Mathematician Spies

Edward Snowden speaks to European officials via video conference during a parliamentary hearing on mass surveillance at the EuropeanCouncil in Strasbourg, France, on April 8, 2014.

Photo by Frederick Florin/AFP/Getty Images

For the past 10 months, a major international scandal has engulfed some of the world's largest employersof mathematicians. These organizations stand accused of law-breaking on an industrial scale and are nowthe object of widespread outrage. How has the mathematics community responded? Largely by ignoring it.

Those employers—the U.S. National Security Agency and the U.K.'s Government CommunicationsHeadquarters—have been systematically monitoring as much of our lives as they can, including ouremails, texts, phone and Skype calls, Web browsing, bank transactions, and location data. They havetapped Internet trunk cables, bugged charities and political leaders, conducted economic espionage,hacked cloud servers, and disrupted lawful activist groups, all under the banner of national security. Thegoal, to quote former NSA director Keith Alexander, is to “collect all the signals, all the time.”

The standard justification for this mass surveillance is to avert terrorism. U.S. officials repeatedly claimedthat mass surveillance had thwarted 54 attacks. But the NSA eventually admitted it was more like one ortwo; its best example was an alleged $8,500 donation to a terrorist group.

We mathematicians enjoy the feeling that what wedo is separate from the everyday world.

Some argue that the information gathered is “only metadata”—phone numbers and call durations ratherthan what was said, for example. This is not true. GCHQ has harvested webcam images, many sexual, ofmillions of people. In any case, it is wrong to believe that collecting metadata leaves privacy intact. As ex-NSA legal counsel Stewart Baker said: “Metadata absolutely tells you everything about somebody's life.”

Others claim to be unbothered by the recording of their daily activities, confident that no one will examinetheir records. They may be right: If you never trouble the state, perhaps the state will never trouble you.But even so, do we want it to hold such powerful tools for stifling dissent, activism, and even journalism?

And so to the mathematicians' role in all of this. The NSA claimsto be the largest employer of mathematicians in the United States.

It may be the largest in the world. It partly funds GCHQ, also a major employer of mathematicians, andworks closely with intelligence agencies in Australia, New Zealand, and Canada. Some mathematicianswork for these agencies full time. Others do so during summer breaks or sabbaticals from their universityjobs.

We will never know exactly what mathematicians have done for these agencies. GCHQ does not commenton intelligence matters, which is to say, anything it does. But revelations by former NSA contractorEdward Snowden suggest some possibilities.

For example, we know the NSA has undermined Internet encryption. Certain encryption methods usepseudorandom-number generators based on the theory of elliptic curves. These are used to create keys forencrypted information, ensuring only the sender and receiver can see credit card details, for example.

Snowden revealed that the NSA inserted a secret back door into a widely used elliptic curve algorithm,allowing it to break the encryption. That could not have been done without sophisticated knowledge of themathematics involved, the details of which were recently described by Thomas Hales of the University ofPittsburgh in the Notices of the American Mathematical Society.

Mathematicians seldom face ethical questions. We enjoy the feeling that what we do is separate from theeveryday world. As the number theorist G.H. Hardy wrote in 1940: “I have never done anything ‘useful.’No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the leastdifference to the amenity of the world.”

That idea is now untenable. Mathematics clearly has practical applications that are highly relevant to themodern world, not least Internet encryption.

Our work, then, can be used for both good and ill. Unfortunately for us, it is the latter that is in the publiceye. Already unpopular for our role in the banking crash, we now have our largest employer running a

system of whole population surveillance that even a judge appointed by George W. Bush called “almostOrwellian.”

So mathematicians must decide: Do we cooperate with the intelligence services or not?

Our situation has been likened to that of nuclear physicists in the 1940s. However, they knew they werebuilding the atom bomb, whereas mathematicians working for the NSA or GCHQ often have little ideahow their work will be used. Those who did so trusting that they were contributing to the legitimatesafeguarding of national security may justifiably feel betrayed.

At a bare minimum, we mathematicians should talk about this. Maybe we should go further. Eminentmathematician Alexander Beilinson of the University of Chicago has proposed that the AmericanMathematical Society sever all ties with the NSA and that working for it or its partners should become“socially unacceptable” in the same way that working for the KGB became unacceptable to many in theSoviet Union.

Not everyone will agree, but it reminds us that we have both individual choices and collective power.Individuals can withdraw their labor. Heads of university departments can refuse staff leave to work forthe NSA or GCHQ. National mathematical societies can stop publishing the agencies' job adverts, refusetheir money, or even expel members who work for agencies of mass surveillance.

At the very least, we should acknowledge that these choices are ours to make. We are human beings firstand mathematicians second, and if we do not like what the secret services are doing, we should notcooperate.

This article originally appeared in New Scientist.