Martin Creed

Simon Singh passed my details on to the Fruitmarket Gallery when they contacted him about talking about the work of the artist Martin Creed.  Initially the gallery were interested in a mathematician talking about the concept of zero. 
However, the exhibition was full of works like Work No. 928 or Work No. 958 and it struck me that the concepts of the discrete vs continuous and limits were much more interesting, and relevant and bought in zero's alter ego, infinity. 

The talk, ‘Much Ado about Nothing’ took place on 13 October 2010.

Back from a blog sabbatical

This blog has been dormant for over a year, a year where I have done more research into the links between science and finance, and I now plan to start posting more regularly.

 In April 2010 the Edinburgh International Science Festival hosted a panel discussion that I organised involving Prof Donald Mackenzie, Dr Gillian Tett and, Ms Terri Duhon.  This is the text of an article published by The Scotsman (3/4/2010) in the lead up to that event, and the joint BMC/BAMC held in Edinburgh at the same time..


On 2 November 2008 the former French Prime Minister, Michel Rocard, was reported in Le Monde as saying that “mathematicians are guilty (unwittingly) of crimes against humanity” in reference to the financial crises that engulfed the world that year. The following March, our own Financial Services Authority, in their review of the financial crisis, listed one of the causes as “a misplaced reliance in sophisticated mathematics”, and pointed their finger at a technique known as Value at Risk (VaR) (see the FT's response at  Maths and markets and my own comment at Maths and the Markets )

A series of events taking place in Edinburgh through April, as part of the Edinburgh International Science Festival and Maths2010, the largest meeting of mathematicians in the UK for five years, will address the question of the role of mathematics in finance, and correct any misconceptions that French premiers and UK regulators might have had – since the FSA have revised their assessment on consideration of the facts.

On April 8 at 11:30, Professor Paul Embrechts, an internationally recognised expert on financial risk management will give a public lecture “Did mathematics really blow up Wall Street”. Paul’s talk will focus on what went wrong; why it went wrong and how, by finance and mathematics working together future crises can be avoided.

The following week, at 8pm on 14 April, Gillian Tett, the Markets Editor at the Financial Times will chair a discussion between Professor Donald Mackenzie, a sociologist at the University of Edinburgh, Terri Duhon, who was involved in the innovation of the financial products traded by the banks and Dr Tim Johnson, a mathematician at Heriot-Watt.

Gillian Tett has emerged as one of the leading authorities of on the credit-crisis, based on her understanding of the activities the banks were involved in, which she describes in her book Fool’s Gold. Donald Mackenzie has been observing the financial markets from his perspective of a sociologist of science and technology for over a decade. He is regarded, both within the industry and by research mathematicians, as having some of the clearest understanding of how and why the mathematics technology failed. Terri Duhon worked for J.P. Morgan when the American investment bank developed the VaR technology and pioneered the use of Collatrorallised Debt Obligations. However, while J.P. Morgan innovated it did not engage in the reckless activities that bought Lehmans down. The key points of Terri’s experience being that not all banks got it wrong and financial innovation is not intrinsically dangerous. Finally Tim Johnson can give insights on the, surprisingly, close relationship between maths and finance and how science can learn as much from finance as finance can learn from mathematics.

Despite the very different backgrounds and perspectives of the panellists, it is likely that there will be some agreement in their conclusions, and like Paul Embrechts’s views, the solution is for mathematicians, social scientists and financiers to work more closely, and also for the public to become more involved in finance, just as society is involved in medical or energy technology.

Gillian Tett mentioned the meeting in here FT column

Greedy, or desperate, bankers

I am completely bemused.

This morning I hear Robert Peston (the BBC's Business Correspondent) arguing the case of the airline industry, that maybe the scientific advice is too conservative and maybe airplanes could fly through the ash cloaud.

The point is that airplanes have been shown to fall out o f the sky if they fly through ash. Clearly not all planes do this but some will. An airline, facing bankruptcy will be risk seeking and so is going to be comfortable about losing a plane or two, may happen, may not but being grounded will result in failure.

