Alfonso Gracia-Saz

Photo courtesy of Nicholas Remedios

Alfonso Gracia-Saz
13 Mar 1976 - 6 May 2021
Triangle Squares


In Memoriam: Professor Alfonso Gracia-Saz, March 13, 1976 – May 6, 2021

We are deeply saddened by the passing of Professor Alfonso Gracia-Saz, who has been teaching in the Mathematics Department at the University of Toronto from 2013. Alfonso was a well-loved and innovative teacher who was just about to receive the 2021 Excellence in Teaching Award from the Canadian Mathematical Society.

Born in Zaragoza in Spain on March 13,1976, Alfonso has lived and worked in Spain, America, Japan and Canada. Alfonso’s interest in mathematics and physics goes back to his teenage years, when he was a winner of the V Spanish Physics Olympiad, which led to his participation in the International competition in Beijing in 1994. He obtained a Licenciatura (BSc) in both Physics and Mathematics from Universidad de Zaragoza (Spain), in 2000-2001, and a PhD in Mathematics from The University of California at Berkeley in 2006 (where he was supervised by Professor Alan Weinstein). He held postdoctoral positions at Keio University (Japan) and University of Toronto before taking faculty positions first at the University of Victoria and then at the University of Toronto where he was an Associate Professor (Teaching Stream). His research interests were centred in active learning, inquiry-based learning, Poisson geometry and Lie algebroids.

Alfonso believed in the power of education beyond his work of teaching mathematics at university. His calculus YouTube channel with 200 videos has over 10,000 subscribers and well over 3 million views. He was active in mathematics outreach through competitions, math camps, science fairs and undergraduate research. He co-led the recruiting and training of the University of Toronto Putnam Math Competition team, who placed 4th in 2017. For more than 10 years, he was an Academic Advisor and an instructor for the Canada/USA Mathcamp. He also volunteered as an instructor for the Prison University Project at San Quentin State Prison (now Mount Tamalpais College).

He leaves behind his beloved partner of six years, Nick Remedios. Alfonso and Nick enjoyed contra dancing and complex board games. They loved cooking together. In Spain, Alfonso is mourned by his mother, Carmen; his father, Antonio; his sister, Rebeca, and her children, Mario and Carla.[1]

Condolences and remembrances may be viewed and left at Gathering Us

University of Toronto math professor Alfonso Gracia-Saz died May 6 after being hospitalized with COVID-19.
Whether it was for a yearlong math course or a short meeting at a conference, University of Toronto professor Alfonso Gracia-Saz had an impact on almost everyone he met.
Priyanshu Arora took away many lessons from his firstyear MAT 137 calculus course with Gracia-Saz, saying he had been his favourite teacher in university. Arora, who moved to Toronto from New Jersey to attend the school’s computer science program in 2019, said the class was challenging, but Gracia-Saz taught him how to approach learning in a new way.
“One thing I learned from him is always question whether you truly understand (something).”
This year’s MAT 137 course was wrapping up when, about 10 days ago, Gracia-Saz sent an email notifying other instructors that he was sick with COVID-19.
Joel Kamnitzer, Gracia-Saz’s friend of 20 years, received the email as another professor and researcher in the course. A few days later, Gracia-Saz sent him an email directly, alerting him that he was being admitted to hospital.
Gracia-Saz died on May 6 at age 45.
Gracia-Saz leaves a legacy of passion that transcends formulas and numbers.
Arora said he walked into Gracia-Saz’s class one day thinking he fully understood the material from the previous night. Over the years, Gracia-Saz had uploaded short videos to YouTube explaining topics that students had to attempt to grasp before the concepts were addressed in class.
The videos, which were part of what he called a reverse-classroom approach, have racked up thousands of views, with one about the math concept of sets and notations hitting around 211,000 views.
During the day’s class, GraciaSaz put up 10 formulas on the board, each with minor differences.
“We were bugging out, like, I don’t understand the difference between all of these,” Arora recalled. “He really engaged with the class and asked them what do you think?”
Although the majority of the class agreed on an answer that turned out to be wrong, GraciaSaz would explain it to them, prompting a eureka moment for students. Kamnitzer described his friend’s dedication and drive in anything he did.
“He always put amazing effort into everything and expected others to put their own effort in as well.”
The two met while attending graduate school at the University of California, Berkeley, in 2001, where Gracia-Saz introduced himself as “Al.”
Kamnitzer remembers a time when Gracia-Saz decided to only greet others by touching their nose, on one occasion leading someone to call the police on him out of irritation.
Gracia-Saz got his Bachelor of Science in physics and mathematics from Spain’s Universidad de Zaragoza in 2001, before receiving a PhD in mathematics from the University of California in 2006, according to the Canadian Mathematical Society.
After a post-doctoral position at Keio University in Japan, he went to the University of Toronto to become an associate professor in 2013.
On top of his role as an instructor, Gracia-Saz was an Academic Co-ordinator for the North American math camp, a program for high school students.
It was announced in March that Gracia-Saz would receive an Excellence in Teaching award from the Canadian Mathematical Society. He would have accepted the award at the society’s virtual ceremony in early June.
Peter Taylor, a math and statistics professor at Queen’s University and president of the society, said they will take time during the ceremony to “celebrate Alfonso’s accomplishments while mourning his loss.”
“He was well-known in the Canadian mathematical community and his loss is a tragedy for us all.”
— Cheyenne Bholla, Staff Reporter[2]

