## Memories of Oded Schramm

### September 8, 2008

To our profound sadness and shock, our colleague and friend, Oded Schramm, died in a tragic hiking accident on September 1, 2008.

Oded was a towering figure, an extraordinary mathematician, widely considered to be the most influential probabilist in the world. His revolutionary work transformed our understanding of critical processes in two dimensions through his introduction of the Stochastic Loewner evolution, tying probability theory to complex analysis in a completely novel way. He also made fundamental contributions to circle packings, random spanning trees, percolation, noise sensitivity of Boolean functions, random permutations and metric geometry.

Oded was a remarkable individual: always calm, humble, generous with his insights and ideas, the best collaborator one could hope for and the person who could always be relied upon. Our heart is with Oded’s family. He will be sorely missed by all who knew him.

Due to the outpouring of emotion at the news of Oded’s untimely death, we created the **Oded Schramm Memorial Page** and this blog is to allow his friends to share their photographs and memories of him, as well as their reactions to the news. (Some of these posts were sent to us in email before we had the blog set up. See also Terry Tao’s blog and Gil Kalai’s blog.)

Sep. 7, 2008

Oded’s sudden disappearance was unbelievable. How could this wonderful person who could do anything just vanish? Would he really not show up in his office any more with his customary good cheer and ready smile, open to any question? How could such an experienced hiker, who was always prepared for any contingency, have fallen? But everyone acted as though he really was dead, so he must be.

I first met Oded when I went to Ann Arbor for a Nevanlinna Colloquium in 1993, which that year was devoted mainly to circle packing. That was not my area at all, but it looked beautiful to me, so I went to learn about it. I quickly realized from the talks that Oded was the champion circle packer. Someone had mentioned a probabilistic theorem of Oded’s, so that gave me an opportunity to introduce myself to Oded. He said the result wasn’t very significant and not really worth discussing, but agreed after persuasion to go to a coffee house to tell me about it.

Some day I had hoped to work with Oded in circle packing, but Itai Benjamini managed to get Oded interested in probability, which was even better for me. In 1996-97, I spent a wonderful year in Jerusalem, where I worked with Yuval Peres. Oded and Itai often came to visit to discuss our common projects. It was so good that after the year was up, I managed to spend 3 more months visiting Oded and Itai at the Weizmann Institute.

To me, Oded’s most distinctive mathematical talent was his extraordinary clarity of thought, which led to dazzling proofs and results. Technical difficulties did not obscure his vision. Indeed, they often melted away under his gaze. At one point when the four of us were working on uniform spanning forests, Oded came up with a brilliant new application of the Mass-Transport Principle. We weren’t sure it was kosher, and I still recall Yuval asking me if I believed it, saying that it seemed to be “smoke and mirrors”. However, when Oded explained it again, the smoke vanished.

As everyone who encountered Oded knows, he combined extreme mathematical talent with generosity, humility, and gentleness. For example, in 1999, after deciding to move later that year to Microsoft Research, he wrote me an email concerning an extended visit I could make at his new location. Then he wrote: “P.S. By the way, I’ve made some mathematical progress, which might interest you. I believe that assuming the conformal invariance of percolation, it can be proven that the Loewner evolution with constant 6 describes the scaling limit of the percolation boundary curve. From this, one can derive Cardy’s formula and higher order analogues of it. With constant 8 the Loewner evolution describes the Peano curve, …” This was truly amazing news, yet he was so humble about it. I responded with great enthusiasm, of course, but he simply wrote “Thanks for the encouragements regarding the new results. I’m quite excited myself. Too bad it’s all conditioned on a conjecture.” It was all totally natural, as always with Oded.

All who knew Oded loved him. The memorial yesterday showed this, as people recounted stories and recalled Oded’s being.

In reading the outpouring of grief occasioned by our loss, I learned a new phrase: Yehi zichro baruch — may his memory be a blessing. I agree.

I remember Oded from when I was a little girl. He would come over to my grandma’s in Jerusalem with Vivit (this was back before they were married) and they would help my grandma cook, both with their backs to me by the kitchen sink, chopping vegetables, while I plopped around begging for some attention. Growing up I would hear stories of Oded sky diving and climbing mountains, and I was always in awe of his sense for nature and adventure.

My favorite moment spent with Vivit and Oded was when I came to visit them in Seattle in 2000. We sat in the living room after Tselil and Pele went to sleep and I entertained us all by doing impersonations of our family. I had them both laughing for about an hour.

My last memory of Oded was from this past December when I had the pleasure of having the Schramm’s visit me and baby Talyah while they were in Israel. As Talyah, my five month old daughter at the time, made goo goo and ga ga noises, Oded pointed out that she was imitating the music of my voice. Her was right. I hadn’t noticed until he said something.

When I heard the news on Tuesday night, Israel time, I couldn’t believe such a loving human being could vanish so abruptly without any explanation. Oded was the pride of the family, though he hardly spoke of his accomplishments…He didn’t need to. We were on to him. It is a tragedy that Oded is no longer with us. We all loved him and will continue to love him. He was a good person. I am sad beyond words that he is gone and that I cannot be here with you all right now.

Karine Koret (Oded’s niece)

David:

This is simply terrible. Do you have time to chat?

I am very sad. Oded was a supernice guy!

Darko

I learnt about Oded’s death from Itai, and I simply didn’t believe, had to call Yuval to check, and it still took a few more hours. Then I felt that everything became much darker than before. A huge loss for mathematics, for his family, for all of us. Oded was the main example for me how mathematics should be done and lived. Even on a practical level: whenever I’m in trouble, about math or many other things, one of the first questions I ask myself is what Oded would do now. I hope I will succeed more often…

It might be more about myself than Oded, but at least it shows how much I feel I owe him: here is a dream that I had a few weeks ago, after I finished my postdoc at Microsoft, before having started my semester at MSRI in Berkeley. I wanted to write him the dream, but never did, sadly.

