Hertz Fellow Justin Solomon Releases Book on Numerical Analysis for Modern Computer Scientists

September 24, 2015

A postdoc in applied and computational mathematics at Princeton University, Hertz Fellow Justin Solomon isn’t just a computational science guru, he literally wrote the book on the subject; well, a book anyway.

For the next year at the prestigious Ivy League school, Solomon, 27, will apply advanced techniques introduced in his recently published textbook, Numerical Algorithms, to solve real-world problems related to shape analysis, imaging, computer graphics and machine learning.

Numerical Algorithms textbook
Courtesy of Taylor & Francis Group

“One of my main goals is to take tools at the intersection of math and computer science and make them usable by people whose background isn’t in mathematics,” Solomon said. “These tools are useless if your outside collaborators don’t understand what you’re doing. Research and teaching are both important to reach that goal.”

The primary focus of Solomon’s postdoctoral research will be in molecular imaging, collaborating with mathematical experts to design algorithms for use in cryo-electron microscopy.

“We’re trying to figure out the 3D perception shape of a molecule from a bunch of flat images, but not only do we not know the shape of the molecule, we don’t know where the images were taken,” Solomon said. “I’m hoping to help design a practical tool that encapsulates most of the specialized math and package it in a way that a biologist can use it.”

Solomon is no stranger to complex problem-solving. He recently earned his PhD in computer science from Stanford University working with professor and Hertz Fellow Leonidas Guibas on methods for processing geometric data. During the course of his studies, he had the chance to collaborate with a diverse set of practitioners outside his field, from theoretical mathematicians to artists designing animated characters and members of school’s psychology department, exploring the structure of white matter in the brain.  

“Developing tools to understand shape can be an insanely messy problem,” Solomon said. "Figuring out what makes a shape unique and what relates it to its peers requires understanding of low-level features like bending and curvature and high-level features like which parts are meaningful to a human. Plus, context matters a lot: Understanding the shape of a brain from an MRI isn’t the same problem as helping artists design creatures for a video game.”

Growing up in Oakton, Virginia—just 20 miles outside of Washington D.C.—Solomon’s love for computer graphics and geometry blossomed at an early age. By high school, his success in writing complicated rendering software caught the eye of a researcher at the U.S. Naval Research Laboratory, where he spent a summer writing code for biometric software for facial recognition from a 3D scan.

“Even though early computer graphics tools were painfully slow, they were so much fun to play with,” Solomon said. “It’s just a great application of math because it’s very tangible. You get to see and interact with what you’re making.”

Solomon’s next logical step was Stanford University, where as a freshman he landed a summer internship at Pixar in the company’s Tools Research group. There, Solomon concentrated on non-photorealistic rendering, working with artists to come up with the right models to express what they wanted to see on-screen.

“Working in the research branch of a movie studio was a unique experience,” Solomon said. “If you’re working on a movie that’s about to come out, you don’t have the time to design new experimental parts of the pipeline. But in the research group there was a lot of freedom to re-think every step. They were applying artistic creativity to tricky technical problems.”

Whether he’s talking to an artist who’s designing a scene, or to a doctor trying to diagnose a patient, Solomon has become highly adept at applying theoretical mathematical disciplines like differential geometry to solving practical problems. 

By mid-2016, Solomon will take on a new role as a professor of electrical engineering and computer science at MIT.