Role of the number systems in mathematics progress Bergman's discovery has a certain relation to such the oldest mathematics branch as "The idea to represent all numbers by the 9 numerals giving them, in addition to the form value, still the position value is looked as much simple that just from behind this simplicity there is difficult to understand how much it is astonishing. How it was difficult to come to this method we can see on the example of the greatest genius' of Greek's learning Archimede and Appolonius for whose this idea was hidden".
Leonardo Pisano (Fibonacci) in his work "Liber abaci" (1202) came forward as the convinced supporter of the new enumeration. He wrote: "The nine Hindi numerals are the following: 9, 8, 7, 6, 5, 4, 3, 2, 1. Using these numerals and the numeral of 0 called "zephirum" in Arabian, one may write some number". Here Fibonacci used the word
However modern computers are based on the "binary" number systems. Who discover the binary number representation and binary arithmetic? The discovery of the binary representation of numbers is ascribed to the Chinese Impair Fo Gi who lived in 4 millennium BC. However the famous German mathematician Leibnitz elaborated the rules of the binary arithmetic in 1697.
Leibnitz did not recommend the binary arithmetic for practical calculations instead the decimal number system but predicted that Brilliant Leibnitz's prediction was realized only in 2,5 centuries when the outstanding American scientist, physicist and mathematician John von Neumann suggested applying just the binary number system as the universal method for computer information coding ("John von Neumann principles").
Thus, many outstanding mathematicians claimed that the discovery of "positional principle" of number representation is one of the epochal mathematical achievements for all mathematics history and the same positional number systems played a revolutionary part both in the theoretical development and in the practical applications of mathematics. In Greek's mathematics achieved the high standard for the first time the mathematics is divided into two parts, the "higher" mathematics, to which geometry and number theory belonged, and the "logistics", the applied science about the technique of arithmetical calculations ("school" arithmetic) and methods of geometric measuring and construction. Already since Plato's time the "logistics" was considered as the "lowest", applied discipline, which did not belong to the range of the scientist and philosopher education. The scornful attitude to the "school" arithmetic and its problems and also an absent of some serious need in creation of new number system in computational practice, which was satisfied fully by the decimal number system and by the binary number system (in computer science) is a reason why mathematics did not attract its attention to development of number systems. And in this field modern mathematics did not move ahead far in comparison to period of its origin. However, situation changed sharply after appearance of modern computer science! Just in this field an interest in new methods of number representation and in new computer arithmetic appears. That is why appearance of Bergman's number system, which turns over our ideas not only about number systems but also about number theory in general can be considered as the revolutionary mathematical discovery of the 20th century! And we will tell about this discovery at the next pages of our Museum. Follow us! |