Jacob Lurie deals with a realm foreign to many, one of algebraic geometry — the study of complex polynomial equations — and algebraic topology, which uses algebra to study shapes.

But since graduating from Montgomery Blair High School’s science, mathematics and computer science magnet program in 1996, Lurie — now a mathematics professor at Harvard University — has been trying to make such topics less foreign. His work has introduced new ways of looking at geometry and other fields, along with how to make such subjects more interesting to the average student.

The way mathematics is taught in many high schools and colleges is like a music class in which an instructor makes students play scales over and over, Lurie said. That does not make a lot of students want to learn the subject, he said.

“I think that it would be much better for a lot of people if they wanted to take one mathematics class in college, that they could take one that focuses on the history of a lot of ideas in mathematics,” said Lurie, 36. “I think there are a number of mathematical insights that are very interesting that you really could teach to someone in a freshman course.”

In September, Lurie won a MacArthur Foundation Fellowship, one of the most prestigious honors in academic and creative fields, sometimes known as “genius grants.” His ideas and methods are “altering a wide range of fields,” including geometry and topology, according to the foundation.

The $625,000, five-year grant — one of 21 bestowed this year from the John D. and Catherine T. MacArthur Foundation — allows Lurie to pursue research without any stipulations. Fellows are nominated through an anonymous, rigorous process, with the foundation’s staff researching candidates and an independent committee recommending honorees to the board.

In June, Lurie won another prize that comes with an even larger $3 million payout, as one of five winners of the inaugural Breakthrough Prize in Mathematics founded by billionaire entrepreneur Yuri Milner and Facebook co-founder Mark Zuckerberg. Lurie will receive the $3 million at a California ceremony in November.

At Blair, Lurie won the science talent search competition sponsored by Westinghouse Electric Co., now sponsored by Intel Corp.

Jonetta Russell, who was Blair’s magnet program research coordinator when Lurie attended and retired about a decade ago, remembers him as a bright, sociable student who quickly grasped complex concepts that confounded even many adults.

“Even the judges of his science talent project had trouble understanding his project,” Russell said.

Lurie is not the first graduate of the Silver Spring high school to win a MacArthur “genius grant.” Maneesh Agrawala, a University of California, Berkeley, electrical engineering and computer sciences professor and 1990 Blair graduate, earned the honor in 2009.

After obtaining a bachelor’s degree from Harvard and a doctorate from the Massachusetts Institute of Technology, Lurie held a postdoctoral fellowship at Harvard. He was affiliated with MIT for a couple more years before joining the faculty of Harvard.

His scientific work has been published in some books, including “Higher Topos Theory” and “Higher Algebra,” as well as numerous papers.

“Mathematics is a giant playground filled with all kinds of toys the human mind can play with,” Lurie said. “Many of these toys have very long operating manuals, but some of them don’t.”

Lurie said he was surprised to hear that he won the MacArthur award, after being similarly surprised a couple months before to hear about the Breakthrough Prize. He plans to use some of the funds on a math summer camp for high school students and a new program supporting graduate fellowships for young mathematicians in the developing world.

“I’ve heard of these fellowships, but I had no idea that they even gave them to mathematicians,” Lurie said.