Duchin was given her first name, Moon, by parents "on the science-y fringes of the hippie classification".[4] She grew up knowing from a young age that she wanted to become a mathematician.[4] As a student at Stamford High School in Connecticut, she completed the regular high school mathematics curriculum in her sophomore year, and continued to learn mathematics through independent study.[4] She was active in math and science camps and competitions, and did a summer research project in the geometry of numbers with Noam Elkies.[4]
Duchin studied at Harvard University as an undergraduate, where she was also active in queer organizing,[5] and finished a double major in mathematics and women's studies in 1998.[4][6] At the time, she was unsure how to combine the two majors into a single thesis, so she decided to write two separate ones.[7]
Duchin's expertise in geometry has led her to conduct research on the mathematics of gerrymandering. A key aspect of this research is the geometric notion of the compactness of a given political district, a numerical measure that attempts to quantify how extensively gerrymandered it is.[12] “What courts have been looking for is one definition of compactness that they can understand, that we can compute, and that they can use as a kind of go-to standard”, she said in an interview with The Chronicle of Higher Education.[13]
To help tackle the challenge of finding an agreed-upon standard, Duchin has developed a long-term, wide-ranging project on the mathematics of gerrymandering.[13] As a part of this project, she founded a summer program to train mathematicians to become expert witnesses in related legal cases.[14][15] In 2016, she founded the Metric Geometry and Gerrymandering Group (MGGG) which is a nonpartisan research group that coordinates and publicizes research on geometry, computing, and their application to the redistricting process in the US.[16][7]
In 2018-2019 she took a leave of absence from Tufts, and was a Fellow at the Radcliffe Institute for Advanced Study at Harvard University. Her research focus was "Political Geometry: The Mathematics of Redistricting".[17] In 2018, Governor of PennsylvaniaTom Wolf enlisted Duchin to help him evaluate newly drawn redistricting maps for fairness.[18] This happened as a consequence of the Supreme Court of Pennsylvania decision which declared the state's 2011 US congressional districting map to be unconstitutional.[19] Duchin prepared a report published on February 15, 2018.[20][21]
As of 2021[update], Duchin has returned to her position at Tufts, and continues her work with MGGG.
In 2022, a panel of judges threw out Alabama's soon-to-be-used congressional maps, citing the fact that the percentage of black people in the state had risen to about a quarter of the population. To draw some new, fairer maps, they turned to Duchin, who came up with 4 nearly-similar maps that would put the Black and Democratic-leaning cities of Mobile and Montgomery together, therefore complementing the one Black and blue-leaning district in the state with a second one.[22]