In my dream, Oded told me that, strangely :-), there are still a lot of things in the world that science cannot explain. In Berkeley there is a repository of 101 such things, and he accidentally has the code that opens this place. And he gave the code to me. When I arrived in Berkeley, I went to the place, and experienced the first of the 101 unexplained things. It was a sound that made me fly. The sound not just made me feel like I was spinning and flying, but I actually did spin and fly, and there was also some dark blueish light. The whole thing was simple and beautiful, then I walked out of the room, then woke up, and was very grateful to Oded.

Oded had a strong and unique mathematical voice. It was highly aesthetic and lucid, deep yet diverse. Oded had a very clear geometric vision. His work was extremely creative, beautiful, and original, always striving for and attaining perfection.

But for me, he was first and foremost a true and very supportive friend. Oded was extremely gentle, sensitive and generous. He was a caring family man. I loved him very much. After many years of close friendship, I already miss him badly.

Oded Schramm was one of the most original and creative mathematicians of our period. His approach was relentlessly elementary; it seemed to be more trouble for him to learn a subject than to invent one. He received his Ph.D. in topology but his impact was in the interface between complex analysis and probability, subjects in which he was self taught. Because he was self-taught, he organized these subjects in a unique fashion and would often see things immediately that other mathematicians could only understand through difficult calculations. Oded was the inventor of a process SLE , Stochastic Loewner Evolution – later renamed Schramm Loewner evolution, which transforms a random growth process into a random differential equation. (Loewner studied the same differential equation in 1923 but without the ingredient of randomness.) Some of the most interesting random processes in the plane, for example “percolation” – in which one studies whether or not random blotches of ink (or crude oil) connect to each other, exhibit a kind of scale invariance called conformal invariance. Schramm used SLE to show that such process could be understood in terms of a much simpler process of a particle propagating randomly along a line ( “one dimensional Brownian motion”). This work has led to a decade of renewed interaction between mathematics and physics that can be compared in scope and importance to the interaction centered around “string theory”.

In stark contrast to String theory, which incorporates at its outset one hundred and twenty years of accumulated knowledge about representation theory and algebraic geometry, Schramm’s mathematics was largely invented from scratch. It is an amazing and wonderful fact that the creative mind can still find such absolute gems of pure thought. A much simpler example of this intellectual fertility is seen in a recent idea of Schramm and his collaborators at Microsoft Research. The idea is that many simple games, like “Hex”, take on new interest if the “order- of – play” does not strictly alternate but instead is chosen at each turn by the flip of a fair coin. The surprising conclusion is that with this “probabilistic” rule certain games which previously defied exact analysis can now be solved; demonstrating that “random may be easier than deterministic”.

Oded Schramm died in a fall while climbing in his beloved Cascade Mountains. He was hiking and scrambling by himself and the exact cause of the accident may never be known. He was experienced in these mountains, having recently climbed Rainier, Shuksan, Stuart, Adams, Tahoma, and many lesser summits. He was known to climb with caution and the site of the fall on Guye peak was not an unusually dangerous place. The accident seems difficult to understand.

Oded was famously relaxed and humble. While hiking with Oded in 2001 I brought up the “Tech Crash” . Oded found nothing to be upset about. I asked him if he did not regret the fact that he would now not be getting rich on stock options. He could think of nothing he would do with the money anyway. When I suggested in desperation that he could have bought a small tropical island, his reply was that he would rather own a small glacier – and on second thought he hardly ever saw people on these little glaciers anyway so there was no need to own it as long as he could visit it whenever he wished. This is exactly what he did.

Dear Oded,

I knew little of you, but what I knew I admired with all my heart. Barely two weeks ago – suddenly it seems it was ages ago now – we did

a bicycle ride in west Seattle, along the beach. What an amazing day it was! As usual you were radiating with energy, tranquility, easy-going ness. You were such an inspirational person too: when one spoke to you, one got the feeling that it was possible to achieve anything.

So how to reconcile that feeling of pure vitality, of pure strength and energy, with the fact that you are no longer with us? I’m still

struggling with it.

As the shock of the dreadful news slowly sank in and gave way to disbelief and then sorrow, another emotion then made its way to me. It

was the feeling of how grateful I was to have known you, the privilege of having been able to exchange some ideas with you, and experiencing

the luminosity of your person.

To paraphrase something I read: Oded, you had the generosity of the heart and the intelligence of the mind. But much more importantly, you had the intelligence of the heart and the generosity of the mind.

Thank you for all you gave to me, and to us.

Nathanael

A couple years ago, during one of my visits to Microsoft, Oded took several of us from the Theory Group on a day hike in the Cascades. It was a mountain Oded had already conquered, and Yuval asked him if he wouldn’t be bored hiking it again, to which Oded replied, he’d never before climbed it in summer, only in winter!

Before we started off, just for the challenge, Oded loaded up his own pack with a few extra gallons of water beyond what we needed. When we got to the top, he refilled everyone’s bottles, and then – mission accomplished – simply dumped out the rest of the water he’d carried all that way. It was so much like Oded – in math as in hiking, he was able to do more, see farther and deeper than the rest of us, but he was always so humble and matter-of-fact about it.

Oded was of course technically amazingly strong in his mathematics and was able to solve problems that the rest of us were stuck on. But the most striking feature was probably his ability to come up with original approaches to these problems. And sometimes, if one approach did not work out, to completely change his own way to look at the problem and to manage to find a completely different route to the solution than the rest of us would have thought of. He was incredibly original and creative. His voice was truly singular and different.

This creativity also often led to really “beautiful mathematics”. For example, the SLE processes (Schramm-Loewner Evolution) that he invented (and SLE is just one example among many other very nice things he did) are not only the right tool and object that has transformed the way mathematicians and physicists understand phase transitions and interfaces in planar systems; they are extremely beautiful mathematical objects. All of us had the same reaction when reading and learning to know SLE from him: “This is just so nice!”

