Intelligence agencies hire lots of mathematicians, but would-be employees must realise that their work is misused to snoop on everyone, says Tom Leinster

(Image: Andrzej Krauze)

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

Those employers – the US National Security Agency (NSA) and the UK’s Government Communications Headquarters (GCHQ) – have been systematically monitoring as much of our lives as they can, including our emails, texts, phone and Skype calls, web browsing, bank transactions and location data. They have tapped 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. The goal, 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. US officials repeatedly claimed that mass surveillance had thwarted 54 attacks. But the NSA eventually admitted it was more like one or two; its best example was an alleged $8500 donation to a terrorist group.


Some argue that the information gathered is “only metadata” – phone numbers and call durations rather than what was said, for example. This is not true. GCHQ has harvested webcam images, many sexual, of millions 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 examine their 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 claims to be the largest employer of mathematicians in the US. It may be the largest in the world. It part funds GCHQ, also a major employer of mathematicians, and works closely with intelligence agencies in Australia, New Zealand and Canada. Some mathematicians work for these agencies full-time. Others do so during summer breaks or sabbaticals from their university jobs.

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

For example, we know the NSA has undermined internet encryption. Certain encryption methods use pseudorandom-number generators based on the theory of elliptic curves. These are used to create keys for encrypted 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 the mathematics involved, the details of which were recently described by Thomas Hales of the University of Pittsburgh in the Notices of the American Mathematical Society (vol 61, p 190).

Mathematicians seldom face ethical questions. We enjoy the feeling that what we do is separate from the everyday 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 least difference to the amenity of the world.”

Mathematicians seldom face ethical questions. What we do feels separate from the everyday world

That idea is now untenable. Mathematics clearly has practical applications that are highly relevant to the modern 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 public eye. 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 “almost Orwellian”.

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 were building the atom bomb, whereas mathematicians working for the NSA or GCHQ often have little idea how their work will be used. Those who did so trusting that they were contributing to the legitimate safeguarding of national security may justifiably feel betrayed.

At a bare minimum, we mathematicians should talk about this. Maybe we should go further. Eminent mathematician Alexander Beilinson of the University of Chicago has proposed that the American Mathematical 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 the Soviet Union.

Not everyone will agree, but it reminds us that we have both individual choices and collective power. Individuals can withdraw their labour. Heads of university departments can refuse staff leave to work for the NSA or GCHQ. National mathematical societies can stop publishing the agencies’ job adverts, refuse their 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 first and mathematicians second, and if we do not like what the secret services are doing, we should not cooperate.

This article appeared in print under the headline “Ethical calculus”