Since John Maynard Keynes rescued a collection of Newton's private papers and declared that "Newton was not the first of the age of reason. He was the last of the magicians" the popular imagination has looked at the influence of esoteric arts on the emergence of Western' science. What is often forgotten is that in almost the same breath, Keynes declared Newton as "one of the greatest and most efficient of our civil servants", in recognition of his work as Master and Warden of the Mint, positions that he held longer than his Chair at Cambridge.

The significance of the relationship between mathematics and finance is often overlooked when considering the development of science. Probability is, to both Poincare and Russell, the foundation of all science, emerged out of the analysis of financial contracts and Bernoulli first identified the number

*e*in the context of interest payments. On a more profound level, historians such as Richard Hadden, Joel Kaye and Alfred Crosby have provided compelling arguments that the uniquely European 'mathematisation' of science came out of a synthesis of commercial practice, following Fibonacci, and scholastic analysis. Copernicus wrote on money before he wrote on planets.While equity options trading dominated the 1980s, today, the Black-Scholes-Merton pricing formula is used more as a gauge of market volatility than to price traded contracts and the problems of finance have moved on to managing the complex interactions of many agents in the economy. It is in recognition of this evolution that the financial world has changed, not just in the last four years but over the past 25 years, that the Institute of Mathematics and its Applications (the British equivalent of SIAM) is sponsoring its first conference on mathematics in finance, to take place in Edinburgh in 2013.

Algorithmic trading is currently the focus of financial innovation. Investors, such as pension funds, will use algorithms implemented on electronic trading systems to , hopefully, optimise their market transactions. Market makers, and speculators, will use algorithms to search the markets for profit opportunities, often executing transactions in milliseconds in high frequency trading. Algorithmic trading is typically light on mathematics, using simple trend following or mean reverting criteria, and relies more on computational developments.

Since the recent Financial Crises society has realised that financial innovation, like any technological development, is not always a good thing. The

*Quant**and**Mammon*report of 1998 called for academics to support banks in innovation, today the emphasis has shifted and the consensus is that academics should be trying to understand the financial system and support society's eyes and ears, the Regulators, as much as the Banks. In response to this, the IMA have invited the Bank of England to help organise the conference and provide guidance on what the Regulators' key concerns are.The Bank of England believes that recent developments in financial mathematics have focused on microeconomic issues, such as pricing derivatives. Their concern is whether there is the mathematics to support macroeconomic risk analysis, how the whole system works. While probability theory has an important role to play in addressing these questions, other mathematical disciplines, not usually associated with finance, could prove useful. For example, the Bank's interest in complexity in networks and dynamical systems has been well documented.

The initial outline of the conference is that it will have three parallel sessions, covering developments in algorithmic trading, the concerns of the Bank of England and contemporary issues in mainstream financial mathematics. For example, in the algorithmic trading stream topics could include data mining, pre-trade analysis, risk management and agent based modelling. As well as the Bank of England’s interest in models of market failure and systemic risk, more esoteric topics such as non-ergodic dynamical systems and models of learning in markets would be interesting. Topics associated with mainstream financial mathematics could include control in the presence of liquidity constraints, Knightian uncertainty and behavioural issues and credit modelling.

In addition to the main mathematics Conference organised by the IMA, the Scottish Financial Risk Academy is planning to organise an "Industry Day" at the end of the Conference.

In addition to the main mathematics Conference organised by the IMA, the Scottish Financial Risk Academy is planning to organise an "Industry Day" at the end of the Conference.

Applied mathematics is developed as a consequence of solving problems. While it is easy to criticise the world's bankers, it is harder to come up with solutions to the complex issues they face. It is always worth remembering that the laws of physics (almost surely) do not change, but finance is constantly transforming itself. Ever since the time that Newton left Cambridge for the City, the UK has built its prosperity on financial innovation, funding the wars with France and the Industrial and Agricultural Revolutions. today financial services account for some 10% of the UK's GDP and it is only fitting that applied mathematicians consider whether they can provide solutions to the difficult problems the sector faces.

The IMA Conference on Mathematics in Finance, scheduled for early April 2013, aims to provide a forum for mathematicians to become more involved in the industry and for industry to become more involved in mathematics, and we would invite any mathematician, academic or practitioner, to attend.

If you would like to register your interest in attending the conference, please contact the IMA.

If you would like to register your interest in attending the conference, please contact the IMA.

Keynes had a much broader view of probability and of its significance for market behaviours (e.g. crashes and sustained depressions) than most. At the same time, many in finance - including bankers - think that Bayesian theory is THE mathematical theory of uncertainty and have accused mathematicians of having much too narrow a view of these issues. The scene is set for an interesting debate.

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