In this case, part of this beauty comes from the fact that SLE ties two fundamental fields of mathematics (probability and complex numbers) at their very roots. Simple, elegant, beautiful and fruitful! And accessible and understandable by any mathematician.

One thing that I heard on several occasions, and that I also experienced myself: Oded was not “trained” as a probabilist (he did his PhD under the supervision of Thurston on more topological questions). So, he did not learn probability theory in classes like the rest of us, who were taught about the theory of stochastic calculus that has been developed throughout the second half of the 20th century. However, he knew it all, not by reading books, but just by himself. As a result, on many occasions (and this is in fact not restricted to probability theory), when he was needing some technical intermediate statement while writing up the proof of some result he was deriving, he was looking in the literature (thinking “this looks simple, it must have been proved somewhere”) to give the appropriate reference and credit and was surprised to find out that this was new stuff. Well, this was not a problem; he instantaneously produced a proof of his own. Sometimes, he found a reference but did not like the way it was proved there, and produced a much more elegant and transparent way to justify it. This happened even for very classical results that had been taught to students many times. One can sum this up in the following way (this image I heard from Mike Freedman): Most of us climb on the top of the mountain of knowledge that all others before us have built, and our contribution is to try to add up a couple of bricks to make it grow. Other truly exceptional people like Oded are able to build up entire mountains of their own, that are beautiful, harmonious, and also often higher! And the view from the top is much clearer.

He was so often way ahead of all of us in his mathematics, but he never thought of mathematics in a competitive way. Just happy to explain and share his ideas. And also simply happy to learn about the ideas of others! I will miss so badly these frequent moments, when just before starting to explain something to you (in mathematics or on other subjects), he looks down, concentrates for a quarter of a second before starting to speak. It looked like he had to slow down his brain in order to tune its speed to that at which words could come out of his mouth. And then, his nice singing voice and accent. These were truly magic instants that so many of us experienced.

It was wonderful to do whatever activity with him. He was a really balanced human being, caring and calm. Smiling sparkling eyes, smiling face, making funny jokes. Often walking or standing with his hands in his pockets. And he was in everyday life like he was in mathematics. With a lucid and simple voice of his own. Society could have its codes (dresscodes, money etc.) but he was not considering them as such. He would on his own choose what to do, and how to behave, independently of what society would push him to do. And his choice would turn out to be simply the right one. One way to phrase this could be to say that he managed to keep his child’s eye about everything around him: Trying to discover, understand and analyse the world, without the compromises and the disillusioned way of thinking that often come when one becomes an “adult”. In a way, he remained “pure”. It looked like he was enjoying life and its simple things, such as playing real soccer or fussball (baby-foot in french), Sokoban (I remember that his eyes became even sparklier when he saw that I identified a Sokoban window on his computer screen: “Are into Sokoban too?”).

All his professional decisions were exemplary, simple and right. It is therefore no surprise that he was truly loved by our entire math community in the world. He was not only doing beautiful and singular mathematics, but also behaving accordingly, being generous with ideas, with time and energy (if you needed a hand to help move something, or a personal tuition about something easy in maths, he would be just glad to help out). Really the exact opposite of the often-used egocentric image of a great mathematician. The relation between mathematicians working in a given field is something peculiar. We are spread over the world, sometimes we are the only specialist of our subject in town. We are spending most of ours days working on our own in our offices. We do not meet that often at conferences (and some of us – Oded was one of them — are in fact reluctant to travel), yet we feel close because we share a lot: We like the same things and have the same emotions when we read mathematics that we like. We also generally share the same values that led us to choose this profession, and which do not always correspond to today’s society’s general trends. In both these aspects, Oded Schramm was the leading figure of our community. Throughout the world, the news of his sudden death was a shock that threw us all in deep pain.

I miss him badly, and being a probabilist does not help in any way to accept such tragic events.

As so many others, I feel so privileged to have met and interacted with such a wondeful person.

Dear friends,

Mazi and I were devasteded by the terrible news. Our hearts and thoughts are with Avivit, Tselil and Pele. We cherish the good memories with Oded, Avivit and the kids. We remember Oded’s days as a student in Jerusalem, walking together in the La Jolla beach with baby-Tselil, the wonderful summers in Seattle, and the recent winters in Jerusalem. I remember the fun years of working with Oded and Itai in Rehovot and Jerusalem.

Let me say a few words about Oded. Oded was a great person and a great mathematician. He was very powerful, very clear, and very original. He had clear views on the large picture as well as on the difficulties along the way. And he had the power, persistence and patience to deal with the big problems and the little details. He always wanted to understand matters completely and from scratch, and then to understand them even better and better. Oded was a modest, a little shy person, and a very good friend. Oded was my first M Sc student and his amazing successes made me especially proud and happy.

This is a time of sorrow but I cannot avoid thinking about Oded’s beautiful smile, and the beautiful smiles of Avivit, Tselil and Pele.

Yehi Zichro Baruch.

Gil Kalai

I am not sure if it is appropriate but let me mention a few anecdotes

1) I visited Oded in Princeton in 1988 and stayed with Oded and Avivit for a few days. These were the days of the Seoul Olympics and I was very excited to see in real time Ben Johnson 100 meter 9.79 record and the next day his disqualification. Avivit and Oded (both practice sport seriously) were not very interested and they found my own interest rather amusing. For the record: At that time Oded was not interested in unicycles.

2) One thing to remember from my visits to Rehovot to work with the amazing Oded and Itai team was the randomized coin-operated coffee machine in the W.I. math building that was giving an unexpected type of coffee every time.

3) I, and many people, had wonderful summers in Seattle visiting MS. Playing “fuss ball” usually after lunch was not at the bottom of the priorities, and I remember playing with the Schramms the following new version: Four players (I think they were Oded, Tselil, Pele, amd me) and two teams: the 4 right hands are playing against the 4 left hands.

4) Returning from a beautiful hike toward a nice mexican diner we had a serious discussion if it is possible to drive a car with one’s shoulders.

