Tuesday, 16 December 2014

Stiffening solids by filling them with holes?

Intuition tells us that when you make holes in a solid, it makes the solid softer. As an extreme example, think of a cellulose sponge, which is made from a material that is essentially wood. While you can only bend, stretch or compress a piece of wood with difficulty, you can easily deform a sponge, because it is highly porous. This intuition agrees with classical mechanics theory. So Rob Style from Oxford Mathematics and colleagues were surprised to find that this doesn't work for soft materials. Taking soft rubber-like solids and filling them with lots of microscopic holes, they found that the more holes, the stiffer the solid became. In fact, mathematical modelling shows that this is controlled by similar physics to that which ensures that small bubbles always stay spherical.

The results are important as they suggest that soft composites (like rubbers or gels) can have lots of new, unexpected properties. For example, if you have a soft, expensive solid, you can save material and weight by filling it with micropores without the usual loss of strength or stiffness. Cells in the body can potentially use this effect to change the large-scale properties of biological tissue like cartilage or skin. The research also demonstrates that you can use this effect to cloak small objects elastically in soft materials so that you can't feel their presence by deforming the soft material - a task which has been considered almost impossible to achieve using simple materials.


Monday, 8 December 2014

A 'Penrosian' snowflake for Christmas

What do you want on the front of your Christmas cards? It might seem an idle question, but many companies (and even people) give it serious thought. But surely not mathematicians?  

Well maybe not, but mathematics and mathematicians are very versatile. You could say they are in everything we do. Have a look at our season's greetings e-card, courtesy of Roger Penrose's P1 Tiling and Willam Joseph's design.

Let it snow.


Thursday, 4 December 2014

The History of Mathematics in 300 Stamps - Public Lecture online


Robin Wilson's entire history of mathematics in one hour, as illustrated by around 300 postage stamps featuring mathematics and mathematicians from across the world.

From Euclid to Euler, from Pythagoras to Poincaré, and from Fibonacci to the Fields Medals, all are featured in attractive, charming and sometimes bizarre stamps.


Tuesday, 25 November 2014

What Maths Really Does - Public Lecture online

How has mathematics emerged over recent decades as the engine behind 21st century science? Professor Alain Goriely, Statutory Professor of Mathematical Modelling in Oxford, explains how mathematics provides the framework and models from which physicists, chemists, biologists, medics, engineers and economists build an understanding of our world and construct the tools to improve our lives.


Tuesday, 25 November 2014

Roger Penrose - Forbidden Crystal Symmetry

In this lecture Sir Roger Penrose describes how crystalline symmetries are necessarily 2-fold, 3-fold, 4-fold, or 6-fold. Yet, in the 1970s, 5-fold, 8-fold, 10-fold and 12-fold, ‘almost’ crystalline patterns were found, often beautiful to behold.

These structures have influenced mathematicians and architects alike, notably in the new Mathematical Institute Building where Roger’s own unique non-repeating pattern adorns the entrance.


Thursday, 20 November 2014

Big Data Lecture now online

Viktor Mayer-Schonberger's Inaugural Oxford-Nie Financial Big Data Laboratory lecture is now online. We should welcome Big Data he argues and all the opportunities it brings, but we should also approach it with humility and humanity. 

Viktor Mayer-Schonberger is Professor of Internet Governance and Regulation at the University of Oxford's Internet Institute. The Oxford-Nie Financial Big Data Laboratory was made possible by the generous support of Financial Data Technologies Ltd and is located in the Mathematical Institute in Oxford.




Monday, 17 November 2014

Martin Bridson Elected Fellow of the American Mathematical Society

Professor Martin Bridson, Whitehead Professor of Mathematics, Vice Chairman of the Mathematical Institute and Fellow of Magdalen College, has been elected to the American Mathematical Society “for contributions to geometric group theory as well as its exposition, and for service to the mathematical community.”  In addition to geometric group theory, Martin's main research interests lie in low-dimensional topology and the study of metric spaces of non-positive curvature.

Friday, 14 November 2014

Axiom - art in the Andrew Wiles Building

Axiom Sculpture

As you enter the main entrance lobby of the Andrew Wiles Building you are greeeted by Axiom. Created by artist Mat Chivers, the sculpture is the winner of the Mathematical Institute's Sculpture Competition. The competition invited artists to propose, and eventually create, a substantial and artistically significant sculpture to be placed in the main entrance lobby. We would encourage you all to visit and meanwhile allow Mat to explain the work and its construction.

Cast aluminium
2.2 x 2 x 1.8 m

‘Axiom’ combines three mathematical ideas - symmetry, asymmetry and entropy - in a sculpture that was made using a combination of hand made and contemporary digital envisioning and fabrication processes.

The complex layering used to develop the sculpture is central to the meaning of the work. The rough quality of some of the areas of the sculpture is a result of digital ‘noise’ resulting from the translation between different modes of fabrication and is intended to act as a memory of the journey through the processes by which it was made.

Alluding to some of the ways that we attempt to understand reality, it is an intentionally open visual proposition, designed to invite interpretation depending on what each viewer sees.

Notes on the process
Six equilateral plywood triangles were physically joined in a symmetrical configuration so that they partially enclose space. Polyurethane foam was then injected into the void which expanded, constrained by the containing geometry.

The resulting object (measuring 20 x 18 x 17 cm) was digitally scanned, resulting in a virtual mesh composed of 4.5 million triangles; the number of polygons in the mesh was then reduced to under seven hundred.

A computer script was applied to the data enabling the mesh to be built as a physical object with the dimensions of the individual triangular profile sections of lattice having a width that is proportional to their length.

A seven-axis robotic milling machine was used to make the full size object in high density polyurethane foam, which was then used as a sacrificial core - encased in plaster and burnt out with molten aluminium. The plaster residue from the casting process remains visible on the surface of the sculpture as a subtle white patination.

Axiom Sculpture

Photographs by Quintin Lake

Tuesday, 11 November 2014

It's all too beautiful - Vicky Neale discusses the beauty of mathematics on BBC Radio 4

In two radio programmes next week Oxford Mathematics' Whitehead Lecturer Vicky Neale will discuss beauty. In the first Vicky, together with historian of science Simon Schaffer and philosophers Barry Smith and Angie Hobbs, examine the mathematics and morality of beauty together with its evolutionary origins and benefits.

In the second programme Vicky and colleagues Ben Green and Peter Neumann discuss the particular beauty of mathematics, with a specific emphasis on mathematics and music.



Monday, 10 November 2014

Marcus Du Sautoy in Bangladesh and New Zealand; and Clacton and Camden


Marcus Du Sautoy, Simonyi Professor for the Public Understanding of Science in Oxford, will be in Bangladesh to give three presentations to the fourth Hay Festival in Dhaka, 22-24 November 2014. On December 9th he will be in New Zealand as the 2014 Royal Society of New Zealand Distinguished Speaker, talking about the Art of Mathematics in Auckland, and the following day he will be in Nelson to give the Thomas Cawthron Memorial Lecture.

By contrast in the New Year, on January 19th, he will be speaking to the Clacton Arts and Literary Society about the Secret Mathematicians and on 29 January and 3 February he will be talking to GCSE and A level students as part of AIM conferences in London. The conferences are intended to explain the stimulation and pleasure that academic subjects provide and are 'aimed' at students, teachers and the general public.