"I am certain, absolutely certain that...these theories will be recognized as fundamental at some point in the future."
Sophus Lie said these words more than hundred years ago. We know now that he was right, absolutely right. The notions of "Lie groups" and "Lie algebras" are in the vocabulary of every mathematician and physicist today. Lie's theories are indispensable tools for understanding the physical laws of Nature.
A Beautiful Mind is a touching, emotionally charged film detailing the life of a brilliant academic who suffers from schizophrenia. This affliction slowly takes over his mind and we watch as his life crumbles apart around him.
This book attempts to take a firm grip on a corner of the slippery issue of consciousness. It is directly related to Roger Penrose's earlier, hugely successful work, The Emperor's New Mind. Although much space is devoted to painstaking replies to the criticisms made of the earlier book, this is not simply a sequel. It contains a number of new ideas, some of which are still being actively debated seven years after the book was first published.
Over the last decade, the discipline of neuropsychology has shed light on many aspects of human thought. Brain scans, carefully structured behavioural experiments, and the study of individuals who have suffered brain damage, have taught us much about which abilities are native to humans and which learned; which abilities can be lost and what happens when they are.
This CD ROM, produced by the Centre for the Popularisation of Mathematics at the University of Wales in Bangor, is a most unusual mixture of mathematical exposition and modern art. A central part of the content is a gallery of sculptures by John Robinson, much of whose work takes inspiration from mathematical objects, such as fractals and knots. This work, described by the artist as symbolic sculpture, uses forms such as the logarithmic spiral, and makes connections with the forces that shape our universe.
This beautifully illustrated book by the world's leading authority on African mathematics provides us with a wide-ranging introduction to mathematical intuition in sub-Saharan African cultures. These cultures are extremely diverse and expressive in their creation of designs and motifs that embody geometrical and topological ideas. No one is better qualified to tell us about it than Paulus Gerdes, who has lived and worked in Mozambique for many years.