The concept of a division algebra generalizes the real and complex numbers by requiring a multiplication with suitable properties to be defined on a normed vector space. There are actually just two new possibilities in higher dimensions, known as the quaternions (dimension 4) and octonions (dimension 8). Spin, on the other hand, refers to a particular way of realizing rotational transformations in 3 or higher dimensions. The distinctive mathematical properties which emerge are also of great importance in physics, since the description of many elementary particles (quarks, electrons, neutrinos) relies on spin representations. There are some fascinating inter-relationships between spin and division algebras, leading ultimately to concepts such as triality, supersymmetry and exceptional Lie groups. My aim in this talk will be to give an overview of some of these ideas.

Dine in style with a champagne reception followed by an exquisite three course meal (wine included), in recognition of another year of The Archimedeans' success.

The dinner will be held at the Crowne Plaza Hotel on Saturday 4th February at 7pm. Tickets sold out in a week last year, so book now to avoid disappointment - especially if you have any dietary requirements. The (heavily subsidised) prices are £15 for members and £20 for non-members.

Places are limited, so please email Dana (archim-events-manager@srcf.ucam.org) to reserve yours. As seating is pre-arranged, please include the names of the people with whom you would like to sit.

IMPORTANT: Please reserve your place by midday 28th January.

To confirm your reservation, please pay by 2nd February - otherwise your reservation will be cancelled. Please send the payment, by cash or cheque (payable to "The Archimedeans"), to Lovkush Agarwal, Corpus Christi College, or you can pass it to any of the committee members in person.

Alternatively, make an online transfer (make sure you include your name/crsID so we know who the payment is from!): Account Name: The Archimedeans Account Number: 20116386 Sort-Code: 40-16-08

Look - no hands! In this Turing Centenary year... you can now go to a logic talk that doesn't mention Turing machines!! Watch while famous logical trickster Dr Thomas Forster proves the Incompleteness Theorem before your very eyes! No but seriously. The Incompleteness theorem is surely one of the most important discoveries in mathematics since the Greeks. And - equally surely - there has been more nonsense talked about it than any other result in the whole of mathematics. Your host this evening will prove the theorem calmly and soberly and try to cut through some of the nonsense.

Winton is a scientific investment management firm specialising in applying advanced statistical techniques to the analysis of financial markets. We have a large research department made up of highly creative applied scientists with strong statistical knowledge and experience analysing large real world data sets. We are particularly interested in PhD students and postdoc researchers with backgrounds in areas such as computer science, machine learning, pattern recognition, signal processing and related data analysis areas.

Where: The Cormack Room, University Centre, Cambridge.
When: Wednesday 15 Feb 2012, 1.00pm to 2.00pm
RSVP by Friday 10 Feb 2012
To reserve a place at the presentation please email recruitment@WintonCapital.com

The talk will include a Q&A session and a sandwich lunch

Location: Stall G1, Main Hall, Kelsey Kerridge Sports Hall, Queen Anne Terrace, Cambridge CB1 1NA

Time: 10am to 6:30pm Tue 4th Oct and 10am to 3pm Wed 5th Oct

Meet new people, grab a free lunch, and of course, membership at reduced prices.

The UK is in the midst of a reform of the National Curriculum. Creating a Curriculum is hard work and the process creates high emotion: anxiety, anger and righteous indignation. I shall say a very little about that and shall use it as a starting point for the question what every mathematician coming to Cambridge ought to know. I shall propose a way to think about that in terms of what I regard as a special category of emblematic problems. I shall give examples from my own experience and reading but the main aim of the talk is to solicit further examples from the Cambridge mathematics community.

Ice is one of the most powerful agents for environmental change on Earth. We are most aware of that in this country when we drive over potholes after a harsh winter. The same forces weather rocks, bring stones to the surface of fields and create landforms, particularly in regions of permafrost. The ice in arctic regions keeps our planet temperate both by storing heat between seasons and by reflecting sunlight. As the oceans freeze, dense brine is generated that drives large-scale circulations, of which the Gulf Stream forms a part. My talk will range over these phenomena, illustrating several of them with experiments, and introduce the ways in which mathematics can be used to make predictions.

