Few things in nature are as dramatic, and potentially dangerous, as ocean waves. The impact they have on our daily lives extends from shipping to the role they play in driving the global climate. From a theoretical viewpoint water waves pose rich challenges: solutions to the equations that describe fluid motion are elusive, and whether they even exist in the most general case is one of the hardest unanswered questions in mathematics.
Many people's impression of mathematics is that it is an ancient edifice built on centuries of research. However, modern quantitative finance, an area of mathematics with such a great impact
on all our lives, is just a few decades old. The Isaac Newton Institute quickly recognised its
importance and has already run two seminal
programmes, in 1995 and 2005, supporting
research in the field of mathematical finance.
Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check
that it is correct. The New Contexts for Stable Homotopy Theory programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results.
The Strong Fields, Integrability and Strings
programme, which took place at the Isaac
Newton Institute in 2007, explored an area that
would have been close to Isaac Newton's heart:
how to unify Einstein's theory of gravity, a
continuation of Newton's own work on
gravitation, with quantum field theory, which
describes the atomic and sub-atomic world, but
cannot account for the force of gravity.
It's official: the notorious Higgs boson has been discovered at the Large Hadron Collider at CERN. The Higgs is a subatomic particle whose existence was predicted by theoretical physics. Also termed the god particle, the Higgs boson is said to have given other particles their mass. But how did it do that? In this two-part article we explore the so-called Higgs mechanism, starting with the humble bar magnet and ending with a dramatic transformation of the early Universe.
In the first part of this article we explored Landau's theory of phase transitions in materials such as magnets. We now go on to see how this theory formed the basis of the Higgs mechanism, which postulates the existence of the mysterious Higgs boson and explains how the particles that make up our Universe came to have mass.