...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Sunday, December 18, 2016

Grant Sanderson…. An Eye for Math Video Instruction

Math-Frolic Interview #40

"Hi Grant, Thank you for making math videos. When I watched the topology video, I was hanging on the edge of my seat in suspense as if watching Game of Thrones, while enjoying the beauty of the problem, the solution, and simply the graphics and animations."
-- a commenter at Patreon

With strong interests in both math and computer science, Grant Sanderson now produces some of the best, most cutting-edge, entertaining and instructional math videos out there on his 3Blue1Brown YouTube site. When you see the beauty and quality of his videos you'll understand how he has turned this into full-time work.  I believe Steven Strogatz was the first to bring Grant’s work to my attention, and you know when Steve recommends something it’s going to be good. 
Grant describes his effort this way:

3Blue1Brown is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective.

He also has a Patreon account here:

And now a little more about him:


1)  You run an amazing math video site on YouTube, “3Blue1Brown.” How many hours per week or month, approximately, do you spend working on that?  And how do you decide what to cover with each new video you do?

It's hard to speculate on specific hour counts.  For one thing, it's only relatively recently that I started doing this full-time, so the honest answer is that I don't have enough data to answer yet.  Also, the question seems more applicable to occupations with less of a work-life blur than I have.  For example, when I read math, does that count as work towards 3blue1brown?  What if some of it eventually makes its way into a video?  When I work on improving the animation tool, but not for a particular video, is that work or just a side-project?  In general, I'd say I work quite a lot, but the word "work" doesn't really do justice to what a playful process it is.  

As far as deciding on what to cover next, there's just a long list of things that I think could make good videos, and every time I have a thought or come across something I think is worthy it goes on the list.  The more interesting question is how to sort the list, and for that I try to prioritize ideas that I don't think are commonly expressed elsewhere on the internet, and which strike the right balance between approachable yet deep.

2)  We’ll go back to some basics:
What is your academic background and your current professional/career role? 

I studied math and CS as an undergrad at Stanford.  The original plan was to continue on the PhD track, and my later years at Stanford were spent increasingly in graduate classes in preparation for that.  But I personally wanted to spend a few years out of academia before doing so, even though for whatever reason that is a less common thing to do.  After graduating, I worked as a content creator for Khan Academy, making things related to multivariable calculus.  At the time, I spent my nights/weekends working on 3blue1brown as an unassociated side-project.  Thanks to the huge support people showed for 3blue1brown, this is actually what I do full time now.  With things going how they are now, and given that I've always tended more towards the teaching/outreach side of math than the research, it's looking less and less like I'll return to the PhD path.  Maybe that's why more people don't take those years in-between.

3)  You say at one point on your site that you’ve “loved math for as long as I can remember.” Do you recall what initiated your interest in math, and when did you know you wished to pursue it professionally?

My dad, definitely.  Even though he would tell you that his own math education ended earlier than he would have liked, sometime shortly after calculus, he has a great appreciation for beautiful problem solving.  That appreciation was matched by his eagerness to pass it on to me, as embodied by the countless times he exposed me to neat puzzles and patterns when I was young.  I remember a particular game when I was very young where he’d stack sugar cubes in some interesting geometric way, and if I correctly gave the number of cubes in the configuration, he'd give me one as a reward.

Beyond that, I had the good fortune of some caring and encouraging math teachers to bump up my interest as I grew up.  I am particularly thankful to Phil Sakashita, my calculus teacher, who did more than almost anyone else to open my eyes to what math could be.

As far as going into it professionally, it was probably sometime in high school that I thought becoming a mathematician would be incredibly cool.  But somewhere in college, I actually toggled to the CS side of things, and had you interviewed me then I would have been quite certain that my future lay somewhere in software or data science.  But at the end of each tech internship that I did, I found myself lamenting the fact that I wasn't doing more math, so I decided to switch gears and point myself towards a math career.

4)  Any idea how long you’ll be putting new material on your site, or what’s ahead otherwise in your life, mathwise? Any special goals for the future you’re actively striving toward?

Right now, the focus is just on getting into a flow of regular content creation.  I'm working on an Essence of Calculus series behind the scenes, and I'll always be working on more "Essence of" series of some sort, so look out for those.

5)  You explain in a FAQ that the odd name for your site is a reference to an eye condition you have, “sectoral heterochromia,” and you say the name puts “a genetic signature on my work.” I’m not quite sure what that means or why it was important for you; can you flesh that out a little more?

I'll be the first to admit that making this my logo is somewhat strange, but my right eye is 3/4 blue and 1/4 brown.  When I say it puts a "genetic signature" on my work, I mean that just as other people put their names on their work, I chose to put a little piece of who I am in a different sense.  The more important point, though, is that the channel is about seeing things, so an eye is somewhat fitting.

6)  Increasingly, there’s more and more competition online for math videos and instruction. Do you have some favorite other sites that you don’t mind recommending to folks? 

Mathologer is, of course, great.  And for classrooms, I really like the work that Desmos is doing.  The Art of Problem Solving site/books/courses were influential for me growing up.  Also, "How to fold a Julia Fractal" is a must-see for anyone not yet familiar with it.

7)  And how about books?… I’m always interested to hear what ‘popular’ math books were especially inspiring to a math enthusiast, that you’d recommend to others?

Again, I quite liked The Art of Problem Solving books growing up.  Vladimir Arnold's book on ODEs is fantastic.  John and Barbara Hubbard's "Vector Calculus, Linear Algebra and Differential Forms" is great for any early undergrad hoping to get a deeper feel for what they're learning.  Munkres' "Topology" (of course).  Cox's, "Primes for the form x^2 + ny^2".  There are also these three little books on number theory by Kato, Kurokawa and Saito which are a delight, though probably best read with a supplement.  "Proofs from the Book" by Aigner and Ziegler is just filled with gems of cleverness.  Larson's "Problem solving through problems".  Many of Terence Tao's books are great, especially the one on measure theory.  I'm sure I'm neglecting some great ones, but those are what come to mind right now.

8)  When you’re not engaged in mathematical pursuits, what are some of your other interests/hobbies/activities?

I enjoy playing violin and mandolin, and pretending like I know how to play guitar, bass and piano.  Hiking and running are also solid default activities.  I do some private teaching on the side, which I count as a hobby because I do it for my own pleasure.


Thanks Grant, hope any readers not already familiar with your site will check it out soon. It's like having a mini-college math education at your fingertips... and the price is right!

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