Geodesic
Three "key" problems of mathematics on the stage of its origin, the "Harmony Mathematics" and its applications in contemporary mathematics, theoretical physics and computer science
We develop a new approach to the history of mathematics based on the three ?key? ideas of mathematics on the stage of its origin: a count, a measurement and a harmony. Two first ideas resulted in the substantiation of two fundamental mathematical concepts, natural numbers and irrational numbers, and to the creation of number theory and measurement theory that underlie ?classical mathematics?. The ?harmony idea? connected with the ?golden mean? underlies the Harmony Mathematics, the alternative direction of the mathematics development. We claim that the Harmony Mathematics will become a fruitful source for the development of many fundamental theories of contemporary mathematics, theoretical physics and computer science. Algebra and Geometry have one and the same fate. The very slow successes did follow after the fast ones at the beginning. They left science in the state very far from perfect. It happened, probably, because mathematicians paid the main attention to the higher parts of the Analysis. They neglected the beginnings and did not wish to develop those fields, which they finished once and left them from behind. Nikolay Lobachevsky
Classification : 00A30 00A66 
@article{VM_2007_9_3_a5,
     author = {Alexey Stakhov},
     title = {Three "key" problems of mathematics on the stage of its origin,    the {"Harmony} {Mathematics"} and its applications in contemporary mathematics, theoretical physics and computer science},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2007_9_3_a5/}
}
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Alexey Stakhov. Three "key" problems of mathematics on the stage of its origin,    the "Harmony Mathematics" and its applications in contemporary mathematics, theoretical physics and computer science. Visual Mathematics, Tome 9 (2007) no. 3. http://geodesic.mathdoc.fr/item/VM_2007_9_3_a5/