Unlike disciplines with empirical backgrounds, mathematics lacks central problems that are clearly defined and universally agreed upon. As a result, the development of mathematics proceeds along a number of seemingly unrelated fronts, which tends to present a picture of fragmentation and division. Adding to the difficulty of evaluating its present state and of (guardedly!) predicting its future, is the fact that during the past few decades mathematics became increasingly isolated from its sister disciplines, and as a result of turning inward there was a marked increase in the level of abstraction and a reinforcement of the ever-present trend to greater and greater generality.
KeywordsBrownian Particle Diophantine Equation Continuum Hypothesis Catastrophe Theory Fundamental Tone
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- 4.Deakin, M. A. B. Catastrophe theory and its applications. Mathematical Scientist 2, 73–94 (1977).Google Scholar
- 5.Fowler, D. H. The Riemann-Hugoniot catastrophe theory and the van der Waals equation. In Towards a theoretical biology,Vol. 4, pp. 1–7. (Ed. V. H. Waddington.) Edinburgh University Press.Google Scholar
- 6.Kac, M. Quelques problèmes mathématiques en physique statistique. Les Presses de l’Université de Montréal (1974).Google Scholar
- 11.Linnik, Y. V. Les nombres entries se pretent-ils aux jeux hasard? Atoms 245, 441–6 (1967).Google Scholar
- 12.Rota, G. C. Combinatorics. Chapter 6 in the present volume.Google Scholar