Nature of Mathematics – Lesson 1

Vocabulary flashcards summarizing the key terms, concepts, historical artifacts, and philosophical views presented in the lecture on the nature of mathematics.

Mathematics (Aristotle)

The science of quantity.

Mathematics (Auguste Comte)

The science of indirect measurement.

Mathematics (Benjamin Peirce)

A science that draws necessary conclusions.

Mathematics (Bertrand Russell)

All mathematics is symbolic logic.

Mathematics as Invention

The human-created side of mathematics, including symbols, numerals, and methods for representing ideas.

Form of language & Body of knowledge

What are the 2 essential characteristics of mathematics

Ishango Bone

A 20,000-year-old baboon fibula with notches tracking lunar phases and menstrual cycles; evidence of early counting.

Sexagesimal System

inventions of people who live in ancient mesopotamia

Sumerian Scribes

Priest-administrators in Mesopotamia who created early numeration to manage irrigation, land, taxes, and celestial events.

Binary Number System

Base-2 numeral system using only 0 and 1; modern form introduced by Gottfried Leibniz in 1679.

Gottfried Leibniz

Seventeenth-century mathematician who formalized the modern binary numeral system.

Pythagorean Theorem

In any right triangle, a² + b² = c², where c is the hypotenuse.

Right Triangle

A triangle containing a 90-degree angle.

Hypotenuse

The side opposite the right angle in a right triangle; the longest side.

Quantity

Concept dealing with how much or how many.

Form

Geometric shape or structure studied in mathematics.

Pattern

Regular, predictable arrangement or sequence analyzed mathematically.

Change

Variation over time or conditions modeled mathematically.