What the airlines will do is force their customers to make a choice - to fly or not to fly. Customers with tickets will be faced with an impossible decision. Do I risk death or risk losing the airfare? This is an unfair choice to put on the public.

Above all, I cannot believe that Peston has not learned the lesson of the credit crisis. Businesses will take unacceptable risks to remain in business, and typically it is the public who end up bearing those risk. Banks and regulators ignored the advice of scientists, if we allow the airlines to ignore the advice, we deserve extinction.

The whole of western science is based on financial maths

A historian Joel Kaye has written widely on the development of science in medieval Europe. In Economy and Nature in the Fourteenth Century he presents a thesis that

In broad terms, the conceptual landscape that emerged in the fourteenth century resulted from a striking shift in the models derived to represent order and activity in the natural world: from a static world of numbered points and perfections to a dynamic world of ever-changing values conceived as continua in expansion and contraction; from a mathematics of arithmetical addition to a mathematics of geometrical multiplication, newly accepting of the approximate and the probable; from a world of fixed and absolute values to a shifting, relational world in which values were understood to be determined relative to changing perspectives and conditions; and from a philosophy focused on essences and perfections to one dominated by questions of quantification and measurement in respect to motion and change. Each of these new directions proved to be of great importance to the future of scientific thought.

Mathematics, Economics and Decision Making

The 2009 Alan Tayler Lecture was delivered by Prof Lord Desai of the London School of Economics and Political Science at the University of Oxford on 30 November.

I did not attend the lecture, but I understand that Lord Desai called for economists to use more sophisticated modeling techniques - i.e. not to rely on single-factor linear models when trying to understand the economy. Makes sense to me.

I shall try and get a copy of the talk.

I also recently attended a talk by Prof Lord Skidelsky who was talking about Keynes, and publicising his book Keynes: The Return of the Master. A key point made by Skidelsky was Keynes belief in "irreducible uncertainty". From the perspective of maths, there is nothing controversial in Keynes is position, the Fundamental Theorem of Asset Pricing, in noting that there are infintely many martingale measure in an incomplet market, makes the same point. As a Russian mathematician has pointed out to me, when economists talk about "rational expectations", ask them under which measure they are calculating the expectation.

Culture clash?

The FSSC report Graduate Skills and Recruitment in The City has the following quotes (p 45) from a graduate recruitment manager at an investment bank

“Sales managers prefer graduates who are academic, with some interest in finance but more social skills with extra-curricular activities e.g. being the Head of the rugby/cricket club. They’re less fussy on the degree subject, but quite fussy in terms of the university they have attended – Oxford, Cambridge, LSE, Imperial.

The [derivatives] trading/research side is much more focussed on the technical. Many of our senior managers are from French universities, with experience of engineering schools and écoles polytechniques in France. They look for expertise in engineering, maths, qualitative [quantitative?] finance. They like Oxford, Cambridge, Warwick”.

This quote resonated by an interview with a former Lehman's executive published in the Sunday Times on 23 August, Lehman Brothers failures exposed:

"Instead of reviewing the bank’s risk management systems, the executive directors would have ndless meetings discussing the corporate dress code as Fuld was a stickler for appearances. A angerous lack of awareness about the technical financial products the bank was playing with didn’t elp matters."

Most people employed in finance are involved in sales and marketing activity, and so the soft skills needed for these roles are frequently highlighted by employers to the likes of the FSSC and Universities. However, the core of the banks' business is is highly quantitative, to quote from p 14 of the FSSC report:

“…[banks] need high level maths skills because that’s how the bank makes money – vanilla roducts have very little margin.”

The financial innovation (or more accurately, the re-introduction of derivative products into financial markets) since the 1970s has changed the nature of banking, has the culture of banking kept up?

Perhaps a solution is to separate financial institutions into "traditional banks", undertaking lending and M&A activities relying on sales and marketing skills and "speculative banks" specialising in trading, derivatives and risk management. However, this is not the only model. Many manufacturing firms, particularly pharmaceutical and oil companies, are based on core expertise in science and engineering but where the majority of employees are involved in sales and marketing. So it appears the cultures can co-exist.

