**By Ryogo Katahira**

On October 6, a man in his thirties wearing a hoodie and jeans entered a mechanics course classroom in the Science Center. He glanced at the blackboard with its simple energy diagrams while students and professors filed in. His demeanor was entirely casual, but he was the subject of the highly anticipated event advertised on the day’s Daily Mammoth announcement: “Join the Physics and Astronomy Department for a conversation with the founder and CEO of Desmos!” The special visitor was indeed Eli Luberoff. If you missed this special talk, read on for a synposis.

“My childhood dream was to be a physics professor at Amherst”

Luberoff started the talk with his personal connection to Amherst, being that he took courses here while doing homeschooling in high school. In fact, Physics Professor William Loinaz recalled their interactions from two decades ago, commenting how impressed students and professors alike were with Luberoff at the time. Growing up in the area, Luberoff said his dream was to become a physics professor at Amherst College.

As an undergraduate at Yale, Luberoff started a tutoring company called Tutor Trove, where he programmed tools to assist online tutoring. He soon realized that one tool in particular was especially powerful: an online graphing calculator displaying equations and graphs side by side. When the equation changes, the graph changes correspondingly, which is impossible on handheld calculators that require switching screens, resulting in learning loss.

Luberoff decided to put it online because “the thing that I care about is more people liking math, understanding math, and feeling confident in math.” He soon received positive reactions. Ultimately, he sold his tutoring company and founded Desmos with his friends. He currently runs the company but still dreams of someday becoming a professor.

With the belief that “making a great math tool is totally useless if it’s not also implemented effectively in the classroom,” he hired math teachers and created a middle school math curriculum. The problem was his job suddenly became distant from what got him invested in the first place.

“I got to the point where I was spending all my time hiring people and none of my time talking with people or writing software, which is the thing that I love to do.”

As a result, he decided to split Desmos into two different corporations: Desmos Studio, which produces computer programs, and Desmos Classroom, which is responsible for curriculums. It remains to be seen whether this was the right decision, he said. Regardless. He seemed very excited to introduce their new product, Desmos 3D, which he calls one of his dreams, being a bigger and more advanced tool.

He closed off his recap there, joking, “that takes me, I think, all the way up to last Thursday. And then I just drove here, and I’m talking to you, and now we’re all caught up.” With that, he opened up the floor to any questions from students.

“We not only don’t advertise — we’ve committed that we will never advertise”

**Q. As far as I am aware, there are no ads on Desmos. Where does your revenue come from?**

Luberoff first clarified that Desmos would never have any advertisement on the website and that everyone, including students and teachers, would never have to pay for their products. This is a big deal considering Desmos would hypothetically make a lot of profit if they included advertisements or collected data from users. People spend more time on Desmos than Khan Academy, he said, so there is no shortage of web traffic. The secret to their revenue, then, is their partnership with other companies and governments. Desmos is, for example, a calculator for digital SAT exams and 44 state exams as of this article’s publishing. These institutions pay Desmos to improve their own products, too.

“Sometimes you need to make a bet”

**Q. How did you advertise Desmos first?**

Luberoff said he had never advertised Desmos. Instead, he relied on patience and the belief that good products would spread naturally among people.

His second point was that it is a pure game of luck. To explain this, he mentioned an early investor in Desmos, Mitch Kapor, who founded Lotus Software, which is known for Lotus 1-2-3 (an early PC spreadsheet program). Kapor once told him, “Sometimes you need to make a bet.” Kapor bet on PC when it was not quite popular; the bet Desmos chose to make was building browser-based applications when native browsers were still “crappy.”

He said, “It was really, really lucky.”

When Chrome came out, Desmos was featured on the web store as one of the most impressive products run by JavaScript.

“I work really hard. But also, I happen to flip the coin.”

“Very, very fun tool that Jason built”

**Q. How does Desmos run so smoothly on the browser?**

Luberoff gave credit to his colleague from Amherst College, Jason Merrill ’06, who is currently a lead engineer at Desmos. He said when Merrill suggested improving the system, he could not refuse his offer because they have a brotherly relationship.

He then continued with the more technical aspect of the answer to the question. He noted browsers are surprisingly high-quality if used correctly. He said his magic was the JIT, Just In Time, compiler, which translates a programming language (source code) to another programming language (target code) while executing a program.

“It’s very, very consistent. We’re compiling the function and then sampling it at minimum 1,000 times once per pixel.”

Another challenging part of the program was the sufficient balance of removing caches, which store data for future requests; if the system caches too aggressively, the system slows down because of the caches, and if the system does not cache aggressively enough, the system also slows down because it is redoing computations unnecessarily. He delightedly explained a “very fun tool” that Jason built to ease this issue, which pulls a random 100,000 recently saved graphs and has a set of 1,000 graphs known to be slow.

