Nature of Mathematics

• Mathematics reveals hidden patterns that help us understand the world around us.
• Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
• As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change.
• As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as means of discovering truth.
• The special role of mathematics in education is a consequence of its universal applicability.
• The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep.
• Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty.
• In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols.
• Experience with mathematical modes of thought builds mathematical power--a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives.
• Mathematics empowers us to understand better the information-laden world in which we live.