Lynne completed her PhD in Number Theory at Dartmouth College under the supervision of Thomas Shemanske in 1987.  She also credited her supervisor with teaching her many useful practical skills, such as roofing. After her PhD she took a position at St. Olaf College, Minnesota, where she lived in an old farmhouse, which did not have indoor plumbing. She solved this problem by building a hand-operated pump, which also enabled her to install a bathtub in the kitchen, next to a wood-burning stove.

In 1990 she became a tenure-track Assistant Professor at the University of Colorado, Boulder. She received tenure there in 1995 and in 2000 became a full Professor. She came to Bristol as a Reader in Mathematics in 2007.

Lynne herself defined her mathematical ambition as 

• solving hard and interesting problems and constructing elegant proofs, 
• success as an expositor and a teacher, 
• enriching and contributing to the community, 
• happiness and fulfilment.

She was a number theorist of renown. The centrepiece of her scholarship was the study of theta series. Theta series have a long and glorious history that has engaged mathematical giants from Bernoulli, Euler and Jacobi to Hilbert, Siegel and Weil, and they remain mathematical objects of intense study. They provide a systematic way for constructing continuous mathematical quantities, called modular or automorphic forms, which encode information about discrete arithmetic problems, e.g., in how many ways one can express an integer as the sum of squares.  Automorphic forms arise in number theory, algebraic geometry, as well as mathematical physics. By studying these quantities and their properties, information about the original arithmetic question is gleaned. And then, following the magic of mathematics, the newly formed objects take on a life of their own and an enveloping theory often leads to yet unimagined places.   

Lynne's work on theta series began in her thesis, Theta Series Attached to Lattices of Arbitrary Rank. Her interest in them extended throughout her career. The word explicit occurs frequently in the titles of her roughly 40 papers. Many of these papers are single authored, delivering a musing and unhasty narrative, evincing the author’s thoughtfulness and intimacy with her subject. This substantial body of work has helped mathematicians understand spaces of theta functions and their structure, and explained how that understanding translates into knowledge about numbers. In her pursuit of elegance as an algebraist, Lynne sought explicit formulas to express certain fundamental quantities discovered, in particular, by Carl Ludwig Siegel in the 1930s.  Lately, she was particularly proud of her 2018 paper in the Ramanujan Journal, called Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series, where she said she succeeded in doing something that had defeated Siegel.  

She would stress that mathematics constituted largely her personal aesthetic quest, rather than the pursuit of fame and honours. Nonetheless, Lynne's career since its early days has been marked by an unambiguous pattern of strong leadership. Her dedication to teaching and scholarship inspired generations of students. Her commitment to Equality and Diversity was selfless, unparalleled and contagious. In the early 2000s, serving in a position of honour as Program Officer for the US National Science Foundation, she was an active member of the managing team of the Vertical Integration of Research and Education Program, aiming at broadening the backgrounds of those who seek careers in the mathematical sciences. There, she was also a lead member of the Early Career Development Program management team. Since 1988 she gave some 20 invited presentations on Women, Diversity, and Education. She became a role model for a whole generation of female scholars.

Professor Lynne Walling was Head of Department of Mathematics in Boulder in 2004-2006. In Bristol she was Head of Pure Mathematics in 2011-2015 and Director of the Institute of Pure Mathematics from 2018. In these leadership positions, she regarded ensuring the well-being of her colleagues, supporting and recognizing their achievements and promoting their success as perhaps her greatest responsibility. 

She knew how to hold her head high and to be unapologetic in advocating for what she believed. She was a true artist in everything she did -- her mathematics; her artwork and craftsmanship, which preceded her mathematics and which she carried with her all her life; and in her general quest for self-realisation. She was a remarkably courageous and generous person, colleague, and friend, and she taught this to people who found themselves within the sphere of her magnetism. The last lesson she taught those surrounding her is that it is possible to face death on your own terms and undefeated.

I would like to thank Lynne’s father, Stuart Walling, and many of her friends and colleagues, in particular Tom Shemanske, Sol Friedberg, Jonathan Robbins, and the members of the Celebration of LW  WhatsApp group for providing material and help in preparing this obituary.

Misha Rudnev