5) We had lovely winter/Chanukah meetings last few winters in Jerusalem, and my last memory is the two families playing bowling together.

I have only known Oded personally for a very short while, since he joined the editorial board at JAMS earlier this year, but I had of course known and admired his work on SLE for many years (here at UCLA we ran a successful summer school on this beautiful topic). So I unfortunately do not have many memories of Oded to share, except for this one: when I contacted Oded to ask him to join JAMS’s editorial board, he asked about the workload, which I had to admit was non-trivial. And of course, Oded was an extremely busy person, with many other commitments, mathematical and otherwise. But, he knew the work of a JAMS editor was important, and he signed on nevertheless. And during our brief tenure together, he was extremely conscientious in his duties, and even read carefully several of the papers that were being handled by the rest of us. I can tell he put his heart into everything he did, and JAMS (and the mathematical community in general) is much poorer for his absence.

I first met Oded when I visited him and Itai at the

Weizmann institute as a grad student. Both in our

mathematical conversations and also at my dinner with his

family I experienced a level of harmony and calm that I

have never felt before.

I only learned about many of his beautiful mathematical

results later. For him it was not enough to solve a

mathematical problem — the solution had to be so

transparent and clear that one would think that proofs

cannot even go otherwise. One of the main goals of

mathematics is not to solve the problems but to create a

language which makes solving the problems easier. Oded was

amazing at this; the language that he created was not only

powerful but simple and beautiful as well. An example that

I just heard this summer is his recent definition of the

state space for the full limit of planar percolation via a

generalization of Dedekind cuts.

He made my mathematical world, probability theory, which

still in many ways a wild frontier, a much better place. He

did this not just by conquering it but by highlighting and

showcasing its inner beauty.

There was a very special atmosphere to conversations with

Oded — he had a calming presence and he also could make

you feel at ease. His personality made you forget natural

obstacles in conversation, like the competitive edge of

mathematics (and the associated fears) or just the mere

fact that you were talking to someone so quick and smart.

He always was attentive and personal — nowadays, when

“thank you” is often said in a way that it sounds like “go

to hell” — his voice was so warm and melodious, so

welcoming. He was personally very attentive and caring:

when I sent him a photo with my first child he pointed out

that I looked very tired but very happy; he got the perfect

presents for my kids when he visited. I felt this

attentiveness even when he gently chided me for not knowing

for his preference for sodas; he would have known mine.

He had the most beautiful light blue eyes. They had the

sharp clarity of water — they always reminded me of the

clarity and transparency of his ideas. He often wore a

matching light blue fleece sweater. Occasionally, he wore a

red sweater with the pink panther, so edgy and original,

yet somehow perfectly right.

He was so fond of his family, he would avoid traveling just

so that he could stay with them. For a long time the main

picture of him on his website was decorated by his

children, and he had Tselil’s literary works more

prominently displayed than his own papers. He picked up

unicycling with Pele, and they traveled to the world

championships. He was so modest that I had to specifically

ask to learn that Pele won in a large number of events. The

dinners with his family were always the highlight of my

visits to Seattle.

With Oded, I lost a good friend and mentor, and I lost an

anchor, a connection to a more perfect world. There is a

great Oded-shaped hole out there now that will never be

mended. Yet, for me he will be always present, in all that

he had taught me, and also, when (as in a previous post) I

ask myself as usual “what would Oded do in this

situation?”.

It is impossible to describe the shock and sadness caused by the sad news about Oded’s accident. I had the privilege to work in the same research group with Oded for 7 years. How can it be that this wonderful person, great colleague and outstanding mathematician is no more with us?

Members of the Executive Committee of the International Mathematical Union have sent me many remarks about their memories of Oded, about their appreciation of his mathematics, and about their deep sorrow, which I am now conveying to his family and friends. As probably in many places in the world, the sad news spread in the Hungarian probability community quickly, with the feeling that one of the greatest personalities in probability was lost.

When joining Microsoft, it was an important factor in my decision that Oded too was coming. At that time, I only knew his mathematical results; later I learned that to know him as a person was equally important.

Thinking of Oded, two memories come most forcefully to mind: his shy, but very friendly smile, and the very deep mathematical remarks he made in connection with many topics. Not only had he the most general and beautiful results concerning generalizations of Koebe’s touching circle representation and about caging of the egg, but to listen to his comments about alternatives to prove these results was most enlightening. This brings up the memory of sitting around in the cafeteria, with the lunch having been finished for long, and listening to Oded’s quiet explanations.

Somehow, we never wrote a joint paper, but there were many topics of joint interest, and it should have happened sooner or later, but for the cruel fate. A few years ago, Kamal Jain raised an interesting problem in flow theory, where the three of us began to think about. Oded came up with an amazingly beautiful proof idea, which we could not finish, but every few months I come back to thinking that a successful completion should be close.

Oded, with Itai Benjamini, were perhaps the first to define convergent sequences of graphs and to describe their limits, a topic on which I was working a lot in the last years. Recently he had several results on this subject that were so important Gabor Elek and I organized a seminar to go through them. I was looking forward to meeting him and discussing these results with him, pressing him for further insights and for his further modest and quiet comments on the methods and ideas that would have meant so much for us.

With Kati and our children, we also want to express our deepest sympathies and condolences to Oded’s family. Memories of joint picnics and excursions come to mind. In our thoughts, we are all with you.

Laci Lovasz

Let’s honor Oded’s memory by exploring his great ideas. Of course many of us would do that anyway, but I mean some extra time. The mention of his paper of Itai Benjamini reminded me that that work has a great definition that has been influential in classical geometry as well as in statistical mechanics and probability. Bowen and Radin picked up on it in the context of geometry. Namely, instead of looking at individual packings or coverings of a space by shapes for the problem of maximizing or minimizing density, you should look at translation-invariant ensembles of packings. This technique greatly clarifies packings in hyperbolic space and it was used to to solve my dad’s conjecture on completely saturated packings.

