The Magical Mathematics of Numb3rs

Numb3rs is a television show that ran for six seasons on CBS from 2005 to 2010 about FBI agent Don Eppes and his brother Charles, a child math prodigy turned math professor at CalSci (a thinly disguised Caltech), who fight crime with mathematics in a sunny, smog-free TV version of Los Angeles filled with an astonishing number of extremely attractive young women. All six seasons are now available on DVD. Numb3rs features some real mathematics used in solving some real crimes as well as pure science fiction. In many respects, Numb3rs is a techno-thriller that features a mix of real present-day technology, advanced technology that may exist, and technology and mathematics that might plausibly exist in the near future. Mathematics and science is especially well integrated into many episodes in the first and second seasons of the show. Unlike over-the-top science fiction shows like Eureka, a viewer could believe that Numb3rs is a realistic presentation of mathematics and science used in crime fighting and other applications today.

David Krumholtz (plays Charlie Eppes in Numb3rs)

Actor David Krumholtz (Charlie Eppes in Numb3rs)

Real life mathematicians including Caltech statistics professor Gary Lorden consulted for the show. Gary Lorden is listed in the credits for each episode as “Math Consultant”. In later seasons, Stephen Wolfram’s Wolfram Research also provided consulting advice to the series. There are scenes with references to Mathematica, Wolfram’s flagship product, and close-up shots of Wolfram’s magnum opus A New Kind of Science on Charlie Eppes desk. Wolfram also has a Caltech connection; he received his Ph.D. in Physics from Caltech in 1979. Gary Lorden and fellow mathematician Keith Devlin published a popular book The Numbers Behind Numb3rs: Solving Crime with Mathematics in 2007: “A companion to the hit CBS crime series Numb3rs presents the fascinating ways mathematics is used to fight real-life crime.” The shadowy National Security Agency (NSA), probably the largest patron of mathematics and mathematicians in the United States and the world, makes several appearances in Numb3rs.

Milikan Library Caltech

Millikan Library at Caltech (appears often in Numb3rs)

CBS, Texas Instruments (a leading maker of digital signal processor or DSP chips), and the National Council of Teachers of Mathematics (NCTM) developed the “We All Use Math Every Day” initiative, sometimes abbreviated WAUMED, to inspire students to achieve more in math by showing how the subject is relevant to their lives:

Using the hit CBS television show, Numb3rs, the “We All Use Math Every Day” initiative provides free classroom activities online at that help students understand how the math they are learning in the classroom applies to the real world. The activities explore the math derived from the concepts used to solve cases in the FBI crime-solving show.

The show used the “We All Use Math Every Day” tagline in the opening introduction to the show in the first and second seasons.

How Realistic is Numb3rs?

Although explicitly fiction, in many respects Numb3rs paints a picture of mathematics and science that is similar to ostensibly factual popular science such as Scientific American articles, PBS/Nova video programs, Congressional testimony by leading scientists, and informal discussions at fundraising cocktail parties — unless the scientists or mathematicians are in the rare and unusual position of having to explain an obvious failure to a lay audience:

“Well, Senator, as everyone knows, science is a risky enterprise. Eighty to ninety percent of our research projects fail. Surely your staff briefed you on that; the proposal committee mentioned this clearly in italics in footnote 83 in Appendix C of the Proposal for the New Manhattan Project that Will Produce Miraculous Results by the Next Election.”

In several important respects, Numb3rs is very unrealistic. It is also the case that many people ranging from Silicon Valley executives trying to use mathematical methods for their businesses — for example, the current fad trying to use machine learning for recommendation engines in social networking and search businesses — to practicing scientists and engineers who one might think would know better often have expectations similar to what is portrayed in Numb3rs. These misconceptions almost certainly contributed in a major way to the multi-trillion dollar global housing bubble and crash through the widespread use of invalid mathematical models for the valuation of mortgage-backed securities. With business and political leaders seemingly floundering in the current economic difficulties, these misconceptions may wreak even greater havoc.

Before launching into a critique of Numb3rs, it is important to realize that there have been many successes in applied mathematics and mathematical software including impressive advances in video compression such as used by YouTube and Skype, audio compression such as the widely used MP3 standard, still image compression such as JPEG images, computer generated imagery in movies and video games, the Global Positioning System (GPS) that tells people where they are, and even speech recognition which is finally finding some practical use. Modern computers are extremely powerful, comparable to the supercomputers of previous decades; this power is mostly unused because we do not have the mathematics to put this power to practical use. Today’s powerful computers and new mathematics probably can solve or help solve many pressing problems, even trillion dollar problems such as energy shortages or major diseases such as cancer. Success in solving problems with mathematics requires realistic expectations, realistic planning, and adequate time and resources.

In The Numbers Behind Numb3rs (page 208), the mathematicians Keith Devlin and Gary Lorden, a full professor at Caltech, write:

One thing that is completely unrealistic is the time frame. In a fast-paced 41-minute episode, Charlie has to help his brother solve the case in one or two “television days.” In real life, the use of mathematics in crime detection is a long and slow process. (A similar observation is equally true for the use of laboratory-based criminal forensics as depicted in television series such as the hugely popular CSI franchise.)

