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Do you have any things (mathematical statements, statements about mathematics) you've believed for a long time were true, but now with enough mathematical knowledge you realize were wrong? For example, my high school teacher used to tell the class that all there is to discover in math has already been discovered. Obviously, now, thinking about her statement makes me laugh out loud. What stories do you have?

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marked as duplicate by Dan Rust, user1729, Git Gud, Rick Decker, rschwieb Jun 18 '14 at 13:03

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    $\begingroup$ See Examples of common false beliefs in mathematics at MO. $\endgroup$ – Git Gud Jun 18 '14 at 11:19
  • $\begingroup$ Have you considered returning to your high school to explain to your former teacher that what you were told is wrong? That's if the teacher is still working there. $\endgroup$ – KCd Jun 18 '14 at 12:08
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    $\begingroup$ all there is to discover has already been discovered. Diagnosis: Philistinism brought on by chronic ignorance. Highly contagious, but luckily some are naturally immune. $\endgroup$ – rschwieb Jun 18 '14 at 13:02