What Is The Difference Between Mathematics And Statistics?

According to Wikipedia:
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Also with prediction and forecasting based on data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities, government and business.

Acccording to Webster's-Online-Dictionary.org:
Statistics is a branch of applied mathematics which includes the planning, summarizing, and interpreting of uncertain observations. Because the aim of statistics is to produce the "best" information from available data, some authors make statistics a branch of decision theory. As a model of randomness or ignorance, probability theory plays a critical role in the development of statistical theory.

According to Wikipedia:
Mathematics is the academic discipline, and its supporting body of knowledge, that involves the study of such concepts as quantity, structure, space and change. The mathematician Benjamin Peirce called it "the science that draws necessary conclusions". Other practitioners of mathematics maintain that mathematics is the science of pattern, and that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life.
Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences such as economics and psychology. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.

Acccording to Webster's-Online-Dictionary.org:
Mathematics is commonly defined as the study of patterns of structure, change, and space. In the modern formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation. It is a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

Mathematics is a proven formula statistics are based on surveys