Probability grew into a fully-fledged branch of pure mathematics in the eighteenth century out of a repertoire of mathematical techniques for solving combinatorial problems generated by an aristocratic partiality for gambling. Huge advances over the last two centuries were largely due to the discipline’s ability to provide a language and methodology for solving very difficult problems in a huge number of areas involving the notion of randomness. Its axiomatisation and secure theoretical grounding within the confines of measure theory, bolstered by its uncanny flair for providing fresh insights and powerful techniques in various disparate areas, bestowed upon it the status of one of the more important fundamental branches of mathematics.
In contemporary mathematics stochastic processes constitutes its most important direction of development with heavy theoretical and practical interest. The keen interest first shown in the subject by theoretical physicists, subsequently entertained by engineers and other academics and researchers specialising in areas of applications of mathematics incorporating randomness, has been surpassed in intensity by that manifested in grandiose ways by researchers working in financial and actuarial mathematics.
Statistics had been for a long time largely identified with its classically central concerns with sampling and hypothesis testing problems. These problems arise continually in almost all attempts at scientifically studying, controlling or managing, contexts involving uncertainty and variability of attributes within groups of individuals. In more recent times the impact of powerful computational techniques and a keener interest in incorporating more changes involving time had developed large areas of interface between statistics and other mathematical areas.
Moreover, a wider, more liberal interpretation of statistical research, both applied and theoretical, reveals a strong underlying current as a more engaging intellectual enterprise within society at large which nowadays cannot be denied its strong cultural undertones. The subject has contributed huge advances in intellectual debate and dialetic while applications amenable to numeric quantification and categorical classification as well as to deep questions some with profound philosophical content have sophisticated their statistical underpinning at a deeper level.
Nevertheless, it could be argued that the proposed solutions to the more delicate problems are still largely in their infancy. In fact, in a more intensive and broad way it is the modelling aspect which has in contemporary times become statistics’ more useful and meaningfully articulated role. This modelling potential is being emphasised and exercised at all levels in a manner which has modified considerably both cultural and technical discourses. But it has also been practised in an abusive and incorrect manner in some instances.
Operations Research historically goes back to World War II when it started off as a compendium of useful algorithms devised to solve practically important problems related to efficient utilisation, storage and allocation of scarce resources. It started off with links to calculus and other mathematical topics which had been nurtured in applications in a number of applied sciences. The management and engineering sciences have been heavily interested, and in many cases productively active, in this area for over fifty years now. Its modelling and simulation aspects have acquired wide recognition ever since computational facilities have become widely available.
Mathematically one could describe Operations Research as being the multifarious academic expression of a recurrent theme in many human transactions and communications: that of performing an activity or a group of activities in an optimal manner relative to some suitably defined objective. Devising and implementing optimisation techniques in increasingly constructive and aggressive ways is the core business of Operations Research.
