Pure mathematics

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/pure-mathematics

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. How big is Pure mathematics?Set Theory, Logic, Number Theory, Abstract Algebra, Topology, Analysis
2. What is the primary domain?Abstract mathematical concepts, structures, and theories
3. What is the core method?Axiomatic systems and rigorous logical proof
4. Why do mathematicians study pure math instead of making things like toys?They are curious about how numbers and shapes work on their own. The patterns they find can later help build technology and science.
5. How do mathematicians prove something in pure math?They start with basic facts called axioms and use logical steps to build new statements called theorems. They can use tricks like direct proof or proof by contradiction.

Axiomatic System: A set of axioms and logical rules used to derive theorems and build a mathematical theory.
Conjecture: A mathematical statement that is believed to be true but has not yet been formally proven.
Topology: The branch of mathematics concerned with properties of geometric objects that are preserved under continuous deformations.