Amanda Folsom facts for kids

Amanda L. Folsom, born in 1979, is a talented American mathematician. She studies numbers and how they work, especially in a field called analytic number theory. This helps with other math areas like combinatorics, which is about counting and arranging things. She is a professor at Amherst College and leads their math department.

Becoming a Mathematician

Early Studies and Degrees

Amanda Folsom loved math from a young age. She graduated with honors from the University of Chicago in 2001. She earned her Ph.D. (a high-level degree) in 2006. She studied at the University of California, Los Angeles (UCLA). Her main project was about "Modular Units." Her professor, William Duke, helped her with this work.

Teaching and Research Roles

After UCLA, she did more research. She worked at the Max Planck Institute for Mathematics in Germany. Then she went to the University of Wisconsin–Madison. In 2010, she became a math teacher at Yale University. She moved to Amherst College in 2014. She is now the head of the math department there. In 2018 and 2019, she was a special researcher at the Institute for Advanced Study.

Amazing Math Discoveries

Uncovering Number Patterns

Amanda Folsom has made exciting discoveries in math. She worked with other mathematicians like Ken Ono. They found a special pattern in something called the partition function. This function counts how many ways a number can be broken down. For example, the number 4 can be broken down in 5 ways (4; 3+1; 2+2; 2+1+1; 1+1+1+1).

They discovered a "fractal" structure in this function. A fractal is a complex pattern that repeats itself. This discovery means they can now figure out any value of the partition function exactly. They use a special math formula to do this.

The Folsom–Ono Grid

Folsom and Ken Ono also have a math idea named after them. It's called the Folsom–Ono grid. This grid is made from two groups of special math series. These series are related to "modular forms," which are fancy math objects. The numbers in these series can be put into a two-dimensional grid.

In 2008, Folsom and Ono guessed that all the numbers in this grid would be whole numbers (integers). Other mathematicians later proved that their guess was correct!

Improving Ramanujan's Work

Folsom also worked with Ono and R. C. Rhoades. They improved some ideas from a famous mathematician named Srinivasa Ramanujan. Ramanujan had studied "mock modular forms." These are special kinds of modular forms. Folsom and her team made his work even better.

Writing a Math Book

Amanda Folsom is also an author. She wrote a book with Kathrin Bringmann, Ken Ono, and Larry Rolen. The book is called Harmonic Maass Forms and Mock Modular Forms: Theory and Applications. It was published in 2018.

Awards and Honors

Recognized for Research

Amanda Folsom has won important awards for her math work. In 2021, she won the Mary P. Dolciani Prize. This award is given by the American Mathematical Society. She won it for her amazing research in number theory. She also won for helping college students learn math. And she was honored for helping women succeed in math.

Award-Winning Book

Her book, Harmonic Maass Forms and Mock Modular Forms, also won an award. It received the 2018 Prose Award. This award is for the best scholarly book in mathematics. It was given by the Association of American Publishers.