On Counting (1925-1949)

"Numbers are not just counters; they are elements in a system." (Scott Buchanan, "Poetry and Mathematics", 1929)

"We take cognizance of all this and learn it without regard for the things. Numbers are the most familiar form of the mathematical because, in our usual dealing with things, when we calculate or count, numbers are the closest to that which we recognize in things without deriving it from them. For this reason numbers are the most familiar form of the mathematical. In this way, this most familiar mathematical becomes mathematics. But the essence of the mathematical does not lie in number as purely delimiting the pure ‘how much’, but vice versa. Because number has such a nature, therefore, it belongs to the learnable in the sense of mathesis." (Martin Heidegger, "Modern Science, Metaphysics and Mathematics", 1936)

"In earlier times they had no statistics and so they had to fall back on lies. Hence the huge exaggerations of primitive literature, giants, miracles, wonders! It's the size that counts. They did it with lies and we do it with statistics: but it's all the same." (Stephen Leacock, "Model memoirs and other sketches from simple to serious", 1939)

"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition 'natural phenomena' includes all the happenings of the external world, whether human or not " (Sir Maurice G Kendall,"Advanced Theory of Statistics", Vol. 1, 1943)

"Mathematics is one component of any plan for liberal education. Mother of all the sciences, it is a builder of the imagination, a weaver of patterns of sheer thought, an intuitive dreamer, a poet. The study of mathematics cannot be replaced by any other activity that will train and develop man's purely logical faculties to the same level of rationality. Through countless dimensions, riding high the winds of intellectual adventure and filled with the zest of discovery, the mathematician tracks the heavens for harmony and eternal verity. There is not wholly unexpected surprise, but surprise nevertheless, that mathematics has direct application to the physical world about us. For mathematics, in a wilderness of tragedy and change, is a creature of the mind, born to the cry of humanity in search of an invariant reality, immutable in substance, unalterable with time. Mathematics is an infinity of flexibles forcing pure thought into a cosmos. It is an arc of austerity cutting realms of reason with geodesic grandeur. Mathematics is crystallized clarity, precision personified, beauty distilled and rigorously sublimated. The life of the spirit is a life of thought; the ideal of thought is truth; everlasting truth is the goal of mathematics." (Cletus O Oakley, "Mathematics", The American Mathematical Monthly, 1949)