I only knew Oded slightly even though I had one minor joint paper with him. He was a guy with a thousand friends and (as far as I know) no enemies at all. Certainly I was one of his thousand friends. His death bothers me more than I might have expected.

Although it does not look possible today, up until the early 1990′s there were few contacts, mathematically and otherwise, between the probabilists in Haifa and in

Jerusalem/Rehovot (the arrival of Yuval Peres and his collaborations changed this). So, while “growing up” I heard a few times about Oded but the first time I actually met him was I believe in the Israel Mathematical Union annual conference that took place in Haifa in 1999. Typically, the audience in parallel sessions of the conference consists of the speakers, and maybe a few locals. In that year, Oded came and described the Loewner equation from complex analysis, and some conjectured links to percolation. I believe this was one of the, if not the, first time he spoke publicly about SLE, to an audience of maybe 8 attendees. I am not sure how many

really appreciated the revolution in probability theory that was about to come out of this (Oded’s humble delivery surely was not giving any hint of this). I do recall

that coming out of the lecture, Dima Ioffe simply told me “wow”!

And then, a few years ago, as a hobby, Oded solved a conjecture of Aldous concerning the random walk of random transposition. Along the way, he gave a wonderful proof of a conjecture of Vershik that

Diaconis, Mayer-Wolf, Zerner and myself had earlier proved. Needless to say, Oded’s proof is nicer, and more general than ours, and truly probabilistic. Other developments follow from this (Oded again was key in these developments, and his mathematical presence will be sorely missed).

Only in the last couple of years I had the privilege

of getting to know a bit better Oded the person. His death saddened me a lot. His smile and quiet voice

will be sorely missed. Yehi Zichro Baruch.

It was a terrible shock to learn about Oded’s passing last week. Oded was someone very important to me. I met him two years ago when we started to work together with Gabor Pete. Later I had the chance to visit him for two summers as an intern. It was an amazing experience for me to closely interact with such a deep mathematician. He was so humble and gentle. Working with him was particularly pleasant, he was always ready to listen to people’s ideas and more striking, he had the ability to make you feel that his numerous great insights are also somewhat yours.

I had a great admiration for him, for his depth thinking, but also for his modesty and his kindness. He had and will continue to have a great influence on me. I will miss him.

I remember that when I learned about Oded’s death my first reaction was fierce anger and disbelief. I couldn’t accept that the laws of the universe, or mathematics (or if there is any higher entity behind them, then him) allowed this to happen. It took me a week until my anger transformed into sorrow.

Oded was a college of mine throughout my Post-doc years at Microsoft and I saw him on a daily basis. Even though he was already a world famous mathematician, he was very accessible for everybody. He was ready to teach me interesting mathematics whenever I wanted to learn and I never felt any touch of authority in his behavior. He had the enthusiasm of a child in every aspects of life and he was also the prototype of person you want to hang out with: easy going, relaxed and a bit of a teenager too. We had a lot of fun playing fussball (table football) together. I and David (Wilson) and Scott (Sheffield) were good :-) but Oded was the best. I will never forget his quick shots from the first line. My wife’s favorite story about Oded (and fussball) is when she joined us for a quick game after lunch but she had never played before. It was obvious that the one who teams up with her was going to lose. Oded was the one who took on the challenge and, it is unbelievable, but they won!

One of my favorite stories about Oded is this: At some point there was an interesting (but extremely hard) problem around in the theory group and some of us (including me and Oded) were immersed into it for a few days. I remember Oded coming into my office one morning wanting to share some of his ideas with me about the problem. We went to the lounge and Oded told me not only one but three beautiful approaches.

I felt that I learned much more from these excellent ideas than he would have just solved the problem.

Mathematics, for me, is now a little bit colder place without Oded, but I am extremely thankful for having known him. His life sets an example for me in many ways.

The unbelievable news left us shocked and devestated, sad and pensive.

I have known Oded since he was a young kid – only a few years younger than me, in Israel.

In fact ours is a third generation friendship. Our grandparents, Max Schramm and Hans Yosef Plonsker were friends in Germany, I believe they studied medicine together in Berlin… both became zionist and emigrated to Israel, where Oded’s parents, Miki and Hanna became best of friends with my parents, Meir and Rachel Avissara. and I mean best friends. I can say I had spent more time in my childhood on trips and hikes and mushrooms pickings and beach outings with the Scramms, than I did with my real blood relative uncles. Oded’s father, Miki was a biochemistry professor and head of the Department in the Hebrew University, an amazing creative researcher who at times it was said about him that he had done to biochemistry what the six day war had done to Israel. But we knew him as one of the sweetest childlike-naiv most attentive and most fun to talk to for a child or a grown up. Hana was tart and sharp tongued and smart- a subject for adoration and imitation. Moti and Oded – like siblings in the good times. No fights, just mutual enjoyment. Together we felt like a dream team family friends and we loved them as we loved no others. When I read what is written about Oded above, I do see the apple has not fallen far from the tree. He reminds me of his father in terms of kindness and genius combined. He may have surpassed the record his father set as being the youngest professor at his time. Back to reminiscing…

It was only natural that the first trip my parents ever took abroad- they took in combination with the Schramms who were then going to Norway and off to their legendary sabaticles in Seattle, the subject of so many stories I heard in my childhood in Israel.

I flew with Hana and Oded, and shared a room with him in the hotel. A pillow fight ensued and some of the pillows ended up flying through the veiled window. I will always cherish our endless loud laughs when they disappeared in front of our surprised eyes.

Throughout the years we followed with amazement, but not with surprise, the meteoric rise of Oded. When he was in Princeton we moved to the U.S.A, finally finding out about these places that stood behing the Schramms’ stories: Mount Rainier, Seattle, Abernathi… we visited his parents in Bethesda…

We have met Oded now only on family occasion. Some happy, some sad. Miki passed away 2002, our mothers – Hana and Rachel, within a month difference in 2003. It is devestating to think about their departing. It is beyond horrific and unfair to include Oded now in the list of the departed. I certainly hope there are mountains in heaven, lakes and reflections as they all so enjoyed when they were with us.

