YSM Issue 95.2

DANIEL
SPIELMAN
ALUMNI PROFILE
BY RISHA CHAKRABORTY
YC ’92
With the advent of social media networks like
Facebook and Snapchat, our world is increasingly
connected and complicated. Understanding the
nature of these networks now requires wading through enormous
amounts of information and performing overwhelming computations.
This problem will only multiply in the future, making arriving at any
meaningful conclusions about data unimaginably difficult.
This was the dilemma that Daniel Spielman (YC’92), Sterling Professor
of Computer Science and Professor of Statistics and Data Science and
Mathematics at Yale, sought to solve. He wanted to use a technique called
sparsification, which takes large data sets and removes points that do not
contribute important information about the data. He found inspiration
in an almost unrelated field of mathematics. This venture helped him
solve a decades-old problem in the field of operator theory, earning him
the Ciprian Foias prize and the Polya Prize.
Spielman had initially thought that his problem was in the realm of
linear algebra. “It’s one of those courses every math major takes that
talks about finite-dimensional spaces,” Spielman said. However, upon
discussion with visiting professors and his graduate students, Adam
Marcus, a postdoc at Princeton University, and Nikhil Srivastava, a
graduate student at UC Berkeley, he realized that his sparsification
problem mirrored an existing problem in operator theory called the
Kadison-Singer problem, developed in 1959. The Kadison-Singer
problem, which examines how to divide a group into two groups that
are as equal as possible, had previously been discussed in the fields of
quantum physics and computer science but had not previously been
explored in the field of data science.
The Kadison-Singer problem, or the concept of partitioning groups in
general, is relevant in everyday decision-making. Suppose a PE teacher
needs to divide a class of students into two equally skilled teams to
play kickball. To achieve this, he will need to rank the students by their
kicking, throwing, and catching abilities and separate students so that
the two teams are approximately equal in all three abilities. Spielman’s
initial paper proved that the Kadison-Singer problem was an equivalent
restatement of the sparsification problem. In a monumental 2014
paper, Spielman and his colleagues proved the existence of a solution,
www.yalescientific.org
IMAGE COURTESY OF DANIEL SPIELMAN
countering Kadison and Singer’s decades-long conjecture that not every
mathematical group could be divided equally. Marcus, Srivastava, and
Spielman’s work earned them the Polya Prize in 2014. Proving the
ability to partition groups provided the impetus to explore new ways
to divide networks into relatively equal groups, which aided in network
sparsification: if one group was simply omitted from the network, there
wasn’t any net loss of information. In subsequent years, Spielman and
his team worked on developing mathematical tools to achieve such
data sparsification, for which they received the Ciprian Foias prize in
Operator Theory earlier this year.
Spielman’s transformation of a linear algebra problem into an operator
theory problem reflects his general approach to mathematics. He first
became interested in solving challenging puzzles in the fourth grade,
took college math and programming classes in high school, and pursued
a bachelor’s degree in mathematics and computer science at Yale. He has
always been interested in using computational tools to solve problems.
“There’s a marriage between [math and computer science]. I was once
trying a proof in my undergraduate lab, and a computer program found
a counterexample in a couple of months that I wouldn’t have found in a
hundred years,” Spielman said.
Spielman now employs computation in all of the problems he chooses
to solve. “I keep a list of problems that interest me, and when I am
interested in working on a problem, I check if there’s a similar problem
on my list and if someone’s already worked on similar problems,”
Spielman said. He claims he cannot predict what problem he wants to
solve next. He may continue working on sparsification, networks, or
topics in linear algebra but will inevitably draw inspiration from other
mathematical concepts and fields. “I completely change my research
agenda every few years,” Spielman said.
He is currently working on establishing the Kline Tower Institute
(KTI) for the Foundations of Data Science to sponsor talks between
experts in different fields who want to employ data science techniques
in their work. Ultimately, Spielman encourages every college student to
try some math classes. “You never know what’s going to be useful, so
you should take classes that interest you. Later in life, you may find that
useful connection,” Spielman said. ■
May 2022 Yale Scientific Magazine 35