Monthly Archives: June 2016

The History of Number Theory

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This post was contributed by James Fisk, graduate administrator at the School of Business, Economics and Informatics. James attended a British Society for the History of Mathematics event hosted by Birkbeck’s Department of Economics, Mathematics and Statistics

bshmBirkbeck welcomed the British Society for the History of Mathematics (BSHM) to its campus on Saturday 21st May, for a conference looking to trace the fascinating, and often surprising, history of number theory.

The event, ‘The History of Number Theory’ had been organised by BSHM with support from the Department of Economics, Mathematics and Statistics and saw speakers trace a history stretching from antiquity to the 21st Century, from thinkers such as Euclid to Fermat and Gang Tian.

Speaking after the event, Professor Sarah Hart said “It brought together a wide array of people; there were many students and academics, but also those with just an interest in the subject. Having such a diverse audience truly enriched the conversation.”

In the second iteration of what both Birkbeck and the Society anticipate to be a continuing annual fixture, the conference welcomed speakers eager to bring to life theories that have engaged mathematicians for centuries (and some, for millennia).

The History of Number Theory - Robin Wilson - Eulers Number TheoryAlmost 100 attendees arrived at Birkbeck for the conference, a place where Louis Joel Mordell, responsible for the Mordell Equation, took a lecturer post in 1913. Ben Fairbairn, Senior Lecturer in Mathematics at Birkbeck, discussed Mordell‘s impact, saying “Mordell’s time at Birkbeck saw him solve two conjectures posed by Srinivasa Ramanujan, the hugely influential Indian mathematician. Of the three conjectures posited in ‘On Arithmetical Functions’, Mordell solved two at Birkbeck, with the third only being closed as recently as 1974!”

The conference also saw Simon Singh discuss the making of his hugely successful ‘Fermat’s Last Theorem’ documentary, produced for the BBC’s Horizon series and chronicling the esteemed mathematician’s problematic last theorem. Those wishing to get a flavour of the event can still find the documentary on BBC iPlayer.

With the conference covering millennia of fierce debate around Number Theory, an anecdote shared on the day by Ben Fairbairn and about Louis Joel Mordell best summarises the human side of the field: “He travelled by a certain train which should have got him to Birkbeck in time. But frequently the train arrived late. He pointed out the discrepancy between promise and performance to the Railway Company, who said that they would do something about it. And so they did: they adjusted the advertised time of arrival and, in consequence, the train now always arrived as advertised, but always too late for him.”

Birkbeck’s Department of Economics, Mathematics and Statistics offer a range of courses covering the material discussed at the conference. You can see how to join the British Society for the History of Mathematics by visiting their site.

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Lost planetary worlds: Evidence of the unquiet early Solar System

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This post was contributed by Birkbeck student, Anja Lanin. Anja attended Professor Hilary Downes’ lecture, ‘Lost Planetary Worlds’ during Birkbeck Science Week 2016.

Solar System

Professor Hilary Downes has been a research scientist in the Department of Earth and Planetary Sciences at Birkbeck for 30 years. Insights from her own and other workers’ research have left her with a strong interest in the evolution of the Solar System. As it turns out, the orderly Solar System we observe today in fact started out as everything but quiet and orderly. In its early days it was a place of violent collisions between planetary bodies. Many of these have been almost completely lost. Almost! We have evidence of their existence, ranging from the macroscopic to the elemental, and this was the subject of Professor Downes’ enthusiastic talk ‘Lost Worlds of the Solar System.’

Theory: Computer models

Starting her talk by showing a real image of a planet-forming region around stars, as observed by telescope, as well as computer models which together may suggest the organised formation of planets within an accretionary disk, Professor Downes moved on to theoretical considerations of a very different-looking chaotic early Solar System.

Computer simulations of Jupiter’s growth, for example, indicate that many planetary embryos were sent onto wildly eccentric orbits. Other models show planets such as Jupiter and Saturn moving repeatedly closer and then away from the sun causing gravitational chaos in the inner Solar System before the system became more settled.

Evidence from our Solar System planets – shaken and stirred!

The audience were then presented with some very odd and interesting facts about our planets. For one thing, they do not orbit the sun in the original plane (the location of the previous accretionary disk) of the Solar System. Some seem to defy the laws of physics by floating above and some below. Furthermore, some of the planets’ axial tilts have gone ‘wonky.’

