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July 2014 issue
Should Mathematicians Co-operate with GCHQ? Response by Tom Leinster
Should Mathematicians Co-operate with GCHQ? Response by Trevor Jarvis

June 2014 issue
Should Mathematicians Co-operate wtih GCHQ? Response by Malcolm MacCallum

May 2014 issue
Should Mathematicians Co-operate with GCHQ? Response by Dr Richard Pinch

April 2014 issue
Should Mathematicians Co-operate with GCHQ? Tom Leinster




Published online 3 July 2014

Two mathematicians associated with GCHQ, Richard Pinch and Malcolm MacCallum, have now replied to my April LMS Newsletter article, which consisted mostly of factual statements based on the Snowden leaks, followed by the mild opinion that mathematicians can choose whether to give GCHQ their cooperation.

Neither of them disputes any specific factual statement that I made (MacCallum disputes one I didn't make; see the longer online version of this article at In both that and my previous article, every factual statement is hyperlinked to supporting evidence). Neither engages with the fact that the intelligence agencies intercept not just terrorists' communications, but everyone's (over 50 billion communications/day, according to GCHQ). Neither discusses the total surveillance mission of GCHQ's closest partner, the US National Security Agency:

Collect it all. Sniff it all. Know it all. Process it all. Partner it all. Exploit it all.

Neither addresses any of the facts revealed by the leaks. Both say, effectively: "Trust us."

But no one needs to trust Pinch or MacCallum, or me, because we now have detailed documentary evidence of what GCHQ and its partners are doing. We can simply test claims against that evidence.

For example, Pinch quotes GCHQ director Iain Lobban's claim that if his staff "were asked to snoop, I would not have the workforce. They would leave the building." In contrast, GCHQ's own documents detail how it secretly captured webcam images, many sexually explicit, from millions of ordinary people. If that is not "snooping", what is?

We all want spies to spy on terrorists. We all agree that the secret services must have secrets. We all support targeted surveillance. But what is at issue is mass surveillance: the monitoring of everyone, all the time.

Pinch and MacCallum blur that distinction. Thus, MacCallum cites MI5 head Andrew Parker's statement that the agencies and police have disrupted many "plots towards terrorism". But Parker did not credit mass surveillance; on the contrary, he added that almost all the plots came from a known pool of several thousand individuals. Even less relevant is MacCallum's observation that phone billing records can be useful in criminal trials. These are obtained from phone companies, not GCHQ.

Heads of mathematics departments would probably like to "stay out of politics". This is wishing for the impossible. It is illogical to maintain that dissenting from cooperation with GCHQ is a political act, but assenting is not. A HoD who runs a working relationship with GCHQ is implementing a political view just as surely as one who declines.

HoDs should at least consult openly. In London, resentment has been caused by the establishment of joint positions with GCHQ without proper consultation. Medicine and psychology departments routinely make ethical assessments. Maybe it is time for mathematics departments to draw up their own ethical policies.

We now have detailed evidence of what we are supporting when we collaborate with the secret services, and we can use it to have a properly evidence-based discussion. Instead of seeking refuge in the comforting myth of political neutrality, we should take responsibility for our actions.

Tom Leinster (School of Mathematics, University of Edinburgh)

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Published online 3 July 2014

This question was posed by Tom Leinster in the April LMS Newsletter. His quite reasonable article referred to widespread allegations that the security services monitor much of our lives.

Richard Pinch (May LMS Newsletter) and Malcolm MacCallum (June LMS Newsletter) each make a valiant attempt to stave off the question.

Their defence is basically 'we don't believe the allegations but we can't say why.'

"Allegations about GCHQ's activities are not going to be confirmed or denied. Either would be helpful to hostile nations, terrorists or criminals."

That is very puzzling. In what way would it help "hostile nations, terrorists or criminals" to know their every moves were being watched? Haven't they caught on yet?

Malcolm MacCallum says that the intelligence services have thwarted 34 terrorist plots. Well, maybe they have, maybe they haven't. We don't know. Mathematicians don’t usually take things on trust. In any case, if the plots have been foiled shouldn't the would-be perpetrators be publicly exposed – pour décourager les autres?

Praising the work of GCHQ and the intelligence agencies in stopping innocent people being killed, Malcolm MacCallum says “Deaths at 9/11 and 7/7 were narrowly avoided...” That is a very strange statement; were those attacks foreseen?

