Current Trends in Mathematics

Mathematics has been advancing in theory and applications. These applications have high impact on productivity and innovation. Recent advances have built strong bridges between different areas or subfields of mathematics. Through literature review of advances in mathematics, we present modern trends, including mathematical biology, uncertainties quantification, social networks, medicine and three-dimensional spaces. In mathematical biology, mathematics has enabled researchers to model biological processes, analyze relationships and patterns, optimize biological processes and interpret the complexities of biological systems. We have also revealed that mathematics supplies the statistical framework required to analyze and model uncertainties. Furthermore, in uncertainty quantification, mathematics investigates how variations in inputs affect outputs. Mathematical optimizations techniques help identify the best strategies or parameters that minimize risk or maximize performance while accounting for uncertainty. We have shown that through game theory, optimization, statistical analysis, machine learning and modeling dynamics, social networks have greatly benefited from mathematics. This research also revealed that mathematical algorithms, biostatistics, mathematical models, optimization, and decision theory have greatly added to the progress in medicine. Three-dimensional spaces have benefited from mathematics through vector calculus, coordinate systems, topology, optimization, 3D modeling, and geometric representations. These trends reveal practical applications of mathematics in the human society.