Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Mathematics is essential in many fields, including natural science, engineering, medicine, finance, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory.