Mathematics is the study of patterns and
relationships, including concepts such as
quantity,
structure,
space,
uncertainty, and
change. It evolved, through the use of
abstraction and
logical reasoning, from
counting,
calculation,
measurement, and the systematic study of
positions,
shapes and
motions of physical objects.
Mathematicians explore such concepts, aiming to formulate new
conjectures and establish their truth by
rigorous deduction from appropriately chosen
axioms and
definitions.
Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics.
