Fractal Geometry and The P vs. NP Problems-Millennium Open Problems

Abstract

The two major unresolved issues in current mathematics and computer science addressed in this paper are fractal geometry and the P vs. NP problem. Benoît Mandelbrot's pioneering work in fractal geometry provides a mathematical basis for comprehending the complex, self-similar forms common in nature defined by non-integer dimensions. Its uses range from computer graphics to erratic systems across several spheres. On the other hand, the P versus A Millennium Prize Problem, NP problem answers the basic question of whether issues with quickly verifiable answers may also be effectively resolved. Emphasizing their status as important frontiers of knowledge, this article explores the basic ideas of both fields, their current knowledge, and the severe consequences their eventual resolution would have on scientific investigation and technology development.