It's academic

On of my favourite quotes from the credit crisis comes from the 2/02/08 edition of The Economist, the article "No Defense" on fraud issues at Societe General, states

"In common with other French banks, SocGen was also thought by many to take an overly mathematical approach to risk. “‘It may work in practice but does it work in theory?' is the stereotype of a French bank,” says one industry consultant."

In response to "Of couples and copulas", Prof Paul Embrects sent the following letter to the FT

Dear Sir
The article "Of couples and copulas", published on 24 April 2009,
suggests that David Li's formula is to blame for the current financial
crisis. For me, this is akin to blaming Einstein's E=mc² formula for
the destruction wreaked by the atomic bomb.

Feeling like a risk manager whose protestations of imminent danger
were ignored, I wish to make clear that many well-respected
academics have pointed out the limitations of the mathematical tools
used in the finance industry, including Li's formula. However, these
warnings were either ignored or dismissed with a desultory
response: "It's academic".

We hope that we are listened to in the future, rather than being
made a convenient scapegoat.

The Royal Society calls for more funding of financial maths

The Royal Society published a report on Science, Technology, Engineering and Maths impact on the service sector. They devote a whole chapter (3) to financial innovation, see Hidden Wealth. The report was covered in the FT.

I was contact by the Royal Society in mid-July, this is (their) summary of what I said:

1. The financial crisis was not a homogeneous events; some institutions did (much) better than thers.

2. The root of the problem is in banks mis-pricing assets. When pricing assets the banks were relying on mathematical models. Some banks had "engineered" their own models, others "bought in" models (either by buying "off the shelf" or by hiring individuals from the innovating banks). Banks who treated models as "black boxes" have done far worse than those that had a reputation or developing their own.

3. Many quants (the majority ?) have a background in physics and engineering (there is a factoid that the majority of engineering graduates from top UK universities go into finance rather than engineering - you could check this. Similarly The City is the largest employer of physics PhDs). They understand deterministic systems but only have a rudimentary understanding of modern probability theory (the majority of maths graduates are in a very similar position, I spoke to a maths teacher who had a degree from Glasgow who told me he had not done probability since he was 16).

4. Financial economics developed in the late twentieth century using relatively straightforward maths. The models it produced are "too simple" (see pp 4-12 in "An Engine, Not a Camera"), but are "elegant".

The physicists / engineers were given a simple framework in which deterministic approaches appeared to give definite results. This approach is related to the "Crash of 87" and "When genius failed" in '98.

5. Throughout the industry a belief emerged that maths, "rocket science" removed risk. In the 1990s, mathematicians began to investigate financial models and re-evaluate them. A more rigorous approach to financial economics revealed the naivety of the assumptions that led to the simple models.

6. Because the financial mathematics community is small and peripheral in British science, it lacks authority , and the theory (from the mathematicians) became disconnected from the practice in industry.

7. In Europe, because they approach probability as a branch of analysis rather than from the perspective of statistics, there seems to have been a better appreciation that simple models that fitted data were inadequate. This is a subtle point. The issue is whether the "quants"
really understand stochastic systems. Does the UK education system (schools to universities) produce the volume of people with (basic to advanced) skills in probability and statistics. There is a view that France & Germany are better at this, as demonstrated by the large number of continental scientists and engineers employed in London banks.

8. The credit crisis provides a tangible example and introduction to a wider problem about our poor understandings of complex and stochastic systems. The concern is that many of the global challenges we face involve these sorts of systems. Is our science up to the task?

9. There is a basic competency issue but also a need to develop new mathematics able to describe what Lord May describes as "ephemeral" systems, but in other areas relating to fundamental maths.

Driving by using the rear view mirror

Last October the EPSRC, my funders, asked me to contact the Science Media Centre about media coverage of the credit crisis. This was because there was a risk, which materialized, that mathematics would come into criticism in light of the credit crisis. A the time the SMC took the view, on the basis I was the only person making the point, that the credit crisis had nothing to do with science. Following my "Was the Credit Crisis a Science Story" piece and an intervention by Lord Drayson’s office, the Science Media Centre arranged for a session on the credit crisis to be included at the World Conference of Science Journalists, which I attended.

