Abstract This paper discusses, from a mathematician’s point of view, the thesis formulated by Israel Gelfand, one greatest mathematicians 20th century, and pioneers mathematical biology, about unreasonable ineffectiveness mathematics in biology as compared with obvious success physics. The author discusses limitations mainstream today when it is used biology. He suggests that some emerging dire...

I would like tobegin on a personal note, in part to expiatepast sins of omission, partly to allow me to illustrate a major theme of this paper. Though I began the study of economics at Oxford in 1960, to my shame the sole work of Peter Bauer’s that I had read until fairly recently was Indian Economic Policy and Development (1961). Leafing through my copy of Bauer’s book to prepare this paper, I...

Three experiments are reported which investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the au...

T HE IMPORTANCE OF THE THEORY OF RELATIVITY for twentieth-century physics, and the appearance of the Göttingen mathematician Hermann Minkowski at a turning point in its history have both attracted significant historical attention. The rapid growth in scientific and philosophical interest in the principle of relativity has been linked to the intervention of Minkowski by Tetu Hirosige, who identi...

At the International Congress of Mathematicians in 1958 (Edinburgh) N.N. Bogolyubov made our common report "On some Mathematical Problems of Quantum Field Theory" [ 1 ], in which particularly a problem of a rigorous prove of dispersion relations in quantum field theory was discussed and in connection with this it was pointed out the importance of the problem of analytic extension of generalized...

1. Introduction. This article is even more provisional and premature than its title suggests. Its author is entitled to no pretensions. Field theories and especially conformally invariant field theories are becoming familiar to mathematicians, largely because of their influence on the study of Lie algebras and above all on topology. Nonetheless, in spite of the progress in constructive quantum ...

We discuss the automation of mathematical reasoning, surveying the abilities displayed by human mathematicians and the computational techniques available for automating these abilities. We argue the importance of the simultaneous study of these techniques, because problems inherent in one technique can often be solved if it is able to interact with others.