Celebratio Mathematica

Com­mu­nic­ated by Hélène Bar­celo and Steph­en Kennedy (with con­tri­bu­tions from Roya Be­heshti; Izz­et Coskun, Laura De­Marco, and Dav­id Du­mas; Elon Linden­strauss; Peter Sarnak; Alex Eskin; Eu­genia Sa­pir; Hélène Bar­celo and Dav­id Eis­en­bud; Ur­sula Hamenstädt; Scott A. Wolp­ert; Alex Wright and Ant­on Zorich).

Maryam Mirza­kh­ani’s Har­vard PhD dis­ser­ta­tion un­der Curt McMul­len was widely ac­claimed and con­tained already the seeds of what would be­come her first three ma­jor pa­pers. All three of these res­ults — a new proof of Wit­ten’s con­jec­ture, a com­pu­ta­tion of the volume of the mod­uli space of curves, and an asymp­tot­ic count of the num­ber of simple closed geodesics on a hy­per­bol­ic sur­face — were deep, beau­ti­ful, and un­ex­pec­ted. Sub­sequent pa­pers re­vealed the geo­metry and dy­nam­ics of the mod­uli space of hy­per­bol­ic sur­faces, cul­min­at­ing in the ri­gid­ity res­ult achieved jointly with Alex Eskin. Her work ex­hib­its great depth of in­sight, wide-ran­ging tech­nic­al mas­tery, and cre­ativ­ity and ima­gin­a­tion of a very high or­der. It earned her a Fields Medal in 2014.

Mirza­kh­ani was born on May 12, 1977, in Tehran and grew up in postrevolu­tion­ary Ir­an dur­ing the Ir­an–Ir­aq War. One of four chil­dren, her fath­er was an en­gin­eer, her moth­er a home­maker. All three of her sib­lings be­came en­gin­eers. It was in middle school that she dis­covered her pas­sion and tal­ent for math­em­at­ics. In high school she par­ti­cip­ated in the In­ter­na­tion­al Math­em­at­ic­al Olympi­ad, win­ning gold medals in 1994 and 1995. She earned a bach­el­or’s de­gree in math­em­at­ics from Sharif Uni­versity in Tehran and headed to Cam­bridge, Mas­sachu­setts, for gradu­ate study at Har­vard.

When Mirza­kh­ani was awar­ded the Fields Medal in 2014 she had already been dia­gnosed with the can­cer that would even­tu­ally claim her life. Al­ways a private and humble per­son, she did not wel­come the at­ten­tion and ac­claim that ac­com­pan­ied the prize. To­geth­er with her hus­band, Jan Von­drák, she wanted to raise their daugh­ter, live her life, and pur­sue math­em­at­ics. No­tices asked friends, col­lab­or­at­ors, and stu­dents of Mirza­kh­ani to write brief re­min­is­cences of her life. We also sought ex­pos­it­ory work on her math­em­at­ic­al ac­com­plish­ments from Ur­sula Hamenstädt, Scott Wolp­ert, and, writ­ing jointly, Alex Wright and Ant­on Zorich. The por­trait that emerges from these pieces is of a warm, gen­er­ous, and mod­est friend, teach­er, and col­league — a math­em­atician of great tal­ent and ima­gin­a­tion coupled with grit and per­sist­ence to a very un­usu­al de­gree. Maryam Mirza­kh­ani died, aged forty, on Ju­ly 14, 2017.

Ed­it­or’s note: The text above is from the in­tro­duc­tion of “Maryam Mirza­kh­ani: 1977–2017” pub­lished in the No­tices in Novem­ber 2018. For the full art­icle, click on the link to the PDF at the up­per right of this page.