While Jupiter and Mercury spin textbook-style perpendicular to the plane, all other planets have been knocked around to the extreme that Uranus has been completely knocked over and is now spinning parallel to the plane. Venus is even more special – it is rotating in the opposite direction to all other planets! These characteristics, according to Professor Downes, strongly suggest violent collisions of the planets with other planetary material.

‘Tangible’ evidence: meteorites within meteorites

So what happened to the impactors? We can actually study collisional space debris which comes to us in the form of meteorites. For many of these meteorites the parent body, for example a planet or an asteroid, is known, but, as Professor Downes emphasises, there are many parentless ungrouped meteorites. Perhaps the most interesting of these are brecciated meteorites which contain fragments of other meteorites. What do we learn from these fragments?

 

Real science reveals real mysteries….

As indicated in the talk, planetary science students at Birkbeck are actively accessing technology (e.g. electron microprobe) that allows them to study the mineralogy and basic chemical make-up of meteorites. This is one way that allows them to determine whether or not meteoritic material comes from a classified or unclassified parent body.

Something that cannot be analysed at Birkbeck yet!, but also yields very important clues, are oxygen isotope ratios. Each known planetary body has a unique oxygen fingerprint, so that previously unregistered ratios hint at lost parent bodies. Professor Downes, relating to her own group’s research, points out a particularly interesting brecciated meteorite fragment, which, surprisingly, turned out to be granitic, i.e. it is mineralogically and texturally similar to granites found on Earth (some of us recognise the rock from kitchen counter tops!).

However! – its oxygen chemistry indicates that it comes neither from Earth nor is it related to the other meteoritic material in which it was included as a fragment. It is therefore not related to the asteroid from which the rest of the meteorite is derived. In addition, a strange associated glass is high in sulfur (S) and chlorine (Cl), and no planet in the Solar System except Mars contains sulfur and chlorine. But the oxygen chemistry again suggests it is not from Mars. Thus, this glass may represent another lost planetary body or planet possibly disintegrated during the early collisional chaos!

There are many examples of odd, unexplained finds in meteorites. Even opal, which we recognise as a semi-precious stone, has been found by Profesor Downes and her colleagues, although its extraterrestrial origin is still unclear. Perhaps a water or ice-rich meteorite crashed into an asteroid and all that is left of this ice or water world is this little piece of opal?

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Eric J. Hobsbawm Memorial Lecture 2016: “European History in the Age of Hobsbawm” by Sir Richard J. Evans – reflections from a Hobsbawm Scholar

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This post was contributed by Antonio E Weiss, a PhD student in the Department of History, Classics and Archaeology and a 2014 recipient of a Hobsbawm Schoalrship.

Sir Richard Evans’ lecture on “European History in the Age of Hobsbawm” provided an excellent opportunity to reflect on the nature and legacy of a towering figure of modern history in general, and Birkbeck College in particuar.

Evans opened with a 23 year-old Eric Hobsbawm on the verge of tears in 1940 as he packed his books in preparation for serving on the front-line in the war effort. Hobsbawm had a voracious appetite for a wide variety of literature – Balzac, Melville – and eclectic musical tastes, spanEric Hobsbawmning jazz and classical. As part of his latest work, Evans has had access to Hobsbawm’s diaries, providing a fascinating window into Hobsbawm’s life. It is Hobsbawm’s keen and wide interest in culture, of all forms and varieties, but with a particularly European focus, which helps to explain his emergence as such a special and influential figure of the twentieth century.

As a hugely grateful recipient of the generous Hobsbawm Scholarship Fund (to fund trips to Scottish and Irish archives as part of my PhD research on the history of the British state’s use of management consultancy firms in the twentieth century), Evans’ words on the unique contribution of Hobsbawm to historical scholarship made me reflect on the great privilege it is so receive support from the Fund. As Evans identified, The Age of Revolution (published in 1962 and the first of Hobsbawm’s trilogy of books on the “long nineteenth century”) was distinctive for two, critical, reasons. First, in an era when the focus of British historian was on nationalism and nation-states, Hobsbawm took a transnational approach, spanning his inquiry across countries. And second, highly influenced by the Annales School, Hobsbawm’s elevation of the importance of economic and social history, was in marked distinction to the focus on political and diplomatic history at the time, favoured by figures such as A.J.P. Taylor.

