Unsolved Mathematical Problems for K-12
The above are candidate problems. Teachers and mathematicians are gathering in November 2013 to select the final set of thirteen unsolved problems. The results are here:
http://www.youtube.com/watch?v=wV5-wMGRM3g&feature=share&list=PLSrbLTVLJpchKVD0uUOEa2S-eSK9a3Kxp
When: November 15-17 2013
Where: Banff International Research Station
The conference will also discuss whether the $1,000,000 rewards are a good or bad idea. People have strong opinions on the topic. Some see no other practical way of getting these beautiful problems the exposure they need to inspire students worldwide. However, there are problems:
1) The joy of learning for its own sake may be compromised if the ulterior motive of a cash reward gets into the classroom.
2) The Clay Mathematics Institute released the seven $1,000,000 Millenium problems in 2000. Their purpose is to inspire mathematicians and the problems are tough to understand for non-mathematicians. Here is the problem... Nick Woodhouse says that the Clay Mathematics Institute gets about six wrong solutions every day! We need a different mechanism for dealing with "solutions" so we are not inundated.
3) The system that is set up must also try to minimize legal challenges. Again, the Clay Mathematics Institute has had its fair share of bad experiences here.
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For those coming to the November 2013 conference... If you are able, think of some unsolved problems that may be understood by a typical classroom of students. The educators at the conference will help place these into the curriculum and develop them so every child experiences both moments of success and moments of struggle. We need to deliver a sense of accomplishment for all children as they come to understand and work on the unsolved problem.
For example, one potential grade 4 problem is the Collatz (3N+1) conjecture. This unsolved conjecture can be paired with the (3N-1) conjecture which is consistently solved by all grade 4 classrooms: http://youtu.be/R4oINmqHXVY
Here are other potential unsolved problems:
Kindergarten: Packing Squares (Erdős and Graham, 1975)
Grade 1: No-Thee-in-a-Line (Henry Dudeney, 1917)
Grade 2: Sum-Free Partitions (Issai Schur, 1916)
Grade 3: Graceful Tree Conjecture (Ringel, Kotzig & Rosa, 1967)
Grade 4: Collatz Conjecture (Lothar Collatz, 1937)
Grade 5: Play Perudo Perfectly (Atahualpa & Pizarro, 1530s)
Grade 6: RSA Cipher (Rivest, Shamir & Aldeman, 1978)
Grade 7: Egyptian Fraction problem ???
Grade 8: Problem using the Pythagorean Theorem ???
Grade 9: Exponents problem or Three-Body-Problem (D'Alembert & Clairaut, 1747) ???
Grade 10: Inscribed Square Jordan Curve (Otto Toeplitz 1911)
Grade 11: Solutions to x^2 + y^2 + z^2 = 3xyz (Markoff, 1879) ???
Grade 12: ??? (The Sudoku problem on the video above has been solved.)
Here is a tentative list of criteria that you might consider in thinking about suitable unsolved problems: http://www.mathpickle.com/K-12/Criteria.html
