Pixar films are widely known for their thoughtful storytelling and groundbreaking animation. One of the most amazing things about these movies, though, is the innovative math that Pixar’s team is actually inventing to improve the audience experience and look of the characters. We caught up with Pixar’s Research Lead (and TED-Ed Educator) Tony DeRose to hear about the mathematical secrets behind these movies and his own progression from building model rockets to creating Oscar-winning characters.

What got you interested in mathematics as a kid?
I can’t remember a time when I wasn’t interested in science, but my interest in mathematics really began when I was in 7th grade. I was into building model rockets, and my 7th grade science teacher (Mr. Belknap) showed me how to use trigonometry to calculate how high the rockets went. I thought it was magical that such a thing could be done by scratching equations on paper, and I’ve been hooked ever since.

Tony DeRose

How did you end up at Pixar?
Before joining Pixar, I was a professor at the University of Washington teaching computer science and doing research in computer graphics. There were only a few people doing computer graphics at that time, so everybody knew everybody. Ed Catmull, the president of Pixar, was part of that community so we stayed in touch from time to time. As Toy Story was being completed, Ed and I started talking about the possibility of me moving to Pixar. The opportunity to help develop the technology needed to tell compelling stories using computer graphics was too good to pass up, so I did the unthinkable and left a tenured position at UW (My parents thought I was crazy, by the way, but they trusted my decision).

Who is your favorite animated character that you have personally worked on?
The character named Geri from the short film Geri’s Game. He was also the first character I worked on, and he won an Oscar. He also made a cameo appearance in Toy Story 2 as the toy cleaner.

Geri from Geri’s Game. Photo courtesy of Pixar.

What advice would you give someone who wanted to use math to make movies?
Learn as much mathematics as you can, particularly applied math. The areas of mathematics we use most heavily today are Euclidean and affine geometry, trigonometry, linear algebra, calculus, and numerical analysis. We don’t really know what the mathematical tools of tomorrow might be, so we’re counting on the next generation of employees to tell us!

What’s your favorite part of your job?
I love learning new things! Learning things that are well-established is fun, but my favorite part is solving problems that have never been solved before.

Check out DeRose’s TED-Ed Lesson below. In it, he delves further into the math behind the animations, explaining how arithmetic, trigonometry and geometry help bring Woody and the rest of your favorite characters to life.