So much has been written and discussed about Eric Hobsbawm’s relationship with the Communist Party and his writings as a “Marxist historian” that attention has, potentially, been deflected from the enduring legacy of his contribution to history as a discipline. It is not hard to see the impact of Hobsbawm on my own research, even though the time and subject matter may initially appear far removed from Hobsbawm’s own historical concerns.

My research, on consultancy and the state, takes an emphatically transnational approach as it seeks to understand the transmission of ideas on management and managerialism from the United States to Europe in the postwar period; this is in a similarly vein to the transnational concerns Hobsbawm brought to the fore in The Age of Revolution. And to understand the relationship between consultancy and the state requires an appreciation of the economic and social trends and forces at play as Hobsbawm achieved in his work; not the mere machinations of political elites.

Evans, in responding to a question from a full floor, responded that Hobsbawm’s legacy was hard to pin down because it was so diffuse and general. It is precisely this diffusion which is so impressive – it can be seen in the multidisciplinary nature of current historical research, in the recognition of the importance of more than just policy and diplomacy in historical inquiry, and in the shift to the scientific and analytical method, away from narrative history. Hobsbawm’s legacy as a “Marxist historian” is huge, but it is his influence on history as a discipline which I feel even more keenly.

Recognizing Entrepreneurial Universities in Academic Rankings

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This post was contributed by Matthew Jayes of Birkbeck’s School of Business, Economics and Informatics. The article concerns an international education project founded by Birkbeck visiting professor, Henry Etzkowitz – who is also a member of Birkbeck Centre for Innovation Management Research (CIMR)

CIMR logo

Initial results and new projects aimed at crediting academic contribution to economic and social development as well as publication and educational activities in international university ranking systems will be announced at Global Entrepreneurial University Metrics (GEUM) Meet.

On 3-5 June 2016, the International Triple Helix Institute (ITHI) in cooperation with the Triple Helix Association (THA) will host the second GEUM workshop in Palo Alto, Silicon Valley, USA.

The Global Entrepreneurial University Metrics initiative (GEUM) is an international Working Group initiated by the International Triple Helix Institute (ITHI), CWTS Leiden University, and the Psychology in the Public Interest Program, North Carolina State University, under the umbrella of the Triple Helix Association. The scope of the GEUM is to catalyze the development of new metrics including entrepreneurship, gender and diversity and furtherance of the public interest in University ranking systems.

Professor Henry Etzkowitz, of Birkbeck Centre for Innovation Management Research (CIMR), and GEUM project founder, said: “Most global University rankling systems privilege publication activity, with the effect of driving out other academic contributions to the economy and society. The purpose of the GEUM initiative is to broaden input into what is ranked and how ranking is accomplished.”

The initiative, led by Professor Etzkowitz – who is also President of the ITHI/THA – coordinated by Alexander Bikkulov (Co-ordination Manager), and with Dr Chunyan Zhou as Proposal Coordinator, begun with seven country teams from:

  • Austria
  • Brazil
  • China
  • Finland
  • The Netherland
  • Russia
  • The US

It was kicked off during a first workshop held on 22-23 June 2015 in Leiden (the Netherlands) supported by the U.S. National Science Foundation (NSF).

GEUM has already produced some new results since the first research projects from the initiative break through: Brazil, Finland, Austria and Russia have conducted the GEUM studies in their countries and will present the results in the workshop that will move between Dinah’s Garden Hotel, Stanford University and a prototypical Silicon Valley “garage Setting” this week-end.

“First GEUM Workshop was a good kick-off for many research teams involved – including Russian team,” says Alexander Bikkulov, Head of Center for Project Development and Fundraising at ITMO University (Russia).

“We can see this in a number of successful projects started in 4 countries during the year. And we definitely see the positive impact of having strong international contacts – both in strengthening the applications for grants and in real exchange of ideas and expertise.”

The founding country teams (Austria, Brazil, China, Finland, Holland, Russia, U.S.A) will be joined by project teams-in-organization from Japan, Spain and the U.K.

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