As for the statement by the Foreign Secretary in the House of Commons – “It is my belief... that GCHQ staff conduct themselves with the highest level of integrity and legal compliance" – many people no longer trust the Orwellian statements of government ministers. Who carries out the ‘independent’ scrutiny of GCHQ?

Finally, can I make a request to Malcolm MacCallum and Richard Pinch: please will you give me an assurance that this email won't be read by the security services?

Trevor Jarvis (University of Hull - ret’d)

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Published online 16 May 2014

Answering Dr Leinster's letter about GCHQ (April LMS Newsletter) presents several difficulties. Detailed responses to polemics with multiple contentious statements always seem weaker and less convincing than the polemic itself, partly because they are much longer and more nuanced.

A second difficulty is that allegations about GCHQ's activities are necessarily not going to be confirmed or denied. Either would be helpful to hostile nation states, terrorists or criminals. A completely open debate is thus impossible, unless one takes the extreme view that all intelligence agency work should be public (which logically would have meant telling the Germans in WWII that Bletchley had broken their codes).

Public debate about the balance between protecting people from crime and terrorism and potential invasion of privacy is also handicapped by the lack of trust in those who do have access to what really happens, i.e. public servants and ministers. As the former Director of GCHQ's Heilbronn Institute, I fully agree with Richard Pinch (May LMS Newsletter) that Leinster's picture of GCHQ is not one I recognize, and with the Director's claim that many staff would leave if asked to snoop on the general public. But will we be believed?

I see GCHQ's work as stopping innocent people being killed and putting guilty people in gaol. For example, the gang behind a close family member (and 25 others) being carjacked at knifepoint were convicted partly on mobile phone billing evidence. Deaths at 9/11 and 7/7 were narrowly avoided by, respectively, another close family member and a graduate student's partner, so I was pleased to hear, in the public session Richard Pinch's response refers to, that 34 terrorist plots had been thwarted in recent years by the intelligence agencies. Had deaths resulted from those plots there would no doubt have been criticism of intelligence agency failures (as indeed there were, to some extent, in 7/7). A recent radio program said that some of the people best at hiding themselves on the internet are paedophile rings.

The powers allowed to intelligence agencies have to enable them to investigate such matters while protecting privacy. Leinster does not address this difficult balance, which I see as the fundamental issue. Meaningful public debate will be difficult for reasons already cited.

Although I cannot comment on the allegations about GCHQ's actions, let me respond to some of Leinster's other points.
The unwary reader may think Leinster's statement that GCHQ is ‘accused of law-breaking on an industrial scale’ means that its staff intentionally break the law. In fact it refers to a legal opinion of a possible conflict between the acts governing GCHQ's work, and their application, and human rights legislation. This has not, as far as I know, been tested in court, and certainly does not justify any imputation of deliberate law-breaking. The quoted opinion is presumably not shared by the many lawyers involved in framing and applying the laws concerned, and I understand that GCHQ and its oversight bodies have obtained substantial and independent contrary legal opinions.

Having been a political radical in the 1960s, convinced at that time that our group was under surveillance, I approached my time at GCHQ with caution. I was pleasantly surprised that my first substantial briefing session was on the legal framework, including human rights laws, within which GCHQ operates. The need for legal authorization of any action which could not be equally undertaken by any citizen was repeatedly referred to during my time there. I have no doubt it was carefully adhered to.

Both GCHQ and its mathematics staff will be amused by the accusation that mathematicians there have little idea how their work will be used. The capabilities being provided by all the work I knew about were very clear to all concerned. Access to specific intelligence gained thereby was limited by ‘need to know’; nevertheless, GCHQ took pains to tell all security-cleared staff as much as possible about what successes it had had.

As for the independent scrutiny of GCHQ, those convinced of GCHQ's wrongdoing see the absence of criticism from the oversight agencies as evidence of those agencies' weakness or credulity. They cannot entertain, as they should, the alternative proposition that there is no wrongdoing to find.

I hope mathematicians thinking of working for GCHQ will not be deterred by Leinster's rhetoric, but, in trying to discern how they see the balance between reasonable intelligence gathering and oppressive measures, will be swayed by those who have worked for GCHQ and have come away, like me, reassured by what they found.

