# Oded Schramm

### Telegraph obituary

Mathematician who made a significant contribution to the study of probabilty and fractals.

Oded Schramm, who died in a climbing accident on September 1 aged 46, was a towering figure in the field of mathematics and widely considered to be the world's most influential authority on probability; he would almost certainly have won the Fields Medal, the mathematical equivalent of the Nobel, had he not done his most important work at too late an age to qualify.

Schramm made contributions in numerous areas of pure mathematics, but his main achievement was in developing a better mathematical understanding of what are known as self-similar fractal phenomena. An object is said to be fractal if it is "infinitely jagged". In other words, it looks jagged not only to the naked eye but also no matter how it is magnified. Ferns and snowflakes are fractals in nature.

Physicists had observed that certain complex physical systems, such as the percolation of water through rocks or the tangling of polymers, exhibited fractal behaviour, but had not devised an equation to explain it.

Schramm took an equation first developed in 1923 by the mathematician Charles Loewner in a field known as conformal geometry and added ideas from probability theory, two previously separate branches of mathematics, combining them into an equation, known as the stochastic Loewner evolution equation (SLE), that explains such phenomena. Physicists had worked out rough answers, but Schramm was able to provide rigorous, exact calculations.

For this work, published in 2000, Schramm received several major awards, but Fields Medals are awarded only once every four years to mathematicians who are 40 or under. Schramm was born on December 10 1961 and by the cut-off date for the 2002 awards was three weeks too old to qualify. Wendelin Werner, a younger mathematician who collaborated with Schramm on follow-up research, won a Fields in 2006.

Born in Jerusalem, Oded Schramm received his bachelor's degree in Mathematics and Computer Science from Hebrew University in 1986 and a masters in Mathematics a year later. He completed his doctoral thesis at Princeton in 1990.

After working at the University of California, San Diego, and the Weizmann Institute of Science in Israel, Schramm was recruited to the theory group of Microsoft Research, an arm of Microsoft dedicated to basic science.

Schramm's doctorate was in the mathematical field of topology, but the most extraordinary thing about him was that in other fields of mathematics he was self-taught. He was not, for example, trained in stochastic calculus, but, as a colleague observed, "he knew it all, not by reading books, but just by himself". Frequently -- and this was not restricted to probability theory -- he would look up references for the first time in order to give an appropriate credit in a paper he was writing, after he had worked out the proof for himself.

As often as not he found that what he was writing was completely original, or where he found a proof he did not like, he would produce a much more elegant one of his own. This creativity, observed Wendelin Werner, led to really "beautiful mathematics".

A modest man, Schramm was never competitive and was happy to share his ideas. When colleagues referred to SLE as the "Schramm-Loewner" equation he would always look embarrassed.

Schramm listed his interests as: "Percolation, two-dimensional random systems, critical systems, SLE, conformal mappings, dynamical random systems, discrete and coarse geometry, mountains". Like many extremely clever people, he took an almost childlike pleasure in the physical world.

He fell to his death while climbing Guye Peak in the Cascade Mountains, north of Snoqualmie Pass in Washington State.

Schramm's awards included the Clay Research Award in 2002, the Henri Poincaré prize in 2003, the Polya Prize in 2006 and the Ostrowski Prize last year.

He was elected to the Royal Swedish Academy of Sciences in 2008.

He is survived by his wife, Avivit, and two children.

18 September 2008 © Telegraph

Schramm made contributions in numerous areas of pure mathematics, but his main achievement was in developing a better mathematical understanding of what are known as self-similar fractal phenomena. An object is said to be fractal if it is "infinitely jagged". In other words, it looks jagged not only to the naked eye but also no matter how it is magnified. Ferns and snowflakes are fractals in nature.

Physicists had observed that certain complex physical systems, such as the percolation of water through rocks or the tangling of polymers, exhibited fractal behaviour, but had not devised an equation to explain it.

Schramm took an equation first developed in 1923 by the mathematician Charles Loewner in a field known as conformal geometry and added ideas from probability theory, two previously separate branches of mathematics, combining them into an equation, known as the stochastic Loewner evolution equation (SLE), that explains such phenomena. Physicists had worked out rough answers, but Schramm was able to provide rigorous, exact calculations.

For this work, published in 2000, Schramm received several major awards, but Fields Medals are awarded only once every four years to mathematicians who are 40 or under. Schramm was born on December 10 1961 and by the cut-off date for the 2002 awards was three weeks too old to qualify. Wendelin Werner, a younger mathematician who collaborated with Schramm on follow-up research, won a Fields in 2006.

Born in Jerusalem, Oded Schramm received his bachelor's degree in Mathematics and Computer Science from Hebrew University in 1986 and a masters in Mathematics a year later. He completed his doctoral thesis at Princeton in 1990.

After working at the University of California, San Diego, and the Weizmann Institute of Science in Israel, Schramm was recruited to the theory group of Microsoft Research, an arm of Microsoft dedicated to basic science.

Schramm's doctorate was in the mathematical field of topology, but the most extraordinary thing about him was that in other fields of mathematics he was self-taught. He was not, for example, trained in stochastic calculus, but, as a colleague observed, "he knew it all, not by reading books, but just by himself". Frequently -- and this was not restricted to probability theory -- he would look up references for the first time in order to give an appropriate credit in a paper he was writing, after he had worked out the proof for himself.

As often as not he found that what he was writing was completely original, or where he found a proof he did not like, he would produce a much more elegant one of his own. This creativity, observed Wendelin Werner, led to really "beautiful mathematics".

A modest man, Schramm was never competitive and was happy to share his ideas. When colleagues referred to SLE as the "Schramm-Loewner" equation he would always look embarrassed.

Schramm listed his interests as: "Percolation, two-dimensional random systems, critical systems, SLE, conformal mappings, dynamical random systems, discrete and coarse geometry, mountains". Like many extremely clever people, he took an almost childlike pleasure in the physical world.

He fell to his death while climbing Guye Peak in the Cascade Mountains, north of Snoqualmie Pass in Washington State.

Schramm's awards included the Clay Research Award in 2002, the Henri Poincaré prize in 2003, the Polya Prize in 2006 and the Ostrowski Prize last year.

He was elected to the Royal Swedish Academy of Sciences in 2008.

He is survived by his wife, Avivit, and two children.

18 September 2008 © Telegraph