Dear Oded,

I have never had a chance to meet you..but thank you very much for too many things that I learned from your emails..Some times I recieved my answer after just 15-20 minutes..

At Oded’s Memorial Service, and now this blog, the majority of the memories are from the mathematics community. I deviate from this majority as my family and I are the next door neighbors to Oded, Avivit, Tselil and Pele. Over the years, Oded and I would talk about Pele’s unicycling, Tselil’s school and the challenges of taking care of a house. My wife, Mary, and Avivit are very good friends and presently we are sharing a vegatable garden in our yard. Mary was with Avivit at the search site when the terrible news arrived from the rescuers that Oded had not survived the fall. I received the call shortly after and was overcome with a profound sense of loss. I cannot claim that Oded and I were best of friends, but the interaction was always very friendly and we always found something to talk about.

Over the past 8 months I was constructing an addition on my garage and occasionally Oded would come over to see what I was doing. As I would explain, he would listen with intensity. He would then commence with a series of questions as he would “build” the project in his mind until eventually he would lead me into responding, “Well, that will be the next thing I will be doing”. It appeared to me that, not unlike the way Oded did his mathematics, he was always interested in learning how something was “constructed”, and quickly understood your explanation and would take it to the next step.

The words that have been used in this blog to describe Oded echo my experience with him also. I always had the feeling that Oded was on the lookout for the next great adventure. As we observed his learning to ride the unicycle(s) with Pele, saw him through the living room window tapping on his laptop, doodling on a scratch pad, or leaving with skis on the car rack, I would think to myself, “Off goes Oded again!” I admired his energy, and thirst for knowledge. Until his tragic death, I did not know much about the mathematician. In reading about his accomplishments, I am awestruck, and wish I had taken the time to learn more about him earlier…not that it would have made any difference, Oded was still Oded, a father to two great kids, a husband to a wonderful wife and a great guy that I’m grateful to have known.

Stephen Compton

Sammamish, WA. USA

Itai Benjamini called me up to tell me about Oded’s death. Having been sleeping, it was very difficult to understand this information and I sat on our living room couch for hours afterwards absorbing this tragic news.

I first met Oded at a conference in Israel in 1996 and then met him at various meetings afterward through the years. Later on, in 2004 and afterwards, I had the wonderful opportunity to work with him. For me, it was an amazing honor and privilege to have had this opportunity. It was also great to be able to discuss various aspects of mathematics with him. He was clearly a very unique person, brilliant, kind and with great modesty. I will miss him in many different ways, one being that I always felt welcome to send him various mathematical questions and could always count on answers.

I find that the combination of his brilliant mind and his extremely kind person is such a profound loss to the probability community. I am afraid that things will now be very much different without him.

Jeff Steif

My personal acquaintance with Oded could not be considered very deep. I met him during several visits I made to Microsoft, and occasionally our paths crossed at other times in Berkeley, the Weizmann Institute, the Hebrew University and at various conferences we both attended. One time I had the very pleasant surprise of meeting him and his family on a plane while flying from Israel to the U.S., and he entertained me through part of the flight by telling me about his latest work on Boolean functions with his characteristic humility.

Despite the brevity of our acquaintance, even our passing encounters left a huge impression on me. You only needed to talk to Oded for a few minutes to be immediately struck by what a kind man he was, utterly brilliant but also completely selfless, at ease with himself and devoid of any urge for boasting or self-aggrandizement. I remember many times thinking what an inspiring person he was and that if there is any one person I could aspire to be more like, both mathematically and personally, it was him. When I received an email from him one time asking me to referee a paper I felt tremendously honored. Similarly, when I needed a letter of reference for a job application I felt very comfortable asking him, despite our limited acquaintance and that my field of expertise is quite different than his – it was clear to me that he would be the best referee of my work possible. Indeed he agreed immediately with his characteristic graciousness and warmth. This was a few days after meeting him in Berkeley when we had a funny conversation in which I told him some crazy ideas I had for a mechanical invention relating to bicycles, and he replied with a similarly crazy idea for a new extreme sport he imagined called “river surfing”. Even this short and completely unserious conversation left me feeling inspired and led me to write to him a few days later with my much more serious request. He was truly a wonderful person and we will all miss him sorely.

Dan Romik

Jerusalem

I am very sadness to hear this accident. Professor Schramm once kindly gave me some suggestons to check my paper after I sent it to him.

I am very grateful to this website giving me a chance to share the photoes and other memorials. From this I understand that Professor Schramm is a great mathematician.

Wish Professor Schramm can be free to his love.

Qingyang

Hi Itai,

I just learnt the terrible news about Oded. Since you knew him so well, I would like to tell you how shocked and sad it makes me. Things like this also makes one so painfully aware how vulnerable and mortal we all are.

From the few times I met Oded in person, he struck me as a truly nice and generous person.

At a time like this, one could feel sorry that probability theory loses such an outstanding mind, but that feels like a small thing compared to how sorry I feel for Oded himself and the ones closest to him.

Best regards

Johan

As for me, SLE is the probability theory of the 21 century, thus, Oded is the first probabilist of the 21 century.

After our pleasant meeting in Jerusalem (Dec 2007) I got his email with a simple and elegant solution of a question open for me several years. Here is the question.

The random set of zeros of a Brownian motion started at time 0 from a point x has a distribution that depends on x; however, treated up to equivalence (mutual absolute continuity) it does not depend on x, as long as x does not vanish (which is assumed). I mean zeros on the time interval [0,1], not [0,infinity).

Consider the union of two independent copies of this random set. (They do not intersect, of course.) The distribution of this union (treated up to equivalence, still), does it differ from the distribution of each set?

His answer (no, it does not differ) is displayed below. Thank you, Oded!

