The proliferation of mathematics cranks on the Internet

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The discussion highlights a concerning trend of individuals promoting incorrect mathematical beliefs online, such as the misconception that 0.999... is not equal to 1 and the denial of the existence of fractional numbers. This phenomenon raises questions about the effectiveness of mathematics education in schools, suggesting that it may leave students confused about fundamental concepts. The conversation notes that attempts to correct these misconceptions often fail to resonate with those holding these beliefs. Additionally, it points out a broader tendency for people to reject established knowledge across various fields. Overall, the dialogue emphasizes the need for improved engagement and understanding in mathematics education.
Gigasoft
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I've noticed on other discussion boards, that there is a surprisingly high number of people sharing a set of similar, unshakeable beliefs that contradict basic thereoms in mathematics and logic. Usually, these include:

- 0.999... not being equal to 1, or not existing
- That natural numbers exist, while fractional numbers don't
- The possibility that the definition of something can be untrue
- The belief that they have "proved" constructivism
- That you can start with a physical observation and conclude with a mathematical theorem

Does this indicate that there is something wrong with the way mathematics is introduced in schools, leaving people confused about mathematical and logical concepts and how they are defined? It's interesting that no attempt at explaining why they're wrong, gets through.
 
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Education is a two way street. If students aren't interested, it is hard for them to learn. Also there are a lot of people who like to disagree with "conventional wisdom", even if it correct. This applies to a lot of other areas besides mathematics.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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