Malcolm MacCallum
Queen Mary, University of London

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Published online 25 April 2014

Dr Richard Pinch, Strategic Advisor for Mathematics Research at GCHQ, who has been a member of the LMS for over 35 years, writes the following response to Dr Leinster's opinion piece Should Mathematicians Cooperate With GCHQ?:

Dr Leinster's opinion piece makes a range of allegations of unethical and unlawful conduct against GCHQ.  The allegations are so widely drawn that it is impossible for GCHQ to recognise them as a description of its activities.

GCHQ, along with the other intelligence agencies of the UK, is subject to some of the most rigorous legislative and oversight arrangements in the world.  These ensure that all the work of the agencies is carried out in accordance with a strict legal and policy framework so that their activities are at all times legal, authorised, necessary and proportionate.

GCHQ does not comment on intelligence matters, but would draw your readers' attention to the comments of the Foreign Secretary in the House of Commons on 10 June 2013, quoting the Interception Commissioner: "it is my belief ... that GCHQ staff conduct themselves with the highest levels of integrity and legal compliance", and to Director GCHQ's evidence to the Intelligence and Security Committee of Parliament on 07 November 2013: "My people are motivated by saving the lives of British forces on the battle field, they are motivated by fighting terrorists / serious criminals, by meeting that foreign intelligence mission as well.  If they were asked to snoop, I would not have the workforce.  They would leave the building."

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In this April issue of the LMS Newsletter we are launching a Members’ Opinions section. All opinions submitted to this section are strictly those of the contributor and in no way represent the views of the London Mathematical Society. We thank Tom Leinster for being the first contributor.


Published online 26 March 2014

One of the UK's largest employers of mathematicians has been embroiled in a major international scandal for the last nine months, stands accused of law-breaking on an industrial scale, and is now the object of widespread outrage. How has the mathematical community responded? Largely by ignoring it.

GCHQ and its partners have been systematically monitoring as much of our lives as they possibly can, including our emails, phone calls, text messages, bank transactions, web browsing, Skype calls, and physical location. The goal: "collect it all". They tap internet trunk cables, bug charities and political leaders, disrupt lawful activist groups, and conduct economic espionage, all under the banner of national security.

Perhaps most pertinently to mathematicians, the NSA (GCHQ's major partner and partial funder) has deliberately undermined internet encryption, inserting a secret back door into a standard elliptic curve algorithm. This can be exploited by anyone sufficiently skilled and malicious — not only the NSA/GCHQ. (See Thomas Hales's piece in February's Notices of the AMS.) We may never know what else mathematicians have been complicit in; GCHQ's policy is not to comment on intelligence matters, which is to say, anything it does.

Indifference to mass surveillance rests partly on misconceptions such as "it's only metadata". This is certainly false; for instance, GCHQ has used webcams to collect images, many sexually intimate, of millions of ordinary citizens. It is also misguided, even according to the NSA's former legal counsel: "metadata absolutely tells you everything about somebody's life".

Some claim to be unbothered by the recording of their daily activities, confident that no one will examine their records. They may be right. But even if you feel that way, do you want the secret services to possess such a powerful tool for chilling dissent, activism, and even journalism? Do you trust an organization operating in secret, and subject to only "light oversight" (a GCHQ lawyer's words), never to abuse that power?

Mathematicians seldom have to face ethical questions. But now we must decide: cooperate with GCHQ or not? It has been suggested that mathematicians today are in the same position as nuclear physicists in the 1940s. However, the physicists knew they were building a bomb, whereas mathematicians working for GCHQ may have little idea how their work will be used. Colleagues who have helped GCHQ in the past, trusting that they were contributing to legitimate national security, may justifiably feel betrayed.

At a bare minimum, we as a community should talk about it. Sasha Beilinson has proposed that working for the NSA/GCHQ should be made "socially unacceptable". Not everyone will agree, but it reminds us that we have both individual choice and collective power. Individuals can withdraw their labour from GCHQ. Heads of department can refuse staff leave to work for GCHQ. The LMS can refuse GCHQ's money.

At a bare minimum, let us acknowledge that the choices are ours to make. We are human beings before we are mathematicians, and if we do not like what GCHQ is doing, we do not have to cooperate.

Tom Leinster
School of Mathematics, University of Edinburgh
28 February 2014

Editor’s note: A fully referenced version of this article can be found at the author's website at

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Published online 26 March 2014

Commencing with this issue a ‘Members’ Opinions’ section has been instituted.  Contributions are welcome from members who should send them to marked ‘Opinions – for publication’.  Items are accepted at the discretion of the editor and subject to available space in any given edition.

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Published online 28 January 2014

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