David Carr ’25 M.S. and Christopher Fakhimi ’24, ’25 M.S. graduated from Notre Dame with more than academic degrees to show for their time. The two created Pi-Squared, a free gamified mathematics app.
Carr, a native of Ireland, studied actuarial mathematics at Dublin City University before coming to the United States to study as a Naughton Fellow in Notre Dame’s Engineering, Science, and Technology Entrepreneurship Excellence (ESTEEM) program.
An ESTEEM elective course, Tech Startup Sprint Series — or “Top Gun,” as ESTEEM associates dub it — gave Carr the opportunity to pitch something he had long sought to create: a math-learning app. Inspired by his love for math and experience as a math tutor, Carr pitched his idea for an app in August 2024. That’s when Fakhimi, a computer science graduate student, self-professed math lover and fellow math tutor, entered the picture. The two paired up to bring the idea to life, and within six months, they had a successful product.
The most-used feature of the app, “The Daily,” is Carr’s favorite. Inspired by the New York Times’ Wordle, this game was one of the creators’ first ideas, featuring six daily, varied math questions. Even more exciting, Carr says, is using the app’s leaderboard feature to forge playful rivalries among friends and family.
Fakhimi favors “Frenzy,” a timed game that requires players to fill in the blanks of an equation with numbers that result in a given solution. The numbers move rapidly across the screen, earning the game its title.
The app also includes a game called “Tilted,” where players are challenged to, under a time limit, choose which of two equations pictured on each side of a seesaw has the greater solution. There’s also “Survival,” which is a timed test of knowledge. Topics begin at algebra and move on to geometry, trigonometry, calculus and statistics — the successful completion of each topic unlocking the next. Within topics, the questions grow more difficult with a player’s continued success.
Carr and Fakhimi update their app every week. Carr meets with users, who give feedback and suggest amendments, before the creators brainstorm changes or additions, which Fakhimi then programs into Pi-Squared.
As the creators tweaked the app’s features during the development process, Carr visited local high schools as well as South Bend’s Regional Innovation and Startup Education (RISE) organization, which provides entrepreneurship education to local students.
Carr says around 300 students tested the beta version of the app between November and January.
During that time, the pair made a consequential realization: Duolingo, a free language learning program, had previously released a math feature, similar to the app Carr and Fakhimi had been developing.
“How can we be different?” Carr asked himself. “We said we’d focus on shifting people’s attitude toward math.”
The pair’s shared love for daily games like those found on the New York Times and LinkedIn, along with Carr’s interviews with users and test runs with local students, inspired their distinctive path. The two also found that the leaderboard feature was the most popular facet of the app.
“Maybe we could lean into the whole gamification and competition aspect,” Carr says.
So the two came up with a range of math games to add to their app, while maintaining some of the original non-competitive learning features. After the app’s release in January, feedback from users confirmed that the gamified features were crowd pleasers.
The app’s mascot, an idea that came from student pitches during Carr’s meetings at local high schools, is called Sparko the Sharko. The latest logo design — a blue cartoon pi-squared symbol with eyes — was created by Carr’s ESTEEM classmate, Cody Bythrow ’25 M.S.
The app didn’t gain traction immediately after its release, Carr says. There is no money behind the app’s marketing, just Carr doing what he can, posting on Instagram and TikTok in his free time. Thus far, Carr and Fakhimi have been more focused on bettering their product than marketing it to the masses.
However, Pi-Squared’s user base rocketed after a freelance journalist’s piece about the app appeared in multiple Irish news outlets.
By early July, the app had grown to about 1,500 daily users, up from 100 to 400 in March, with over 16,000 downloads. Pi-Squared hit the top of Ireland’s free education apps chart and was second among all free apps on several days in May.
Though the two do not make money from the app, Carr says, “You get a nice message like, ‘Gee, we had the best fun after dinner as a family; I haven’t seen my son love maths ever,’ something like that.” Such positive words come as a heartening reward as the pair puts great time and effort into their creation.
“I think it’s really been rewarding to have something that I made put out there in the world,” Fakhimi says. “It gives me confidence for future things, that I can really make and do this.”
Working on the app takes Carr and Fakhimi, the only full-time employees, a great deal of time, even with some help from interns. “We’ve probably been like full-time Pi-Squared workers, part-time students, zero-time social life,” Carr jokes. Since graduation, Pi-Squared continues to take up most of his extra time. Carr returned to Ireland after commencement but moved back to the United States in July to begin a full-time job as director of strategic insights and innovation for AEBetancourt, a recruitment firm based in Grand Rapids, Michigan. He completed his master’s capstone with the same company and will be helping to integrate AI and technology into the firm’s work.
“I was just really pouring myself into it,” Fakhimi says. Following graduation, he returned to his hometown, Walnut Grove, California, and is applying for jobs. He works on Pi-Squared on nights and weekends.
Fakhimi acknowledges that there will come a time when the pair will have to add advertisements to the app or create a premium option with a paywall. A self-proclaimed “engineering purist,” Fakhimi says he won’t feel comfortable including ads until he is fully satisfied with the in-app experience. “Obviously, I would like to make some money,” Fakhimi says, “but that’s not really what it’s about for me.”
Adelyn Rabbitt is a rising sophomore journalism and psychology major from South Bend and this magazine’s summer intern.