At the conference I explained the links between modern financial markets and science, gave a “scientific” perspective of what happened and why, discussed the role of mathematics in relation to finance and in relation to science in general, emphasizing the fact that maths is looking to describe complex and stochastic systems. An issue critical to the future development of all of science.

Three other people were on the panel. During the Q&A an Italian print journalist (I believe from the Italian equivalent of New Scientist) reported that his magazine had devoted a whole issue to the crisis and it had generated the most positive feedback the magazine had had all year. At the end of the session, the Chair asked me what the next big story in finance would be, I said the big story is that successful finance is based on good science, the Chair informed me this was not a story that could be sold to her editor.

Following the session a stream of European science journalists came up to me and told me that in their countries, science journalists had been covering the story and generally there had been a very positive response from the public.

In particular I had a lengthy discussion with two German journalists. One reported that the main German TV science magazine show had, also, devoted a whole program to the crisis, and again it had been very well received. What was disturbing was that he was scathing about the level of understanding of the crisis his British counterparts had displayed in the session. The fact that one of them did not recognize the importance of basing finance on good science “completely misses the point”.

We talked about why British science journalists take this view, and the conclusion was it came down to the British tradition of empiricism; science is about gathering data to build models that explain the world. There is a blind spot to Cartesian rationalism, that science also involves abstract reasoning. In relation to the credit crisis this explains the British (and American) dismissal of French Risk managers with the saying that worry “That’s all very well in practice but what about the theory”. The point is, Anglo Saxon risk management techniques were all very well in practice, up until the point they went wrong. French mathematicians (Artzner) had a theoretical basis for dismissing Value at Risk long before British financiers found out that in practice, it was flawed.

The empiricist-rationalist divide also explains why Continental Europeans have a more catholic view of science. If science is about rational thought it encapsulates mathematics, sociology, anthropology and even history. If it is about the interpretation of numerical data, it does not. Ironically, it looks as if to understand one aspect of the credit crisis, the fact that bankers made decisions based on what they saw in their rear view mirrors, seems to be a sociological question, not a question that can be addressed by the physical sciences.

P.S. Gillian Tett (17/7/09) has discussed the sociological interpretation of "herd behaviour".

Maths and the Markets (II)

Following my last post I drafted a letter on behalf of the leading researchers in financial maths in the UK. After some edits, Sir David Wallace, Chair of the Council of Mathematical Sciences, sent this on our behalf to Lord Turner.

The FSA have responded positively to this, as discussed by Clive Cookson in the FT today.

Its a good result for both the FSA, who need the support of mathematicians that is out of their price range to employ and tghe research community will get some sort of support.

There is an angle that is not so positive. The government is keen that academics do more public engagement, and I think this is a good thing. If financial mathematicians do something that is not pointless, they should be able to inform the FSA on good regulatory practice. My concern is that the institutions between the government and academics are not efficient at enabling academics to engage. Typical examples are the RAE/ REF process, which focus academics on learning more and more about less and less until they know everything about nothing. Similarly the Research Councils are keen to facilitate public engagement, but at the end of the day most grant applications are assessed by a panel who are only (in maths at least) in world clas smathematics research - and pure mathematicians don't like being associated with anything as messy as the real world.

These are general comments, there is a specific example. The Technology Strategy Board recently conducted a call to establish a Knowledge Transfer Network in Financial Services. Some of the signatories to Lord Turner's letter submitted a proposal, which was unsuccessful. The question is, did the successful group make any submission to the FSA regarding the Turner Review? My point is that sometime government funding of research activity results in activites that "tick the boxes" but that is about all. These comments are informed by a private conversations with people from a number of consotiums who submitted proposals to the TSB.

Is there a better way? When I explore issues like the shortcomings of the RAE and research councils, members of the government counter that "that is what the (elite) universities want". It was Universities UK that lobbied government to keep the RAE as was/is. The high and mighty like the research councils panels, because it enables them to control science funding. However, people tell me that the US system, managed by the National Science Foundation, is more researcher focussed and less buraucracy focussed.