LCP is one of the UK's leading actuarial partnerships. We are looking to recruit up to 18 highly numerate individuals to train as actuarial consultants within our pensions, general insurance, investment and business analytics consultancies.

Come and meet us for drinks and you will be able to experience why we have a reputation of being an exceptionally friendly and professional firm. You will also learn about work, the extensive training programme and what is it like to study for actuarial exams

We will also be attending the Cambridge Careers for Mathematicians Event on 2nd November.

When: 7pm - 9pm
Where: CMS Central Core

Interested in a night of fun, food, and an opportunity to meet other mathmos? Come along to our games evening! Board and card games (including but not limited to: Set, Cluedo, Blokus and Balderdash) will be provided, but please do bring along your personal favourites. Snacks and drinks will also be supplied. Feel free to drop in for just a game or two, or better yet, come for the entire two hours!

Free for members, £2 entry for non-members.

Our staff will be on hand to speak to students and answer and questions they may have.

Will it be a continous night of laughter? Will the humour have no upper bound? Will there be any maths references at all? Only ICE has the answer!

Location: MR2 in the Centre for Mathematical Sciences (CMS)

We are holding an evening presentation for Mathematics students in Cormack Room, University Centre, time TBA.

Apparently simple questions about adding whole numbers have led to some beautiful mathematics, involving ideas that at first sight seem to have nothing to do with the integers. In this talk, we'll get a flavour of this area, and we'll see how two great Cambridge mathematicians from the last century played a key role. We'll also see an application of the important fact that 1 is the smallest positive integer.

A scorpion wants to catch a beetle, a porter wants to catch a student, and a lion wants to catch a man. The beetle, student and man do not want to be caught. What tactics should they adopt?

To bridge the time between exams and May Week, why not go punting while others are still sitting in the library? Meet at 10:45am, 13th June, at The Avenue (Trinity backs). Click here for a map.

The best thing about it? It's free for members! Refreshments will be provided. Places are limited, so please get in touch with Dana (dm537) to reserve a place.

Another year, another round of lectures, work, and exams. But with the end just over the horizon, we are excited to be able to offer the perfect antidote by inviting you all to the annual Science Societies' Garden Party! Come and relax with us in the sun* with a cool glass of Pimms and lots of delicious food. There will also be a Band and and non-alcoholic drinks for those already feeling pickled by May Week.

Here are the details:

Venue: Springfield Gardens, Harvey Court (Gonville and Caius College) - Along West Road from Queen's Backs. Click here for a map.

Time: 14:00 - 17:00, Tuesday 21st June

Price £3 / £5 Members/Non Members** - Pay on the door

Hosted by: The Archimedeans, BioSoc, CUPS and SciSoc

We look forward to seeing many of you there! Spaces at the Garden Party are unfortunately limited by capacity so make sure to arrive promptly to ensure a place.

*Sun not guaranteed
** Members of The Archimedeans, BioSoc, CUPS or SciSoc

In his unique and appealing style, Prof. Siksek will shed light on the following questions:

(i) Given a Diophantine equation, what information can be obtained by following the strategy of Wiles' proof of Fermat's Last Theorem?

(ii) Is it useful to combine this approach with older approaches to Diophantine equations such as Baker's Theory.

Champagne Reception: 6:30pm
Dress Code: Black Tie

Dine in style with an exquisite three course meal at the Crowne Plaza, in recognition of another three years of The Archimedeans' success (or for the 2nd years, the end of their CATAM projects!).

Fabulous food, a champagne reception and inclusion of wine, all at a heavily discounted price of £15 (£20 for non-members), make this evening a wonderful start to the term.

Places are limited, so please email The Events Manager to reserve yours. As seating is pre-arranged, please include the names of the people with whom you would like to sit.

IMPORTANT: If you have dietary requirements that we need to accomadate, you must reserve your place and inform us by 3pm, Thursday 20th January.

