Mathematics, Science, And Cultural Change

Abstract

According to Roger Bacon (1214-1294), “Mathematics is the gate and key of the sciences. Neglect of Mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world, and what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy”.

Mathematics enables various branches of science draw implications of their observations and experimental findings. A computer is now an inevitable tool in science; its internal working rests on basic mathematics -arithematic to base₂

Mathematics is at the heart of our important scientific theories; Newtonian mechanics, Electromagnetic theory of Maxwell, Einstein’s theory of relativity, quantum theory of Planck etc. Further, vast areas of mathematics grew out of efforts to find solutions to problems in science. We give two examples. The first one is about geometry, also sometimes referred to as the gift of the Nile. The story goes that in the 14th Century B.C., King Sesotris divided the land among Egyptians, each receiving a rectangle of same area, and was taxed accordingly. If anyone lost some of his land during the annual overflow of the Nile, he had to report the loss. An overseer would then be sent to measure the loss and make an abatement of tax. Some sources claim that this is the origin of geometry. The second example is more recent; it is about topology, whose origin is associated with a problem on a bridge. During the 18th century, in the German town of Konigsberg (now the Russian city of Kaliningrad), people enjoyed strolling along the banks of the Preger river, which meandered through the town, and was crossed by seven bridges which ran trom each bank of the river to two islands in the river, with a bridge joining the islands. One question asked is as follows:

“How can you take a stroll so that you cross each of the seven bridges exactly once?”.

Leonhard Eu!er ( 1707 -1783) converted this problem to one on vertices and networks in a diagram. He made general discoveries about networks, and found that the answer to the Konigsberg bridge problem, is in the negative, namely, that it is impossible to take a stroll so that each of the seven bridges is crossed only once! In the process of obtaining this result, he originated a new kind Of geometry, a geometry which does not depend on the size or shape of the figure, but about places, and how they are connected by arcs. Out of this grew the branch of mathematics called ‘Topology”.