From: Oded Schramm

To: "tsirel@math.tau.ac.il"

Date: Mon, 24 Dec 2007 04:14:22 -0800

Subject: absolute continuity

Hi Boris,

I think I have an answer to your absolute continuity question - I hope I did not misunderstand

the problem. Suppose you start a planar Brownian motions X(t) at some point X(0) that is not

on the imaginary line. Let A be the set of times in [0,1] at which Re(X)=0 and let B be the

set of times in [0,1] at which Re(X)Im(X)=0. The question is if the law of A and the law of B

are mutually absolutely continuous.

I believe that if X(0)=0, then it should be easy to see that they are singular, but this is

not your question, I think. Likewise, we should have singularity if the time interval is [0,infty),

instead of [0,1].

Note that a.s. X[0,1] is a compact set that does not contain 0.

Let tau_0 be the first time such that X meets the coordinate axes. Inductively, let sigma_j

be the first time t>tau_j such that |Re(X)|=|Im(X)|, and let tau_{j+1} be the

first time t> sigma_j for which X(t) is on the coordinate axes. Then a.s. lim_j tau_j =\infty.

That is, there is a.s. finite minimal N such that tau_N>1.

For simplicity, suppose that Re(X(1)=1+i. Define sigma_0=0. Given X, let Y be defined as follows.

First, we take Y(sigma_j)=\pm X(sigma_j), where the sign is chosen so that Re(Y(sigma_j))>0.

Next, we take Y(tau_j)=|X(\tau_j)|. Finally, in [tau_j, sigma_j] and in [sigma_j,tau_{j+1}],

we take Y(t) to be the appropriate image of X(t) under the linear isometry that maps the

corresponding boundary values of X in the time interval to the corresponding boundary values

of Y.

Well, I got to go now, but I assume that you see the rest…

O.

Dear Oded’s family and friends,

My name is Dror and I’m an international student from Israel at the University of Washington, Seattle.

As part of my experience of studying abroad, I decided to join King County Explorer Search And Rescue (KCESAR) two years ago. This is 100% volunteer organization and we work under the King County Sheriff’s Department.

I remember when the pager went off around 10pm with the message “lost hiker on Guye Peak”.

I was free on that evening, so I got into my car and drove to base-camp. When you get to base camp, you get some extra information about the missing subject: name, clothes and etc.

When I heared the name Oded, I asked to know for his last name because Oded is an Israeli name. After explaining to my volunteer-friends that Oded is an Israeli name and I told them how it should be pronounced, we got out to the mountains for a night search.

We searched all night and morning unitill the Seriff’s helicopter arrived and spotted Oded’s location.

There were more than 30 volunteers on that mountain looking for Oded on that night.

I feel proud for taking with KCESAR,

looking for this special, brilliant Israeli man.

I’m sorry for your lost. Wish I could know him in different circumstances.

Yours,

Dror.

Oded was my mentor. I learned many many things from him. Now he has left us forever. I miss him sadly!

May Oded rest in peace.

Oded:

you must do not know who i am because i never had chance to talk to you, though i saw you this summer in Montreal SLE workshop. I never expect i miss the chance forever. Now my office is only several meters from yours, and whenever i walk through your office and see your pictures and those flowers there, i fall into an imagination that suddenly one day you may be in your office again.

I hope you happy with your math and mountains in another world.

Weiyang

I have not come to terms with the loss of Oded. He was a powerful fixture in my world view. It is as though someone has told me that Canada or California has ceased to exist. How can this be?

Here is the prepared text of my memorial service remarks:

I miss Oded.

I feel I should apologize for wearing a tie. This is not Oded’s style. The Oded I knew was happiest wearing shorts and sandals and a

smiley face T-shirt, usually carrying a bagel. He needed coaxing to dress up for things like a banquet with the Queen of Norway and the other fancy events to which he was often invited.

Oded was not impressed by formality. He was not impressed by prestige. He was recruited by the most prestigious centers of mathematics in the world. Of course, these were complex decisions, but if he ever felt something boiled down to mountains versus prestige, that was an easy choice for him.

There are few things in life more enjoyable than doing math with Oded. I discovered this as an intern and postdoc at Microsoft Research. You’d spend a week coming up with an idea — and in just half an hour Oded would understand it and appreciate it and praise it. Then he’d explain why it was really unsalvageably wrong, but

he’d have some other beautiful idea, and you’d keep working. He had a great sense of humor. It was nonstop fun the whole time.

Oded was like Michael Jordan in his prime. Nobody could quite touch him, but it was a pleasure to watch him play. All of the mathematicians my age wanted to be like him. He seemed to do everything without breaking a sweat.

Oded was a great friend to my family. Through job changes, moves, crises, the births of my children, the death of my daughter’s twin,

he always took a sincere interest. He gave thoughtful gifts to my children. He was just incredibly kind and giving, and like everything else, he made this look easy.

One day he took me cross-country skiing, but due to a power outage, we were unable to rent skis. Oded is not the sort of guy who can be

deterred from a skiing adventure by a lack of skis. So we took off stomping through snow in tennis shoes up a steep mountain trail. We

thought we were all alone, high in the mountains, when two very large skiers came along and yelled at us for making holes in their

ski trail, which I guess you’re really not supposed to do. They became very threatening and stood there cursing at us. I guess it’s

a little awkward to start an actual brawl while you’re wearing skis, but one of them promised to meet us in the parking lot.

Throughout the whole very tense exchange, Oded was calm, polite, apologetic. Never angry. Never afraid. Never nervous. His heart rate did not change during confrontations.

That’s also how Oded responded to professional competition, to potential priority disputes, to people proving results he had proved or could have proved. Some mathematicians are incredibly anxious over such things, but never Oded. He was completely above pettiness. Always generous. Always relaxed. Always happy to give

credit to others.

Most of us struggle with inner demons of one kind or another — we procrastinate, we’re disorganized, we’re jealous, we neglect important things we don’t feel like doing. As far as I could tell, Oded had no inner demons.

