I have discussed scaffolding the curriculum for gradient descent and its variants by leveraging
52K
Alex Smith
@ninja_maths
Jul 1, 2024
Some tips on how to learn math independently: 1) Active Learning You don't become proficient in math just by reading books or watching videos like those from 3Blue1Brown or Khan Academy. This is known as "passive learning." To truly grasp mathematics, you need to engage in
54K