Also unrealistic is that one mathematician would be familiar with so wide a range of mathematical and scientific techniques as Charlie. He is, of course, a television superhero — but that’s what makes him watchable. Observing a real mathematician in action would be no more exciting than watching a real FBI agent at work! (All that sitting in cars waiting for someone to exit a building, all those hours sifting through records or staring at computer screens… boring.)

It’s also true that Charlie seems able to gather masses of data in a remarkably short time. In real-life applications of mathematics, getting hold of the required data, and putting it into the right form for the computer to digest, can involve weeks or months of labor-intensive effort. And often the data one would need are simple not available.

(Emphasis Added)

In their discussion of the episode “Manhunt” (Airdate: May 13, 2005,The Numbers Behind Numb3rs, page. 78), in which Charlie Eppes uses Bayesian statistics to predict the actions and location of an escaped killer, Devlin and Lorden also write:

As is often the case with dramatic portrayals of mathematics or science at work, the length of time available to Charlie to produce his ranking of the reported sightings [of the escaped killer] is significantly shortened, but the idea of using the mathematically based technique of Bayesian analysis is sound.

(Emphasis Added)

Real-life mathematics and mathematical software development involves much more time, much more trial and error, much more debugging, and much more risk than depicted in Numb3rs. Scientists often claim an eighty to ninety percent failure rate in their research projects, frequently when explaining an obvious failure to disappointed graduate students, donors, policy makers, and others who expected more. Charlie Eppes almost never fails! There is historical evidence that the failure rate in genuine “breakthroughs” is higher, quite possibly ninety-nine percent or worse. Some of the mathematics that Charlie whips up in a few “television days” in the show would actually qualify as breakthroughs in real-life, notably some mathematics and algorithms for artificial intelligence and pattern recognition (see below). Historically, genuine breakthroughs have usually involved at least five years of effort when successful. To give a recent example, Grigoriy Perelman’s proof of the Poincare Conjecture took him at least seven years. There appear to have been about one hundred failed published attempts to prove the conjecture by mathematicians prior to Perelman’s success.

The reality is, in fact, worse than Devlin and Lorden concede in their book. Numb3rs has several episodes that portray artificial intelligence (AI), pattern recognition, machine learning, and similar technologies far superior to reality at the time the show aired (2005-2010) or even today (2011). In one episode, Charlie whips up an image/object recognition algorithm in a few hours to enable the NSA to track a yellow truck carrying a contraband missile guidance system through their satellite images of LA to a terrorist (“Finders Keepers,” Original Air Date: January 12, 2007). Similarly, remarkably effective face recognition algorithms play a role in several episodes. Many of Charlie’s AI and pattern recognition algorithms and the other pattern recognition technology shown in Numb3rs works much better than the real algorithms and math.

The Specter of 9/11

Numb3rs is a fast-paced entertaining show with sexy, idealistic, highly effective heroes and heroines. Although it is sometimes critical of security agencies like the CIA and powerful institutions like pharmaceutical companies, in many respects it is Hollywood product placement for the post 9/11 world of massive, expensive high-tech surveillance and security measures both overseas and at home — in which mathematics plays an important and growing role. It reminds one of President Eisenhower’s speeches during the 1950’s:

The worst to be feared and the best to be expected can be simply stated.

The worst is atomic war.

The best would be this: a life of perpetual fear and tension; a burden of arms draining the wealth and the labor of all peoples; a wasting of strength that defies the American system or the Soviet system or any system to achieve true abundance and happiness for the peoples of this earth.

Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed. This world in arms is not spending money alone.

It is spending the sweat of its laborers, the genius of its scientists, the hopes of its children.

The cost of one modern heavy bomber is this: a modern brick school in more than 30 cities.

It is two electric power plants, each serving a town of 60,000 population.

It is two fine, fully equipped hospitals. It is some 50 miles of concrete highway.

We pay for a single fighter plane with a half million bushels of wheat.

We pay for a single destroyer with new homes that could have housed more than 8,000 people.

This, I repeat, is the best way of life to be found on the road the world has been taking.

This is not a way of life at all, in any true sense. Under the cloud of threatening war, it is humanity hanging from a cross of iron.

Chance for Peace (April 16, 1953)
President Dwight David Eisenhower (shortly after the death of Joseph Stalin)

President Dwight D. Eisenhower

President Dwight D. Eisenhower

Eisenhower and his advisers were no shrinking violets. They were well aware the world can be a nasty, dangerous place. They presided over a massive military buildup and controversial covert operations in Guatemala, Iran, Vietnam, and other countries. By the end of his Presidency Eisenhower and his advisers found that it was never enough. Even thousands of nuclear weapons, ships, tanks, spies, and what we now know was a massive lead over the Soviet Union was not enough to satisfy what he famously labeled the “military industrial complex” in his Farewell Address. Eisenhower found himself attacked by Republicans and Democrats alike for not spending even more money on guns and preparations for war!