Oded was intensely honest and loyal. Loyal to mathematics. Loyal to family, colleagues, and friends. I should add that no man was ever more fond of or more proud of his children than Oded. We’ll all miss him terribly, but we are also just so grateful we had the chance to know him.

Oded has been on my thoughts ever since I heard about the accident. We both enjoyed hiking up mountains, we were both researchers, both immigrants in a foreign country, and both parents of teenage children: I keep thinking that it could have been me!

I did not know Oded very well. Years ago, he sent his children to an alternative style elementary school. I asked him why: because, in his view, teachers in traditional educational systems had too much power over their students, so that a single bad teacher would be enough to make his students’ lives miserable; and he wanted his children to be free from such risks. I asked him about not raising his children in the Jewish religion: he strongly felt that religions had caused too much harm, too many wars. Truth be told, he often made me slightly uncomfortable: sometimes I would utter some straightforward, commonly held opinion. Instead of accepting it at face value, he was liable to ask me why I was saying that, and suddenly I would find myself scrambling for some hasty justification of my opinion, feeling rather stupid, while he listened attentively.

Oded was a very original thinker. He had a knack for questioning what other people take for granted, and that could be vaguely threatening for our familiar, worn-out ideas that we do not always wish to reconsider. At the same time, he was never aggressive about it. I think that in his way of life, he was very principled and deliberate, yet at the same time he was always open to discussing his views. Very unusual! Although he made me want to challenge his choices (and some of them were always mysterious to me), I could not help but reluctantly admire him. Sometimes I thought that it must not always be easy being the child or spouse of someone who liked you to always be able to explain the reason behind your actions!

Our scientific interactions never went beyond the superficial; what we had most in common was a deep interest in parenting. It seemed to me that often, in life, he was primarily led by the desire to do what was best for his children. I like to think that his last thought may have been one of gratitude that he got to spend so much time with his family instead of letting work dominate his life. Avivit, Tselil and Pele, my thoughts are with you every day.

It was with a dreadful sense of shock that I learned of Oded’s death two weeks ago. I will never forget his bold, enormously insightful, patient and peaceful presence.

I had a sense that he pursued his work never driven by a competitive motive, but with a fascination for understanding and uncovering the beauty in mathematics.

Vital, creative, absent now: consoled by the memory.

I feel as devastated about Oded’s untimely death as most other contributers to this blog. At

http://www.math.chalmers.se/~olleh/Oded.pdf

I have posted an obituary (in Swedish) that I wrote for the newsletter of the Swedish Mathematical Society.

I first met Oded Schramm and his lovely wife when he was a graduate student at Princeton. He was asking me about a rigidity conjecture on infinite circle packings on the complex plane. I thought the conjecture was impossible to solve, although I did not say that to him. In the next few months he presented a proof of the conjecture, and made it part of his Ph.D. work. I was not able to fully understand this proof until a few years later, when he and I together solved Koebe conjecture for domains with countably many boundary components. Our work was not possible without many new ideas invented in his earlier work. The Koebe conjecture, still open as of today, says that all plane domains are conformally homeomorphic to circle domains, i.e., domains whose boundary components are all circles and/or points. Oded Schramm continued to work on this conjecture for several more years. Although he did not prove the conjecture, he made a lot of surprising progress. During all this time I was very fortunate to spend a lot of times together with him and to see first hand his creativity and originality at work. Oded had been an inspiration for me.

Oded was always kind and patient to all people — whether experts or starters. He was never intimidating. His early death is a great loss to many of us.

Why do I write in Oded’s memory nearly 4 months after the tragedy?

I had not written before because I felt that I did not know Oded well and I was not sure what can I add to the people who had written before me. Still, I received the news of the tragedy with enourmous sadness, shock and disbelief. The idea of writing has not left me since and I felt that I should at least write what I can. Also, I wanted to emphasize, to Oded’s family and to all others who read this blog, that Oded’s memory has not faded. Indeed, not a week goes by without me hearing Oded’s name from someone expressing grief at the loss. It is a great tragedy. First, to Oded’s family where the loss is greatest. But also to a huge extent, to the mathematical community at large. It seems that Oded contributed so much to so many fields that people from all parts of mathematics know his name and to this day, recall it and remember him with sadness.

I saw Oded for the first time in Berkeley, during my Ph.D., when he came to give a talk there. I remember being very excited that he had come, but also shy to approach him. My next encounter with him was when he received the Loève Prize in Berkeley. But I think it was only in the third time I met him, at the 2006 ICM meeting in Madrid, that I approached him to ask a question. For a junior mathematician to approach a famous senior mathematician he does not know and ask a question is a scary task. First, it is quite likely that the question will expose some big gap in your knowledge or understanding and be quite embarrassing for you. Second, it is not at all clear that you will understand the answer that you receive. And third, such a person is obviously busy. Who are you to take of his time? Hence, I was very much relieved to discover the wonderful personality of Oded, the same personality talked so much about above. My question was a not a nuisance to him, he did not make it sound like it was a complete triviality and he went to the effort of making his answer clear to me despite the huge level gap between us. In all my future encounters with Oded, this was always the case. Oded was always ready to answer a question, to explain his answer again when necessary and to do all that with a smile and without hurrying his listener. It is an amazing ability which we can all aspire to have.

Later, I got to spend one semester at Microsoft Research in Seattle. Unfortunately, although my time there was productive, I did not get to work closely with Oded. I was lucky to work on a project with him and with Russ Lyons, but my work in that project was mostly disjoint from Oded’s and we did not get to discuss much. I hoped then, as I am sure all of the people who worked with Oded did, that more collaboration could be done in the future, perhaps when I learn more and am better prepared.

These were most of my encounters with Oded and I am sorry that I did not know him better. Oded’s works are an inspiration to us all. His personality was remarkable. His legacy is not only in what he taught us, but also the aspiration he gave us all, to become more like him.

From what I see written above and from what I hear from people around me, I am sure that this legacy will continue to be with us for a very long time.

Yehi Zichro Baruch.