*“I have never been able to think of my mathematical work as a job. Some of the greatest pleasures come from both the learning and sharing process"—Edward Waymire*

Edward Waymire, a widely admired professor of mathematics, has retired after 36 years of teaching and research at Oregon State University. An eminent probabilist, Waymire has made fundamental contributions to advance understanding of uncertain natural phenomena that range from rainfall and river networks to population dynamics through the framework of mathematics.

Throughout his career, Waymire conducted highly significant research concerning applications of probability and stochastic processes to problems of contemporary applied mathematics involving flows, dispersion and random disorder. Particularly outstanding is his research combining mathematics with a vast number of scientific fields that include hydrology, physics, geosciences, biology, statistics, oceanography and others.

Waymire’s leadership and visibility as an exceptional probabilist are reflected in various ways. He was an editor of *Annals of Applied Probability *(2006-2010), widely considered one of the most influential and trend-setting journals in the field.

Waymire also served as editor of Bernoulli (’94-2006), a top journal of mathematical statistics and probability as well as on the editorial boards of several international journals. He also served as president of Bernoulli Society for Mathematical Statistics and Probability (2013-2015).

In addition, Waymire received the 2014 Carver Medal from the Institute of Mathematical Statistics (IMS) for exceptional contributions to the IMS in many capacities, but in particular he was commended for outstanding service to the Annals of Applied Probability “far beyond his role as its editor.”

“Ed Waymire has been a pillar of the Department of Mathematics and has played a major role in the development of the field of probability at OSU. In addition to his role in the math department, Ed has wide-ranging interests in science, and he has been generous in committing his time and knowledge in the larger science community at OSU,” said Bob Smythe, statistics emeritus professor.

Waymire was born in Alton, Illinois, an industrial town near the confluence of the Mississippi and Missouri Rivers. The oldest of four brothers, he had a natural talent and love for abstract thinking and mathematics since childhood. His grandfather, Mathias Waymire, who worked his way up from a ditch digger to operations and management at Standard Oil Refinery, was admittedly a big influence on the young Waymire.

“My earliest memories of math are those of my self-educated grandfather teaching multiplication tables and temperature conversion formulae to me,” said Waymire.”

Alton was home to a number of oil refineries during Waymire’s boyhood. His father had a career in Shell Oil Company and his mother was a home- maker; both avidly encouraged their children to get a college degree and be self-sufficient.

Thinking he could teach math in high school, Waymire attended Southern Illinois University where he studied mathematics and physics. A National Science Foundation (NSF) grant enabled Waymire to conduct research on lightning with a physics professor, while he was still an undergraduate student, and sparked his lifelong interest in mathematical models of natural phenomena.

“By the time I finished my undergraduate major in math and an NSF undergraduate research experience grant in physics, I had fallen head over heels for mathematical thinking,” observed Waymire.

At the height of the Vietnam War, Waymire joined the Mathematics Department at the University of Arizona for his graduate studies fully expecting to be inducted to the army in December that year after being picked for the draft through a lottery. But as luck would have it, with popular sentiment turning against the war in Vietnam, President Nixon moved toward ending the draft that year. As a result of this serendipitous turn, Waymire stayed on course at Arizona where he earned master’s and doctoral degrees in mathematics.

At Arizona in the early seventies, Waymire was introduced to stochastic processes or the mathematics of non-deterministic or random phenomena. His graduate education came at a fertile historical moment when probabilistic models to make sense of and comprehend variation in the world were taking off.

#### Entry into academia

Quite a few rewarding and enduring research collaborations emerged from Waymire’s time at Arizona that include significant works of research with his Ph.D. advisor Rabi Bhattacharya—a deep engagement that continues today. Waymire and Bhattacharya have a four-volume textbook project under contract at Springer Publishing.

They have co-authored *A Basic Course in Probability Theory* and Waymire has co-edited *Rabi Bhattacharya: Selected Papers (Contemporary Mathematicians)*. Their graduate textbook, *Stochastic Processes with Applications* was reprinted by the Society for Industrial and Applied Mathematics (SIAM) for their Classics in Applied Mathematics series.

Waymire’s first academic job as an assistant professor in the Department of Mathematics at Clarkson University took him to Potsdam, New York. While he found the place inhospitably cold, upstate New York proved to be most fortuitous in other ways. He met his future wife Linda there.

After short research stints at the University of Mississippi and the University of Arizona, Waymire arrived at Oregon State in 1981 to join the Department of Mathematics as an assistant professor where he has remained ever since.

Chief among Waymire’s earliest research directions in applied probability has been the mathematics of rainfall. He became interested in random fields and point processes, especially how they appear on different scales of space and time and relate to rainfall observations and models in hydrology after gaining exposure to rainfall observations and models in hydrology.

“While mathematics has a life of its own, from numbers to geometry, I tend to resonate most strongly with its origins and connections to our natural world. Mathematics is a remarkable human construct in which to abstract seemingly disparate natural phenomena,” said Waymire.

While he was at Clarkson University, Waymire began work with hydrologist Vijay Gupta (now an emeritus professor at The University of Colorado) that resulted in the mathematical theory of cascades and the application of that to analyses of river networks, rainfall and floods.

Waymire’s research has led to new mathematical theorems to establish three-dimensional bell curves (normal distributions) in large-scale limits, and fractional dimensional (fractal) distributions in the fine scale limits to characterize important linkages between atmospheric dynamics and rainfall and determine drainage and flooding from rivers. This has resulted in seminal publications with math and science colleagues, here at OSU as well as at other universities.

