The solution of the gravitational n-body problem

The Resolution of the Great 20th Century Debate in the Foundations of Mathematics

“…In science, the appropriate methodology is qualitative mathematics and modeling [13] that explains how nature works its tool qualitative mathematics. It is the main contribution of [14] and was applied to physics for the first time to solve the gravitational n-body problem [64]. Qualitative mathematics and modeling shifts the subject matter of science from the appearances of nature (natural phenomena) to nature itself and how it works and lifts traditional science to the new science [65] articulated by GUT and its theoretical applications [13] [68].…”

The grand unified theory

“…Classical mathematics directly and indirectly involved with GUT and applications include: Young's generalized curves and surfaces [20,21,23], rapid oscillation [9], Hubble's law [11] and the integrated Pontrjagin maximum principle [2,22].…”

“…Despite these great achievements, long-standing problems of mathematical physics remain such as the gravitational n-body problem [2] posed by Laplace at the turn of the 18th century to prove the stability of the solar system (thought to be our universe then).…”

“…They are: rectified foundations [12], generalized fractals [3,5,9] and integrals [3,5,9], set-valued functions and derivatives [3,5], the new real number system (new reals) [1,6,10], new real line [10], new nonstandard analysis [12], solution of the gravitational n-body problem [2], quantum algebra [3,11,16] and qualitative mathematics. Qualitative mathematics is the crucial factor for the development of GUT as physical theory, i.e., synthesis, summation and integration of the human collective experience and accumulated information anchored on the laws of nature.…”

Chaos, Turbulence and Fractal: Theory and Applications

“…For example, chaos connotes disorder which is not amenable to computation. Therefore, the present methodology of quantitative modeling [7,8] (formerly called mathematical modeling) that describes appearances of nature and natural phenomena mathematically and relies mainly on computation and measurement is inadequate and has left long standing problems of physics unsolved, e.g., the 200-year-old gravitational n-body problem [9], and outstanding issues such as the basic constituent of matter, unresolved. Furthermore, it is known that over 90% of matter in the Cosmos is dark [10] (now updated to over 95% [11]), one of the two fundamental states of matter which is not observable and known only by its impact on visible or ordinary matter, the other fundamental state [12].…”