Mathematical thinking

"Developing mathematical thinking is about developing habits of mind: defining, systematizing, abstracting, making connections, developing new ways to describe situations and make predictions, creating, inventing, conjecturing, and experimenting (Cuoco et al., 1996)."

From the The Journal of Mathematical Behavior Volume 15, Issue 4, December 1996, Pages 375-402 Habits of mind: An organizing principle for mathematics curricula Al Cuoco, E. Paul Goldenberg, June Mark

There are many aspects to the philosophical, maybe even epistemological, notion of mathematical thinking.

However, in its most basic form, mathematical thinking is the mental process by which a given, quantitative, problem is solved using only established definitions, mathematically or scientifically proven theorems or propositions, and the strictest principles of deductive or inductive logic.

Lessons in logic

Discussions about the essence of logical thought, tenets of formal logic, some common errors in logical thinking (or fallacies), and the surprising mathematical proof that, collectively, we can never know everything using mathematical logic.

Applied mathematical solutions

Some of which also included applications of the Scientific Method to resolve.

Pure mathematical theories

These are hypotheses of a mathematical nature which had no known, at the time of inception, applications in science.

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