To confirm your reservation, please pay by midnight of 24th Jan, otherwise your reservation will be cancelled. Please send the payment, by cash or cheque (payable to "The Archimedeans"), to Philipp Kleppmann, Corpus Christi College, or you can pass it to any of the committee members in person.

Alternatively, make an online transfer (make sure you include your name/crsID so we know who the payment is from!):
Account Name: The Archimedeans
Account Number: 20116386
Sort-Code: 40-16-08

In his popular science book about the Millenium Prize problems, Keith Devlin admits defeat in trying to describe the Hodge conjecture, claiming that it cannot be visualised, and advising the reader to give up. In the New York Times, May 25th, 2004, he is quoted: "Mathematics has reached a stage of such abstraction that many of its frontier problems cannot be understood even by the experts".

Obviously this is nonsense, as I shall try to convince you. (But I'll assume a little knowledge of holomorphic functions, so perhaps he's right and that makes you an expert.)

The practical implications of this problem affect all areas of modern life, from data encryption to curing cancer!

The only Millenium problem to be solved to date, and who better to tell you about it then a member of the advisory boards which awarded the Millenium prize.

How far can you get before being chased down by a raptor?
How many raptors can you fit in a hypercage?
Can you avoid being stabbed by the Applied Mathmo?

Find out at The Archimedeans' Annual Problems Drive.

Date: Sunday 13th March
Time: 14:00 to 15:15
Location: CMS Core

Compete in pairs in this light-hearted contest in witty mathematics and mathematical wit.

There'll be various prizes for different achievements, and of course, lightrefreshments for all those who attend.

There is a limit on the number of pairs that can compete, so please reserve your pair's place by emailing the Events Manager.

Be at the AGM where there will be an annual review, a chance for you to raise any questions and the election of the new committee!

This is your opportunity, not only to continue the success of the Archimedeans, but to make the Society even better. It's an experience we highly recommend: it's enjoyable, you will learn a lot during your time on the committee, develop old and new skills (teamwork, communication, etc., which is always handy on the good ol' CV) and, not to mention, meet new people!

The available roles, along with their descriptions, can be found here.

Please do consider joining the committee. Even if you're unsure which position to run for, we are keen to hear from anybody who is interested and will come up with a solution which works for you.

Please submit your nomination by e-mailing (with subject "Archimedeans Nomination") the following information to the Secretary:

Name:
College:
Position:
Name of Proposer:
Name of Seconder:

Please note that the Proposer and Seconder must also be current members of The Archimedeans.

Cockcroft Lecture Theatre
Find out about the most widely known of the Millenium Maths problems. (Even Hollywood recognises it with the film Proof!)

Meet new people, grab free pizza and of course, membership at reduced prices.

Find out about the closest thing to a sure thing in your career as an actuary. Join our sponsor, Lane, Clark and Peacock for drinks. For more info visit www.lcp.uk.com

A rare opportunity to hear a talk from a winner of the Senior Whitehead Prize, holder of an 'Erdos Number' of 1 and simply one of the best speakers in Mathematics. In this talk, he will present three results by some of the most eminent Cambridge mathematicians of the last century.

Find out about a career in one of the fastest growing quantitative proprietary trading firms.

What is a Turing machine? And is a Turing Machine smarter than a 10 year old? There's only one way to find out, of course ... yet by thinking about it instead, Turing reckoned they were about the same. We shall try to say why, and to offer a brief panorama of the mathematics behind computers, leading on to some tantalisingly simple-sounding open questions.

Gloucester Research Ltd invites Part III Maths and PhD students in Maths, Physics, Engineering, Statistics, Computer Science and Computational Biology to join them for an informal evening with drinks and canapes. Find more info here.

The Yang-Mills equations govern the strong nuclear force which binds quarks inside the proton and neutron. They are a generalization of Maxwell's equations, though unlike Maxwell's equations, they are non-linear and correspondingly much harder to solve. This talk will describe the equations and explain some expected properties of the solutions, including the meaning of the famous "mass gap".

Will it be a continous night of laughter? Will the humour have no upper bound? Will there be any maths references at all? Only ICE has the answer!