Gratitude for the life of Alfonso Gracia-Saz
Our dear friend and dancer par excellence, Alfonso, died this past May 6th, 2021, after being hospitalized with the COVID-19 virus. Alfonso was 45 years old and is survived by his parents, sister and young niece and nephew (all in Spain), and his partner Nick Remedios.
Alfonso was by all accounts a brilliant mathematician and a mathematics professor (University of Toronto) whose passion and belief in the power of education reached far beyond his work of teaching mathematics at the university. Alfonso’s work has been recognized nationally by the Canadian Mathematical Society and he will receive their 2021 Excellence In Teaching Award, in absentia, at their summer meeting in June.
The Toronto Contra Dance regulars knew Alfonso best as a wonderful dance partner, a regular wearer of terrifically flowing dance skirts, (with pockets!), and a frequent initiator of “Shenanigans” on the contradance floor.
This was Alfonso’s genuine talent. He saw contra dance, and Modern Square Dance, as simply an extension of the mathematical patterns he saw in his head all the time, and for the rest of us, it completely extended the joy of contra dance into another realm altogether.
Alfonso was kind. He knew how to have fun and how to make fun happen. He did it all with a lovely generosity of spirit. His impish smile would let you know that you’d been in cahoots on this very special experience of creating group mirth. You were laughing so hard, you’d struggle not to cry. Alfonso just couldn’t help but make everything even more fun in every part of his life.
Alfonso introduced Nick to contra dancing on one of their first dates. Little did Nick know, that was just the start of many wonderful years of dancing all across North America. For Nick, when he and Alfonso danced together, it was like there was no one else in the world. For the rest of us, we wholly enjoyed being expertly partnered with a joyfulness that knew no bounds.
We will miss Alfonso more than we can ever possibly say. We extend our sincere gratitude to Nick, and to Alfonso’s family: Mom: Carmen, father: Antonio, sister: Rebeca and her children Carla and Mario, for sharing him with us.
We will dedicate a dance to Alfonso when COVID restrictions permit us to gather in person again.
Elizabeth Szekeres, 12 May 2021


OTTAWA — The Canadian Mathematical Society (CMS) is pleased to announce that professor Alfonso Gracia-Saz (UofT) has been named the 2021 recipient of the CMS Excellence in Teaching Award. Professeur Gracia-Saz will receive his award at the 2021 Summer Meeting which will be held virtually from June 7 to June 11.

It is said that when Dr. Gracia-Saz teaches, he reinvents teaching. His work with the University of Toronto’s legendary MAT137 (Calculus with Proof) is an excellent example of his dynamic teaching style; his reorganization, his attention to detail, his famous problem sets, and his inspiring lectures and videos have given this challenging course a new level of energy–particularly significant in this recent time of pandemic challenge. A second example is found in his design of the instructor training program at the University of Toronto, a program that has now been extended to all Teaching Assistants in the Mathematics Department.

According to his Toronto colleague, Professor Galvao-Sousa, Professor Gracia-Saz “belongs to this rare breed of born teachers that possess not only the knowledge and creativity but also the warm and dynamic personality that allows him to teach students in such a natural way that the barrier between teacher and student ceases to exist.”

Jeremy Quastel, the Chair of the Mathematics Department at Toronto makes it clear that Alfonso Gracia-Saz’ work with MAT137 was a great achievement:

Alfonso has very high standards and expects a strong commitment on the part of his students. But he is very generous with his time and makes it abundantly clear that he is more than willing to offer help to anybody who needs it. The upshot has been staggeringly good course evaluations for Alfonso personally, but also very good results for the course overall.

Peter Taylor, the Chair of the CMS Excellence in Teaching Award Committee, remarks:

an important reason for Alfonso’s success as a teacher of mathematics who is exigent with his students is the elevated standard of performance he sets for himself. For example, his videos are remarkable, both technically and conceptually––they give you an experience that is both challenging and joyful.

Alfonso Gracia-Saz obtained a Licenciatura (BSc) in both Physics and Mathematics from Universidad de Zaragoza (Spain), in 2000-2001, and a PhD in Mathematics from The University of California at Berkeley in 2006 (supervisor: Alan Weinstein). He held postdoctoral positions at Keio University (Japan) and University of Toronto before taking faculty positions first at the University of Victoria and then at the University of Toronto where he is now Associate Professor (Teaching Stream). His research interests are centred in active learning, inquiry-based learning, Poisson geometry and Lie algebroids.

Over the past 13 years, Alfonso has served as an instructor and the Academic Coordinator of the Canada/USA Mathcamp. His calculus YouTube channel with 200 videos has over 10,000 subscribers and well over 3 million views. He is active in mathematics outreach through competitions, math camps, science fairs and undergraduate research. He has worked in a prison university project (currently Mount Tamalpais College) and has written a mathematical play. He and his partner, Nick, enjoy contra dancing, cooking and complex board games.

About the Excellence in Teaching Award The Excellence in Teaching Award recognises sustained and distinguished contributions in mathematics education at the post-secondary undergraduate level at a Canadian institution. The award was established in 2004 to recognise teaching excellence as exemplified by effectiveness in the classroom and/or commitment and dedication to teaching students.

For information about past recipients visit: Excellence in Teaching Award

About the Canadian Mathematical Society (CMS) The CMS is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including: scientific meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements.[3]


I ❤️ YouTube! When my Dad died almost 6 years ago, between the family members, we had hundreds of photos of him. But what I desperately yearned for was to hear the sound of his voice. His was a different time and a different generation. Alfonso Gracia-Saz was an exceptional contra/square dancer. He was a kind, attentive, gentle and playful partner, just a joy to dance with. After he unexpectedly and tragically died last Thursday, I looked for photos of him and found several lovely ones in the Toronto Contra Dance FB albums. When Jake mentioned on Saturday that Alfonso had a YouTube channel, I was delighted! Alfonso was an inspirational Associate Professor at the University of Toronto in the Mathematics Department. He had just been named the 2021 recipient of the Canadian Mathematical Society’s Excellence in Teaching Award, that he was due to receive virtually in June. His incredible work with MAT137 (Calculus With Proof) has been immortalized on YouTube in the form of 178 short videos in 14 playlists/chapters that he created over years. It’s the most wonderful thing, to listen to Alfonso’s voice with its lovely Spanish lilt talking passionately about calculus. I’ll admit, I mostly have absolutely no idea what heck he’s talking about. He lost me pretty quickly after Sets and notation, and that was the very first video. But I’ve been listening to one every day. I hated math in highschool. I had the head of the department in my last year and while she may well have been a good mathematician, she was a *terrible* teacher. I wish I’d had Alfonso as a teacher. I read so many comments from his students and colleagues saying that he was the best professor they’d ever had, that he’d changed their lives. Even if you’re like me, “not a math person”, I encourage you to listen to a few of these videos to hear Alfonso’s voice and his passion. I’m *so* thankful that YouTube will allow me to hear his voice whenever I want to. My heart goes out to his partner Nick and every one of us who knew Alfonso.
Bev Bernbaum

Bev Bernbaum, gosh, I remember dancing with Alfonso at the Pittsburgh Fall Dance Weekend. What a fantastic, fun, intuitive, and creative person he was on the dance floor! Sorry for such a loss. 😢
Janine Smith

Janine, a favourite memory is of driving to the Pittsburgh Fall (Contra) Dance Weekend with him in 2010. He had taken a faculty position at the University of Victoria in BC and was feeling dance withdrawal. He came to visit Toronto that November and I talked him into coming to Pittsburgh with me. To this day, that’s always been one of my favourite weekends. I was calling and he’d never been. We talked non-stop on the 5 hour drives down and back.
Bev Bernbaum

So sad. I met him at a Puddletown fly-in back when he was teaching at the University of Victoria. He was so much fun to be around. He had little challenges for higher-level dancers to do when dancing Mainstream, which were really fun. He was so full of life and positivity. The world is a little less bright now.
Paul Weiss

Sincere condolences to your club and his family.
Tom Maturo

That’s so sad! He was a charming man. He will be missed
Peter Brych

That's such a shock! Too young. I had fun talking about square dancing as category theory with him.
Moneesha Mehta

Alfonso introduced us to square dancing. This is such sad news.
Charlotte Chaffey

Alfonso encouraged interest in mathematics by running a math club at the university of Toronto. He invited me out the time he gave a talk on the mathematics of square dancing. He had the most impressive software I’ve ever seen, tracing the path of a given dancer through a sequence. Experienced dancers know that there are sequences which work for a square but which may or may not work for hexagons. Alfonso demonstrated that if there was a lift (as defined in algebraic topology) relating one path to another, then the sequence would work. What a mind we had among us.
Don St Jean


  1. Department of Mathematics, University of Toronto
  2. Toronto Star (Toronto, ON) Monday 10 May 2021, p. A12
  3. Canadian Mathematical Society Media Release, 17 Mar 2021