2. The Nature of Mathematics

Study of Numbers

The definition of mathematics up to 500 B.C. during the period of Egyptian and Babylonian mathematics.

Study of Numbers and Shapes

The definition of mathematics from around 500 B.C. to A.D. 300, primarily concerned with geometry, during the era of Greek mathematics.

Study of Numbers, Shapes, Motion, and Change

The definition of mathematics after the invention of calculus in the middle of the 17th century by Newton and Leibniz.

Study of Numbers, Shapes, Motion, Change, and Space

The definition of mathematics by the end of the nineteenth century and into the 20th century.

Science of Patterns

The modern definition of mathematics, agreed upon within the last thirty years, where mathematicians examine abstract patterns.

Keith Devlin

The person who provided the quote that mathematics is for Making the invisible visible in 2000.

Mathematicians

Individuals, categorized as pure and/or applied, who use math.

Everyone

Practically all people use math, but different people use different mathematics at different times for different purposes.

Pure Mathematicians

Those who study theoretical constructs in math, pursued largely to discover new insights into mathematics itself, seeking to generalize mathematical concepts.

Applied Mathematicians

Those who address problems in the real world, working in all fields of science, engineering, and industry, focusing on forming mathematical models.

Egyptian/Babylonian Mathematics

The period up to 500 B.C. where mathematics consisted almost solely of arithmetic and was largely utilitarian and of a 'cookbook' nature.

Greek Mathematics

The era from around 500 B.C. to A.D. 300 where the interest in mathematics was intellectual, having aesthetic and religious elements, and concerned primarily with geometry.

Theorem

The bedrock of mathematics, which was born when Thales introduced the idea that precisely stated assertions could be logically proved by a formal argument.

Euclid's Elements

The publication in which the Greek approach to mathematics culminated, reputedly the most widely circulated book of all time after the Bible.

Newton/Leibniz

The two individuals who independently invented the calculus in the middle of the seventeenth century.

Arithmetic

The branch of mathematics that studies patterns of number and counting.

Geometry

The branch of mathematics that studies patterns of shape.

Calculus

The study of motion and change, which allows mathematicians to handle patterns of motion.

Logic

The branch of mathematics that studies patterns of reasoning.

Probability

The branch of mathematics that deals with patterns of chance.

Topology

The branch of mathematics that studies patterns of closeness and position.

Abstract Notation

The algebraic expressions, complicated-looking formulas, and geometric diagrams that reflect the abstract nature of the patterns mathematicians study, and are necessary to avoid being prohibitively cumbersome.