“Understanding what the pedagogical goals are…is almost as important as understanding the mathematical goals”

**Q. Is there any math intuition that tends to play into the final product or domain knowledge that comes from understanding that helps with Demos as a product?**

There is a “very interesting dichotomy between math and math education,” Luberoff emphasized.

He referred to GeoGebra to describe the importance of understanding pedagogical goals. In GeoGebra, there are various features that one can use to self-teach, such as building an equation based on a graph that one constructed, which achieves different goals from Desmos.

“What you want is for someone to try to figure out the equation of the line using the map that they know, and then check if it matches up by looking at the visual.”

“I’m still pretty bad at business”

**Q. How did you learn what you needed to know on the business side?**

“I think the short answer to that one is that I didn’t.”

However, Luberoff believes it might have been necessary. Since Desmos was not aiming for fast growth, he had room to make mistakes. He recognized that the revenue could be higher, but it wasn’t detrimental to his vision that it wasn’t.

Nevertheless, he said he had pushed himself to be a good CEO who raises money and hires executives. Sometimes, he became disheartened that some areas of business weren’t his strong suit.

“I talked to 15 investors in a row. And then I would see that they wrote a check to a much shinier company that was motivated. And I’d be pretty, pretty sad about it. Genuinely quite sad.”

At the same time, he could make decisions such as not advertising because profit was not their first priority. Funnily enough, the fact he was not good at business in a traditional sense might have partially contributed to his success.

**Q. How do you grow and develop more while keeping the group size small?**

First, he said firmly, “small companies don’t do less than big companies.”

According to Luberoff, Desmos is developing faster than when there were 100 people because small groups with very collaborative people work well. Although he said it was a choice to keep it intimate, he was interested in making a group slightly bigger, and he half-jokingly declared that Desmos would take over Mathematica next.

“The thing I care most about is… the curiosity”

**Q. What do you seek in people when you hire someone?**

In the early stage, he said, he hired people he trusted since they were mostly his friends.

“The thing I care most about is,” he says, “the curiosity.”

Luberoff used to think expertise was the most important. While it remains a major factor for him, he feels a group would not work properly if members are not curious about one another’s ideas. His experience from learning physics taught him that, he told us.

“Connect the familiar 2D space to 3D space”

Luberoff stood up, walked to the computer, and with a big smile, asked the audience if he should demonstrate their new product, Desmos 3D.

Few have a good understanding of 3D space, Luberoff says, because the tools to do so are not widely available. Therefore, his design goal was to “connect the familiar 2D space to 3D space.”

Their method to show the connection was as follows:

If you type y=x^2 in the equation box, Desmos 3D would look like this:

Here, if you press the button with the meshed plane at the upper-right corner (circled with red), Desmos 3D shows the function on the xy-plane, indicating that this 2D function exists in the 3D space.

Now, the function can be interpreted as either a 2D function with two variables or an implicit 3D function with one free variable (z). To show that, you can check “Extend to 3D” under the equation.

Now you can see that it is actually a sheet representing a set of values.

Additionally, you can do many things that would be impossible in 2D Desmos, such as graphing functions using cylindrical and spherical coordinates.

The most challenging thing in the development of the system was displaying 3D functions on a 2D screen. Desmos solved the issue by allowing for graph manipulation with the mouse, intuitively enabling exploration of the space through movement.

Luberoff told us that he was surprised by the number of details in 3D modeling, including roughness, metallicity, color, and opacity. They also had to make the system intuitive to operate without requiring user training.

He then pulled up a newsletter from his email to demonstrate three impressive graphs and show what he meant. The first one was a trace of an object experiencing a projectile motion. One can easily see that 45 degrees is an optimal angle to maximize distance traveled. The second one was an electromagnetic vector field where one can detect an object’s force and velocity at a point. The last one he showed us was a working scaled model of the entire solar system.

**Q. I learned that now Mathematica has an AI. Is it something that comes for Desmos?**

Luberoff believes that AI and Desmos are almost opposite in philosophy. While everything about how Desmos works is transparent without any hidden equations, most large language models (AI) are entirely unclear about the processes inside, even for people who made the models. However, he said he would be interested in the uncontroversial uses of AI, which is to generate declared tasks, such as producing a table of radii and masses of planets of the solar system.

**Q. Where did the name of Desmos come from?**

Desmos comes from desmology, the study of ligaments, one of the hundreds of names provided in the naming contest he held among friends and family. He ultimately liked the meanings in Greek: friendship and bonding.

There is a continuation of the story, though, that he usually does not tell, which is that he later learned the word also refers to bondage. This surprise prompted laughter from the audience, capping off an inspirational yet casual and humorous shared hour and a half.