What is the Collatz Conjecture and How Can High Schoolers Have Fun With It?

In summary, the conversation discusses a fun mathematical conjecture called the Collatz Conjecture. It involves multiplying odd numbers by 3 and dividing even numbers by 2 until the sequence eventually reaches 1. It is interesting to play around with using large numbers, and there are online resources available to calculate the results. The Collatz Conjecture generates Hailstone numbers and is further explained on Wikipedia and Numberphile.
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Adam Kohnle
21
5
Hello everyone and I hope you had a happy Easter if you celebrate it and even if you don't, I hope you had happy day at least! I was wondering if anyone knew of any interesting or "fun" mathematical conjecture, equations or whatever that an inexperienced high schooler (me or anyone else curious) could understand and have fun with it. My twin told me of one where you multiply odd number by 3 but divide even ones by 2 and it will always eventually get 1. I could have remembered that wrong but either way it is interesting and fun to mess with by using numbers like 294329058492458430950869839065893685930. Thankfully for a number like that their are online resources that can do the math for you because that would take a while.
 
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1. What is a mathematical conjecture?

A mathematical conjecture is a statement or idea that is believed to be true but has not yet been proven. It is often based on patterns or observations and is considered to be a hypothesis until it is proven to be true or false.

2. How are mathematical conjectures different from theorems?

A theorem is a statement that has been proven to be true, while a conjecture is an unproven statement that is believed to be true. The main difference is that a theorem has been rigorously tested and proven, while a conjecture is still being investigated and debated by mathematicians.

3. Can mathematical conjectures be proven?

Yes, it is possible for a mathematical conjecture to be proven. However, it can be a very difficult and complex process that requires rigorous mathematical reasoning and evidence. Some famous conjectures have taken decades or even centuries to be proven.

4. Why are mathematical conjectures important?

Mathematical conjectures play a crucial role in the advancement of mathematics. They can inspire new ideas and research, and even if they are not proven, they can lead to new discoveries and theories. Additionally, proving or disproving a mathematical conjecture can have real-world applications and implications.

5. Who can come up with mathematical conjectures?

Anyone can come up with a mathematical conjecture, but it is typically mathematicians and researchers who actively work on solving and proving them. However, even non-mathematicians can contribute to the field by proposing new conjectures or providing insights and evidence for existing ones.

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