Railway safety in the nineteenth century relied heavily on the use of Commissions to analyse the causes of individual accidents and to decide on methods to avoid repetitions. Stokes played an important role in these. Following the collapse of the Dee bridge in 1847 he carried out the first mathematical study of the deflection and liability to break of a rail due to a moving railway engine. Following the Tay bridge disaster of 1879 he provided expert advice on the possible effects of the wind on railway bridges, and as an important member of the Commission on wind speeds he played a major role in the creation of a series of guidelines that have helped to keep railway bridges safer ever since.

George Gabriel Stokes was one of the giants of hydrodynamics in the nineteenth century. He made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him, the Navier-Stokes equations, are capable of describing fluid flows over a vast range of magnitudes. They play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter we put the primary focus on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier-Stokes equations and the theory of finite amplitude oscillatory water waves. Stokes became an undergraduate at Cambridge in 1837. He was coached by the ‘Senior Wrangler-maker’, William Hopkins and, in 1841, Stokes was Senior Wrangler and first Smith’s Prizeman. It was following a suggestion of Hopkins that Stokes took up the study of hydrodynamics, which was at that time a neglected area of study in Cambridge. Stokes was to make profound contributions to hydrodynamics, his most important being the rigorous establishment of the mathematical equations for fluid motions, and the theoetical explanation of a wide range of phenomena relating to wave motions in water.

This chapter outlines the 'engineering' and 'scientific' approaches to the study of information in classical physics, and the fairly minor changes that came with the arrival of quantum theory in the early twentieth century. The main advances came from the mid-1990s when quantum information theory developed enormously, with important work, theoretical and experimental, carried out in quantum computation, quantum cryptography and quantum teleportation. The concept of information as the fundamental building-block of the Universe also became important, and also the idea that the Universe was a quantum computer.

It is traditional to take virtually for granted [1, 2] that John Bell’s work on the foundations of quantum theory led fairly directly to the founding of the discipline of quantum information theory, and thus it is natural to give Bell credit perhaps for the very existence of this subject.

John Stewart Bell was one of the most significant physicists of the twentieth century; his work has led to a much enhanced understanding of quantum theory and what it says about the physical universe, particularly about realism, determinism, and locality. This book describes Bell's relatively humble origins and his struggles to obtain secondary and university education. It then describes his work at Harwell, where he made important theoretical contributions to the development of particle accelerators, in particular with his pioneering work on strong focussing. Later, he proved the extremely important CPT theorem. At CERN, Bell made a range of important theoretical contributions to elementary particle physics; these contributions include the physics of neutrinos, the existence of different types of neutrinos, the suitability of gauge theory for all physical interactions, and the Adler–Bell–Jackiw anomaly, which shows how classical symmetries are lost under quantum theory. In his work on quantum theory, he criticized the orthodox 'Copenhagen' interpretation of quantum theory, which did not allow the actual state of the physical world to be analysed. He showed that the famous von Neumann theorem, which claimed to show that 'hidden variables' were not allowed in quantum theory, was incorrect; his famous Bell's theorem, or Bell's inequality, showed that any such variables much be non-local. Bell's work led to greatly increased freedom in the discussion of quantum theory, and the development of quantum information theory.

"The Third Irish History of Mathematics Conference." BSHM Bulletin: Journal of the British Society for the History of Mathematics, 30(3), p. 260

The results of measurements on thermal properties of common substances provided a backdrop to the successful development of heat engines in the eighteenth and nineteenth centuries. Early in the nineteenth century, Carnot’s theory of an idealised heat engine provided the stimulus to the ongoing studies, both practical and theoretical, of the properties of materials and of mechanical and thermal processes. By mid-century, the First and Second Laws of Thermodynamics had been established, in various equivalent forms. These clarified the role of energy and its transformations and led to the introduction of a new thermodynamic function, entropy, to complement energy and, from its thermodynamic properties, to clarify the limitations imposed by the Second Law. The understanding of thermal properties of matter from the laws and techniques of classical thermodynamics was enhanced by the introduction of and alignment with statistical thermodynamics. This provided an understanding of properties of assemblies of large numbers of molecules by incorporating the rules of probability theory, leading to a statistical interpretation of entropy. A merger with the well-known laws and processes of chemistry led to substantial advances in chemical thermodynamics, permitting an insightful subsequent reassessment of thermodynamics as a whole.

In his Belfast notebooks, James Thomson demonstrated deep thinking about the nature of heat and work, and his analysis of the lowering of the freezing point of water under pressure was a crucial step towards a complete theory. Throughout this period, James and William Thomson worked together, but when this theory emerged as thermodynamics, it was credited to William, and to Rudolf Clausius and MacQuorn Rankine. James’s claim to be added to the list of founders of the theory is discussed.

Any reader who expects David Kaiser's new book about quantum-information theory to be an orthodox treatise will be disabused by the book's front cover, which depicts a naked man standing on his head, his modesty retained by a bright yellow, strategically superimposed image of a nucleus in a Bohr-type atom.

A: QUANTUM THEORY: AN INTRODUCTORY SKETCH B: INVESTIGATING QUANTUM THEORY C: QUANTUM INFORMATION THEORY

This book presents an account of all aspects of Einsteins achievements in quantum theory, his own views, and the progress his work has stimulated since his death. While some chapters use mathematics at an undergraduate physics level, a path is provided for the reader more concerned with ideas than equations, and the book will benefit to anybody interested in Einstein and his approach to the quantum.