Usama Bin Laden (FBI Wanted Poster)

Osama Bin Laden: The Trillion Dollar Man

Following the reported death of Osama Bin Laden, Andrea Millen Rich, writing in the libertarian Reason magazine, estimated the direct cost of getting Bin Laden at $1.1 trillion. Tim Fernholz and Jim Tankersley, writing in The Atlantic estimated the total cost at $3 trillion over fifteen years. Sam Stein of the Huffington Post, citing a Congressional Research Service report of March 29, 2011, put the cost at at least 1.283 trillion.

According to the United States Centers for Disease Control, the leading causes of death in the United States in the calendar year 2007 were:

Number of deaths for leading causes of death

* Heart disease: 616,067
* Cancer: 562,875
* Stroke (cerebrovascular diseases): 135,952
* Chronic lower respiratory diseases: 127,924
* Accidents (unintentional injuries): 123,706
* Alzheimer’s disease: 74,632
* Diabetes: 71,382
* Influenza and Pneumonia: 52,717
* Nephritis, nephrotic syndrome, and nephrosis: 46,448
* Septicemia: 34,828

All homicides, of which terrorist attacks are a small fraction even in 2001, do not make the top ten. In 2007, the Centers for Disease Control listed all homicides as the 15th leading cause of death:

All homicides

* Number of deaths: 18,361
* Deaths per 100,000 population: 6.1
* Cause of death rank: 15

It is worth noting that the US invasion of Iraq in 2003 resulted in a dramatic drop in Iraqi oil production, undoubtedly contributing substantially to the large increases in oil and energy prices in the last decade. So too the US invasion of Afghanistan in 2001 seems to have scuttled any chance of constructing a pipeline for natural gas from Turkmenistan to the Indian Ocean, also undoubtedly contributing to high energy prices.

It is difficult to improve on President Eisenhower’s words today. Bayesian statistical analyses that predict terrorist attacks, even if they work, don’t make up for dwindling supplies of inexpensive oil and natural gas. They don’t feed people. They don’t cure diseases like cancer or prevent heart attacks. How much more could have been and could still be accomplished if today’s powerful computers and new mathematics were applied to substantive problems such as energy, food, and health instead of the will-o’-the-wisp of perfect security or the pseudo-scientific financial engineering that helped cause the current Great Recession? Mathematicians, scientists, business leaders, and policy makers can do better than we have done.


Numb3rs is a fun, entertaining show. If you are a mathematician, it will probably make you feel great about your profession unless you are in the unfortunate position of dealing with an employer, client, investor, or funding agency that expects you to do what Charlie Eppes does in every episode of Numb3rs. Some of the math and science in Numb3rs is completely realistic. Some of the math is somewhat exaggerated. Some of the math is pure science fiction even though it generally seems very real and believable. As Devlin and Lorden admit in their book, the time frame is, in most cases, completely unrealistic.

The world is presently confronted with serious and worsening problems, possibly due to a dwindling supply of inexpensive oil and natural gas. The political and economic leadership of the world appears paralyzed and unable to deal with the problems, bickering over debt ceilings and other silliness. We do have vast unused resources in the computational power of hundreds of millions of computers and other devices. With the proper mathematics and creative thinking, we may be able to harness this power to resolve many of the current problems, without waiting for paralyzed governments or blundering Too Big To Fail banks to act wisely.

Most mathematics and mathematical software has been developed by individuals and small teams working over periods of several months to several years with total costs of tens of thousands to a few million dollars per project. Success requires realistic expectations about the size, scope, difficulty level, and risks of developing and implementing mathematics and mathematical software. In these difficult times, mathematicians and scientists must gain support for realistic projects that can find real solutions to our pressing problems, and honestly reject the fantasy elements of Numb3rs.

Suggested Reading/References
The Numbers Behind Numb3rs: Solving Crime with Mathematics
Keith Devlin, Ph.D. and Gary Lorden, Ph.D.
Penguin Books, New York, 2007

The Shadow Factory: The Ultra-Secret NSA from 9/11 to the Eavesdropping on America
James Bamford
Doubleday, New York, 2008

The Cost of Iraq, Afghanistan, and Other Global War on Terror Operations Since 9/11
Amy Belasco, Congressional Research Service, Washington, D.C, March 29, 2011

The picture of actor David Krumholtz at the Serenity Premiere is from Wikimedia Commons, licensed under the Creative Commons Attribution 2.0 Generic license.

This image was originally posted to Flickr by RavenU at It was reviewed on 10:00, 30 April 2007 (UTC) by the FlickreviewR robot and confirmed to be licensed under the terms of the cc-by-2.0.

Millikan Library at Caltech Image from Wikimedia Commons.

Official Portrait of President Dwight D. Eisenhower, May 29, 1959

(from Wikipedia) This image is a work of an employee of the Executive Office of the President of the United States, taken or made during the course of the person’s official duties. As a work of the U.S. federal government, the image is in the public domain.

The image of Usama Bin Laden (Osama Bin Laden) is from the FBI Ten Most Wanted Poster.

© 2011 John F. McGowan

About the Author

John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing video compression and speech recognition technologies. He has extensive experience developing software in C, C++, Visual Basic, Mathematica, MATLAB, and many other programming languages. He is probably best known for his AVI Overview, an Internet FAQ (Frequently Asked Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at [email protected].


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