Mathematics is the abstract study of subjects encompassing quantity, structure, space,  change,  and more  it has no generally accepted definitiod
Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures bymathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosenaxioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.