Open problems and conjectures in Mathematics

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SUMMARY

The discussion centers on the vast number of open problems and conjectures in mathematics, emphasizing that while no exact count exists, there are likely hundreds of thousands of problems being investigated by mathematicians worldwide. The Collatz conjecture is highlighted as a notable open problem, with questions raised about the classification of variants of such problems. The Mathematics Genealogy Project lists approximately 210,000 mathematicians, indicating a significant number of ongoing inquiries in the field. The complexity of defining and counting open problems is acknowledged, suggesting that each mathematician's work contributes to the ever-expanding landscape of mathematical challenges.

PREREQUISITES
  • Understanding of mathematical conjectures and their significance
  • Familiarity with the Collatz conjecture and its implications
  • Knowledge of the Mathematics Genealogy Project and its relevance
  • Basic comprehension of problem classification in mathematics
NEXT STEPS
  • Research the Collatz conjecture and its variants
  • Explore the Wikipedia page on unsolved problems in mathematics
  • Investigate the Mathematics Genealogy Project for insights on mathematicians' contributions
  • Study the methodology for classifying open problems in mathematical research
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Mathematicians, students of mathematics, researchers in theoretical fields, and anyone interested in the landscape of unsolved mathematical problems.

flamengo
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I know this can be a silly question but it's a curiosity of mine and I have no idea what the answer is, so I'll ask anyway. The question is: How many open problems and conjectures are there in Mathematics currently ? I'm sure nobody knows the exact number but an approximation would be nice. Thanks in advance.
 
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I don't think you can count them. There are a few famous ones, a few less famous ones, but every topic a mathematician works on (or plans to work on in the future) is an open problem - otherwise they wouldn't work on it. The Mathematics Genealogy Project knows about 210,000 mathematicians, most of them still alive, the actual number will be even higher, so going by that we have at least hundreds of thousands of problems someone is investigating.

How do you count open problems? The Collatz conjecture is certainly an open problem. If you replace the 3n+1 rule by 5n+1, is it a different open problem, or is it a variant of the same open problem? If it is different, we can generate infinitely many open problems. Otherwise: How much do we have to vary it until we count it as separate problem?
 
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