Over time, Waymire’s mathematical studies of hydrology have expanded to applications to phenomena in statistical physics, biology and even erratic financial markets. These include applications to dispersion, problems in Brownian motion, the connections between Navier-Stokes equations, which are used to analyze fluid flows in engineering and physical and biological sciences, and stochastic cascades.

At OSU, Waymire has enjoyed a rich and distinguished career marked by several momentous research collaborations across many disciplines.

“I have never been able to think of my mathematical work as a job. Some of the greatest pleasures come from both the learning and sharing process,” remarked Waymire.

Various research grants have helped him nurture collaborations with several scientists at OSU. Most notable were the NSF Award on Navier-Stokes equations, an Interdisciplinary Graduate Education Research & Training (IGERT) grant in Ecosystems Informatics, and the NSF funded Math/Engineering grant Dispersion in Highly Heterogeneous Media.

Current research awards include a NSF-supported project on Stochastic Analysis Associated with Problems in Fluid Flow with fellow mathematician Enrique Thomann and former postdoc Nicholas Michalowski and an NSF Research Traineeship (NRT) in Risk and Uncertainty Quantification in Marine Sciences.

The research and training grants allowed Waymire to work closely with students and colleagues in environmental engineering, hydrology, geosciences, oceanography, ecological and geographic sciences, computer science, statistics, social sciences, resource economics, and forestry, in addition to mathematics.

“It has been a remarkable experience as I look back,” said Waymire.

A generous and inspiring colleague, Waymire has co-authored several papers over the years on a diverse range of theory and applications with fellow OSU mathematicians.

“Ed has been a wonderful mentor, collaborator, colleague and friend to me since I arrived at OSU in 2006. I always found it easy to ask for Ed’s advice and have always received valuable feedback from him,” said Vrushali Bokil, an associate mathematics professor in the department and a co-author.

#### A “great teacher and a deep thinker”

As an emeritus professor, Waymire will continue his involvement with the department in various ways, although he will be greatly missed as a teacher.

The mathematician has spent his career guiding students toward an understanding and appreciation of the joys of mathematics in the classroom and in directing research. He has supervised/co-supervised eight Ph.D. students, with a ninth student expecting completion in the spring. He has also supervised 20 MS degree students and served on dozens of doctoral, masters and undergraduate thesis committees.

He connects his passion for mathematical research with his pedagogy.

“One must realize that mathematics is an evolving subject. From its origins in counting and geometry to the dynamics of the motion of planets and molecules it continues to grow in all matters of depth and perspective.”

“We can engage students in the beauty and opportunities of mathematics by viewing its significance to the past, present and future. This is best achieved by active engagement in mathematical research by teachers,” explained Waymire.

His students describe him as a gifted and open-minded teacher and adviser, who teaches mathematics with the flair of a philosopher and the breadth of a historian. Initially in awe of his reputation, his students have found Waymire to be both a brilliant and kind mentor.

Mathew Titus, who graduated with a Ph.D. in math in 2017, found his classes with Waymire to be memorable because of his professor’s distinctive manner of explaining a proof.

“Ed takes time to dissect the core ideas of proofs, which is invaluable; he was often inadvertently humorous as he might have to pause and work out some simple algebraic calculation in a series of halting chalk-strokes, only a few moments after divulging the entire conceptual essence of the proof with absolute ease.”

Titus felt honored to be advised by a mathematician who has contributed significantly to the progress of probability mathematics in the present day.

“It is inspiring to meet someone who never misses the truth underlying a proof, and Ed's hunger for the fundamental mechanisms behind natural phenomena is one of his greatest strengths as a teacher and as a mathematician,” added Titus.

Waymire’s former doctoral student Jorge Ramirez is a mathematics professor at the National University of Colombia, Medellin. Ramirez praises Waymire for not just his qualities as a great probabilist but also for being a “role model for how to live a good life.”

Ramirez, who had first encountered Waymire through his “amazing book on probability” as an undergraduate student in Colombia, was quite struck by his mentor’s warm, caring and empathetic nature.

“Although he taught me most of the technical skills that have helped shaped my career, there is much more I found in Ed. I would say that Ed’s defining quality as a mentor is his ability to empathize. As I got to know the man better through the years, it is clear to me that this empathy is a big part of what makes Ed the amazing person he is, beloved by his friends, wife, colleagues and students.”

Waymire devoted considerable time and energy through the eighties to expand the diversity of opportunities for mathematics students, at a time when the economy was doing poorly and summer internships for math students were few and far between.

Interested in pursuing the connections between mathematics and business as well as opportunities for students to connect with Portland actuarial companies, Waymire and his colleague pioneered the creation of internships in actuarial sciences and resources to support talented students. Over time, these efforts blossomed into the actuarial sciences minor in the department, which continues to thrive today.

Waymire is the recipient of the 2006 OSU College of Science Milton Harris Award in Basic Research and the College of Science 2014 F.A. Gilfillan Award for Distinguished Scholarship in Science. The Gilfillan award recognizes distinguished scholarship in science by honoring a faculty member in the College of Science who demonstrates a long and exceptional scientific career and scholarly achievements that are widely recognized nationally and globally by his or her peers.

He is a member of the American Mathematical Society and the Society for Industrial and Applied Mathematics, an Elected Member of the International Statistical Institute and a Fellow of the Institute of Mathematical Statistics.

In his free time, Waymire enjoys skiing, hiking and camping with his wife Linda. The duo also plays bluegrass music with friends and at small venues in Corvallis.

Waymire looks forward to remaining active with his currently funded research group pertaining to research on the Navier-Stokes equations, and continue mentoring graduate students on a number of PhD committees, both at OSU and with the Math Alliance — the national alliance for doctoral studies in the mathematical sciences headquartered at Purdue University.