An Unrestricted Notion of the Finite Factorization Property
Jonathan Du, 18, of Mountain View, explored how factorization works in different mathematical spaces for a Regeneron Science Talent Search mathematics project.
Factorization is breaking numbers, polynomials or other mathematical objects into a product of simpler parts: factors. Factorization has enthralled mathematicians since antiquity, and it now underpins the encryption of most information on the internet.
Jonathan鈥檚 project investigated a new idea called the unrestricted finite factorization property and showed how it relates to other types of factorization. Whole numbers have the simplest factorizations, with a specific set of factors associated with each number. But in more complicated algebraic systems, some elements have several factorizations while others may not factor at all. Jonathan鈥檚 project studies systems in which the elements that do factor only do so in a limited number of ways. This work could help mathematicians understand how strange multiplication can get.
The child of Zilin Du and Mingyi Xia, Jonathan attends Los Altos High School and is president of the math, physics and hacker clubs.
Beyond the Project
Jonathan is a leader in the math, physics and hacker clubs at Los Altos High School. Jonathan spent 3 years building solar-powered refrigerators to keep vaccines cool in communities with unreliable power.
FUN FACTS: Jonathan has enjoyed working with Photoshop since fourth grade, when a stray trash bag inspired the creation of the character 鈥淏ob the Bag.鈥�
