"I am remembering him singing the Yeti song from the Backyardigans, and pondering onks, twoks, and threeks, to go with our forks."

Friend

"Landon would greet me at the office door asking 'What have you got for me?' This was how he initiated an immediate mathematics collaboration. He said it with a twinkle in his eye, and I delighted in the conversations that followed. Landon had a way of latching on to the most wide-reaching ideas. It seemed like he was looking for some kind of miraculous, universal theorem. We called it The All Things Theorem. This theorem was a myth, but it represented Landon’s approach very well. If there were such a theorem, he was on a mission to find it.

Earlier this year, Landon and I took a long walk through San Francisco. It had been many years since grad school, so we had a lot of catching up to do. He told me about his meditation, his artificial intelligence research, and the journey of introspection that naturally came along with those pursuits. His new goal was to understand intelligence itself. In a sense, I think he was still on the same mission he had always been: to find that big idea that would shed light on all the small ones.

As he was headed home that day, Landon explained that he used ride-sharing apps to get everywhere. This was sometimes expensive, but it freed him from the tedium of memorizing maps. As long as he had his phone, he could get where he needed to go and meditate during the ride. This is how I choose to remember him: a person who cleared his mind of mundane details to make room for the eternal endeavor to understand all things. He was a remarkable person, a dear friend, and I will miss him terribly."

Dr. Peterson Trethewey

Landon Rabern

1981-2020

Landon Rabern (May 07, 1981 - October 19, 2020) was a mathematician and software engineer.

He was most well-known for his work on the Borodin-Kostochka conjecture and related topics in graph theory.

Landon was born and raised in Roseburg, Oregon. As a child he developed a deep interest in computers, machine intelligence, and science fiction. Starting in the 1980s with a Commodore 64, and making simple programs in BASIC, then Pascal, C, and so on, he taught himself how to code. In high school he programmed a chess AI (codenamed "Betsy") and experimented with using neural networks. This program has been credited as the first published chess engine able to play Fischer Random Chess (see here).

He went on to study mathematics and computer science at Washington University in St. Louis, spending a year abroad in the Netherlands, and then earning a Masters degree in Mathematics at UC Santa Barbara. After a few years working as a software engineer, and while working on graph theory "on the side" he proved a conjecture of some prominent mathematicians. He went to Arizona State to work with one of them (Hal Kierstead) and finish his PhD (see dissertation).

Landon always set his own paths in life, and ignored common societal conventions. He sought ways of expanding and sharpening his mind. He read extensively, including from cognitive science, machine learning, literature on meditation, existentialist, analytic, and eastern philosophy, and of course high-level mathematics. He practiced meditation and went on long Vipassanā retreats. He looked up to scientists that were intellectually daring and determined, such as Nicola Tesla and Paul Erdős, and would often quote Taoist and Existenialist philosophers such as Zhuangzi and Nietzsche.

While he was often content to be left alone with his computers and thoughts, he also enjoyed discussion and debate, hanging out with good friends, and getting outdoors, for example, to the beaches or forests of Oregon. Most importantly, he loved his sons, Atticus and Alfred.

Landon tended to have one foot in academia and one in industry (the former he called "thinking" the latter "making things"). He taught math as a university professor, and published numerous articles on topics in discrete mathematics and combinatorics (see his bibliography). But he also co-founded a successful software company, worked as a software engineer, and data scientist—this included jobs at artificial intelligence and social media companies.

Landon was always searching for answers. He was relentless in the pursuit of truth and knowledge. He spent the last few years of his life trying to better understand himself, his mind, and his place in the world. A few months before his death he started a second PhD, in Cognitive Science, at UC Boulder working on issues at the intersection of psychology and machine learning and returned to his childhood interest in chess programming.

This page is to remember, and to pay tribute to his life and work. (See also a notice from the American Mathematical Society here.)

"Our collaboration was highly productive and I will always cherish it for everything that Landon taught me, both about math (particularly, graph theory) and about how to conduct research. My confidence and skills grew tremendously during our peak time of collaboration, and I will always be grateful for having known and worked with him." (see full statement here)

Prof. Daniel Cranston

Jeff Malkowski

"I have two memories of Landon; the first is me finally (luckily) beating him at chess in 5th grade at Winchester Elementary, knowing that he was WAY better than me at that game and someone I regarded as extremely intelligent. The second was in high school when I observed his (far superior) programming abilities and that convinced me to pursue careers outside software engineering. I remember him as one of the smartest people from my early childhood."

"Landon and I were in the same math class our Junior year of high school in Roseburg, Oregon. Landon was quiet at first but as I got to know him he was incredibly funny and full of wit. I was struck by his profound intelligence and had troubling understanding how we were in the same class. That was the year I learned the quadratic formula, which I would have long sense forgot if not for him (I majored in English in college, leaving math behind). Landon programmed my TI-86 graphing calculator with a program that could solve the quadratic formula by inputting the values for a, b and c. It was brilliant, it worked every time, and I was truly astounded. So much so, I’ve never forgotten him, that class, or that calculator."

Kaylyn Emma

"A memory of Landon I will never forget involved his remarkable mind and his endless determination. Upon beating him in chess, Landon immediately declared that he could build a chess program that could beat me. I told him I didn't think he could do it. He went on to build that program from scratch and teach it to look ahead several moves, teaching it common opening strategies, etc. That chess program did end up defeating me. One of the most amazing things about it was he did this while he was still in high school, back in the late '90s."

Ryan Finlay

"Landon was willing to collaborate and talk with anyone who was interested in higher life purpose. Like Erdős, the mathematician he admired so much (and was proud of his Erdős Number of 2!), who always had a math problem to challenge his mentees with, Landon always had a book recommendation for people he was talking to based on their interests, and often gave them his personal copy or sent it to them right away."

Friend

"He was perhaps the epitome of a different thinker. I only needed to point Landon at a problem and he'd quickly understand it, and then quickly find novel things to do in the space---and he found a few interesting things to do on his own, too. We had a request to do something in quantum computing (although none of us in research knew anything about it), and in a few weeks Landon had not only learned the literature, but was implementing novel quantum applications. Along the way, he also started work on explaining AI systems, something that will benefit our customer, though I'm not sure who I can get do it without Landon. He was extremely bright, but nevertheless was a genuinely good person. Many smart people treat their intelligence as if it endows them with special powers to ignore or demean others, but Landon was always down-to-earth, eager to help, and humble. A genuine nice guy. I will miss him greatly."

Dr. Robert Filman

Landon's basic template for effective meditation

1: focus on the breath

2: smile and bring back focus when it strays

3: smile at your self-loathing for failing to focus

4: smile at your self-congratulation for succeeding to focus

5: smile at your self-loathing/self-congratulation for

failing/succeeding to smile at your failure/succeeding to

smile at your self-congratulation/self-loathing

6: continue to meta-smile until you forget what you were

smiling about

7: go back to the breath

Prof. Matt Jones

"I knew Landon only a few months but had come to like him very much. We had many excellent conversations ranging from computational theories of mind to metaphysics of consciousness. Our formal research focus was human learning and conceptual semantics. He was clearly driven by deep existential questions. I’m sad that I didn’t get more time to get to know him."

"A memory I have is of us playing with his electric cars, which most had been taken apart to add bigger batteries or an extra motor for something. There was one time we gutted one of my plastic boats, strapped a small rocket engine to it, and sent it skipping across the water. I remember our clubhouse code phrase was “grass grows greener over the septic tank”. To this day, I know Pi to the tenth digit because Landon went through a phase one summer where he repeated it constantly to me.

My oldest son's name is Landon. After he was born we were undecided on a name. As I thought of names, I would think of someone I knew with that name and decide against it just because of the way that person turned out or acts. When the name 'Landon' popped into my head, I immediately thought of my childhood friend Landon Rabern and knew that was going to be my son's name."

Jeff Brown

I lived with Landon during his first year of graduate school at UCSB. I met him in person for the first time when I picked him up at the Santa Barbara airport. He playfully mocked me for a while for hesitantly shaking his hand. He felt like a best friend right away. I bet everyone who knew Landon felt that way too. He was very special. Of course he was the smartest person I've ever met. We played chess together frequently and of course I rarely won or even came close. Betsy was even harder. I also remember playing a computer game he and his brother had made as kids. We would talk for hours every night about everything, mostly math and physics and computing and chess and religion and girls and philosophy. There was never a boring conversation. We raced each other at solving Rubik's cubes. This was the only competition we had that was close (perhaps also a game we invented that I think we called Reiben-Ball that involved throwing hackysacks at a bookshelf). He made me coffee every morning, I'm still addicted. He would wake me up by playing Radiohead (Kid A). His favorite book was Notes from Underground. He prided himself on eating for about $2 a day: a box of pasta and a can of tomatoes. He would do 200 pushups daily. Although he was a vegetarian, he liked to eat burnt pepperoni off a pizza. We went to a transcendental meditation class and discussed becoming Buddhists. I wish I remembered more. We grew apart when he moved away, although I always assumed we would reconnect at some point and I was looking forward to it. He had reached out a couple times over the last year but I didn't respond because I was thinking up an impressive reply and never completed it. I will always have that regret. I wish I had more time with him, he will be missed.

Dr. Jarrod Pickens

landon taught me that love could be kind and uplifting again; he showed me what it truly felt like to be seen, in a way i never realized i hadn't been before, for all of me. he always encouraged, often demanded, me to be even more open, compassionate than i already thought i was, to meditate, to push my boundaries in every way possible, to always be learning and growing. all he wanted was to be accepted as he was, feel safe, be loved, and to love. he changed me forever, made me look at people, humanity, much more deeply, and redouble my efforts to create a better world. he made me a better mom, a better human every day. he was a gift most of us didn't know how to fully appreciate while we had him. i imagine he’s up there levitating in the clouds, smiling from all his cells inside out, one of his favorite meditations. i miss him, and those piercing blue eyes that saw everything, his love for his boys, and will remember him in every forest, cold beach, anytime i see eggnog, heavy cream, tillamook cheese, or umpqua dairy chocolate milk, a game of chess or Set, philosophy or math books, and so many more moments. I know i will see him in another life to come.

bulbul gupta

Please send further memories or photos to: brian.rabern@gmail.com

A few of his most important articles in mathematics are the following:

- “∆-Critical graphs with small high vertex cliques”, Journal of Combinatorial Theory, 2012.
- “Planar graphs are 9/2-colorable”, Journal of Combinatorial Theory (2018) (with D. Cranston)
- “Improved lower bounds on the number of edges in list critical and online list critical graphs”, Journal of Combinatorial Theory, 2020. (with H. Kierstead)

He also published work in philosophical logic including these:

- “A simple solution to the hardest logic puzzle ever”, Analysis, 2008.
- "Dangerous reference graphs and semantic paradoxes", Journal of Philosophical Logic, 2012.

See a full list of publications here.

The mathematical problem that occupied him for many years was the Borodin-Kostochka conjecture, on which he wrote his PhD dissertation. A "graph" is a collection of nodes, some of which are connected by edges. Graph coloring assigns a color to each node of a network so that any two nodes linked by an edge get different colors. It is easy to find a graph coloring: simply give each node its own color. Things get interesting when we ask how few different colors we can use. If D denotes the maximum number of nodes adjacent to any node in the graph, then it is simple to find a coloring that uses at most D+1 colors. The clique number of a graph is the largest size of a set of nodes that are pairwise linked by edges. Each coloring must use at least as many colors as the clique number, since all nodes in a clique must get distinct colors. In 1941, Brooks showed that every graph has a coloring with at most D colors, provided that D is at least 3, and that the clique number of G is at most D. In 1977, Borodin and Kostochka conjectured that this upper bound could be improved: If G has maximum degree D at least 9, and has clique number at most D-1, then G has a coloring with at most D-1 colors. Landon helped prove various partial results toward the conjecture.

"We are dissociated identities of mind-at-large in a shared dream. When I die, I will rejoin the stream of Mind. My death is just the dissolution of the dissociated complex of Mind that is me. At least, that's the current idea I am playing with. I find it useful to take on an idea for real, live it, and see how it goes -- a kind of 'sandboxing'."