Fuzzy Mathematics & Science of Ahangyol

Mathematics: An Experimental Science

Albert Einstein once said “You can confirm a theory with experiment, but no path leads from experiment to theory.” But that was before computers. In mathematical research now, there’s a very clear path of that kind. It begins with wondering what a particular situation looks like in detail; it continues with some computer experiments to show the structure of that situation for a selection of sma...

Mathematics and Science

Mathematics : Art and Science

Editor's note: Apart from some minor changes, the following article is a translation of the text of a lecture delivered, in German, at the Carl Friedrich von Siemens Stiftung, Munich, on May 7, 1981, and, in a slightly modified form, as the first of three "'Pauli-Vorlesungen", on February 1, 1982, at the Federal School of Technology, Zurich. The Intelligencer requested permission from the autho...

Mathematics for Computer Science

ly, taking a step amounts to applying a function, and going step by step corresponds to applying functions one after the other. This is captured by the operation of composing functions. Composing the functions f and g means that first f is applied to some argument, x, to produce f .x/, and then g is applied to that result to produce g.f .x//. Definition 4.3.1. For functions f W A ! B and g W B ...

Mathematics | the Pure Science?

The philosophy of mathematics provides a severe test for a materialist explanation of science. This is because mathematics is mostly abstract and mathematical theory is rarely tested directly in practice. All the main schools of the philosophy of mathematics | platonism, logicism, intuitionism, formalism | are varieties of idealism. Nevertheless all human ideas, including mathematical ideas, or...