Conjecture facts for kids

A conjecture is a smart guess or an idea in mathematics that looks like it's true, but nobody has been able to prove it yet. Think of it like a puzzle solution that seems right, but you haven't shown all the steps to prove it's the only answer.

Once a conjecture is proven to be true by mathematicians, it stops being a conjecture and becomes a theorem. A theorem is a statement that has been shown to be absolutely true using logical steps.

Famous Math Puzzles

For a long time, one of the most famous conjectures was called Fermat's Last Theorem. It was named after a mathematician named Pierre de Fermat, who said he had a proof for it, but he never wrote it down for others to see. For over 350 years, mathematicians tried to find this proof!

Fermat's Last Theorem

In 1992, a British mathematician named Andrew Wiles finally found a complete proof for Fermat's idea. Because it was now proven, it officially became a theorem and was no longer just a conjecture. This was a huge moment in the world of mathematics!

Other Big Conjectures

There are many other interesting conjectures that mathematicians are still working on today. Some of these big math puzzles include:

• The idea that there are no odd perfect numbers (a perfect number is one where its factors, not including itself, add up to the number itself, like 6 = 1+2+3).
• Goldbach's conjecture, which says that every even number greater than 2 can be written as the sum of two prime numbers (like 8 = 3 + 5).
• The twin prime conjecture, which suggests there are endless pairs of prime numbers that are only two apart (like 3 and 5, or 11 and 13).
• The Collatz conjecture, a simple idea about numbers that leads to a very complex problem.
• The Riemann hypothesis, which is about the pattern of prime numbers.
• P versus NP, a very important problem in computer science about how quickly certain problems can be solved.
• The Poincaré conjecture, which was about the shape of the universe. This one was proven by a Russian mathematician named Grigori Perelman.

Ideas That Can't Be Proven

Not every conjecture can be proven true or false. Some ideas in mathematics are so tricky that they can't be decided using the usual rules or "axioms" that mathematicians follow.

The Continuum Hypothesis

One example of such an idea is the continuum hypothesis. This hypothesis talks about the size of different kinds of infinite sets (sets with an endless number of items). It has been shown that you can't prove this hypothesis true or false using the standard rules of set theory.

This means that mathematicians can choose to believe the continuum hypothesis is true, or they can choose to believe it's false, and either choice won't break the other rules of mathematics. It's a bit like choosing a new rule for a game that doesn't mess up the existing rules.

Images for kids

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  A four-coloring of a map of the states of the United States (ignoring lakes).

See also

In Spanish: Conjetura para niños