By Wolfgang Konig
The ubiquity and value of arithmetic in our complicated society is mostly now not unsure. notwithstanding, even a scientifically layman will be challenging pressed to show elements of our society the place modern mathematical examine is vital. most well liked examples are finance, engineering, wheather and undefined, however the manner arithmetic comes into play is commonly unknown within the public. And who thinks of software fields like biology, encryption, structure, or vote casting systems?
This quantity contains a few good fortune tales of arithmetic in our society – very important components being formed by means of leading edge mathematical study. The authors are eminent mathematicians with a excessive experience for public presentation, addressing scientifically laymen in addition to execs in arithmetic and its software disciplines.
Keywords: arithmetic within the public; arithmetic in structure, biology, weather, encryption, engineering, finance, undefined, nature shapes, physics, telecommunication, and balloting platforms; experimental arithmetic, arithmetic museums, arithmetic for complicated information
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There are lots of bits and items of folklore in arithmetic which are handed down from consultant to pupil, or from collaborator to collaborator, yet that are too fuzzy and non-rigorous to be mentioned within the formal literature. routinely, it was once an issue of success and site as to who realized such folklore arithmetic.
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However, when it comes to issues like risk management which deal with extreme events, the use of these models is highly misleading. After all, we have to keep in mind that these models were not invented for such purposes as risk management. A similar fate of misuse happened to the “4:15 number” of Dennis Weatherstone which was originally designed as a very rough but focused information for the senior management of a MATHEMATICS AND FINANCE 45 bank. But this magic number quickly became very popular under the name of value at risk and used for other purposes, notably for the calculation of capital requirements.
If one encounters this difficulty, one tries once more, one starts to ask questions, one automatically starts a conversation with some other visitor – and finally one gets and sees the solution. Success. Each experiment has a “positive result”. In mathematics, there are also nonexistence theorems (for instance, “there exists no covering of the chess board, from which two opposite corners have been removed, by domino pieces”), but these kinds of theorems do not have a positive effect when dealing with experiments.
As in research, one has to get the right conception, the right idea of what’s going on. And sometimes, after a while of thinking, and sometimes with luck, one finds the solution. As an example we take the “Conway cube”, an invention of John H. Conway. It is a puzzle consisting of three small cubes of side length 1 and six 2×2×1-cuboids, which should be assembled to form a cube. One first calculates how big the cube will be. Even with this knowledge, most people struggle – until they get the idea where to locate the small cubes in the big cube.