Conjecture

High school (ages 12+)
Thinking & Learning

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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/conjecture

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. What is the modern examples?Riemann Hypothesis, P versus NP problem, Hodge Conjecture
2. What is a conjecture in math?A conjecture is a smart guess about something that might be true but hasn't been proven yet. It comes from noticing patterns and thinking it could be true for all cases. It guides mathematicians to explore and try to prove it.
3. Why do mathematicians like conjectures?Conjectures are exciting because they challenge mathematicians to find new ideas and tools. Solving them can create whole new areas of math. Even if a conjecture is wrong, the work still teaches us new things.

Inductive Reasoning: Drawing general conclusions from specific observations and patterns.
Axiomatic System: A system of statements based on fundamental assumptions (axioms) from which theorems are derived.
Mathematical Induction: A proof technique used to establish that a statement is true for all natural numbers.