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UNSOLVED PROBLEMS |
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In Number Theory, Logic, and Cryptography |
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What’s New |
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This page lists recent developments, and changes to the web-site. If you intend to be a regular user of the site, you might like to bookmark this page so that you can see at a glance what has changed since your last visit.
June 2013: Andrew Beal has raised his prize for a proof of, or counter-example to, the Beal Conjecture to one million dollars. See for example here. May 2013: A very interesting article discussing the possible proof of the ABC Conjecture can be found here. April 2013: A contribution to the Riemann Hypothesis has been added to the Solutions page March 2013: A proposed solution to Fermat’s Last Theorem has been added to the Solutions page. February 2013: This site will now offer prizes of US $500 for the solution to most of the problems listed on the site. For details, please see the Prizes page. January 2013: A new unsolved problem, the Lonely Runner conjecture, has been added to the site. December 2012: Lists of Euler bricks, edge cuboids, and face cuboids are available from the Solutions page. October 2012: There’s currently much excitement in the professional mathematics community about Kyoto mathematician Shinichi Mochizuki’s claim to have proved the ABC conjecture. Unfortunately, the mathematics in his proof is so cryptic that a decision on its validity is unlikely for some time. August 2012: The Dorabella Cipher decryption is referred to by Robert Padgett here, and contributions to the Perfect Cuboid problem and the Riemann Hypothesis have been added to the Solutions page. July 2012: An interesting perspective on the Perfect Cuboid problem from Ruslan Sharipov can be found here. May 2012: The DLP (Discrete Logarithm problem) has been added. April 2012: The Diffie-Hellman problem, which plays a central role in modern cryptography, has been added, and there is a new contribution to the Beal Conjecture on the Solutions page. March 2012: Seventh place in the Intel Science Talent Search 2012 was awarded to Anirudh Prabhu of Indiana, who received $25,000 for his investigation of the Odd Perfect Number problem, and his suggestion that odd perfect numbers do not exist. February 2012: A paper describing the solution to the Dorabella Cipher can be found on the web site of the National Cryptologic Museum Foundation (NCMF). October 2011: An interesting paper on the lower bounds for an odd perfect number by Anirudh Prabhu can be found here, and a proposed solution to the Collatz Conjecture has been added to the Solutions page. September 2011: An interesting paper on the Perfect Cuboid problem by Ruslan Sharipov can be found here. More contributions have been added to the Solutions page. August 2011: An interesting article on the Collatz Conjecture by Terence Tao can be found here. July 2011: Some recent research on the Magic Square of Squares is reported here. June 2011: A proposed proof of the Collatz Conjecture by Gerhard Opfer can be found here. A paper on the lower bounds for an odd perfect number can be found on the Solutions page. February 2011: Due to popular demand the Legendre Conjecture has returned, and Grimm’s Conjecture has been added. June 2010: The ABC conjecture and the problem of finding a four-dimensional Euler Brick (or proving its non-existence) have been added to the web site. May 2010: I believe it is now beyond reasonable doubt that the solution to the Dorabella Cipher presented as item #12 on the Solutions page is the correct decipherment. This makes it the only problem on this site to have been solved thus far. December 2009: The Legendre Conjecture has been removed, and Fermat’s Last Theorem added.
Some earlier items have now been removed ——————————–- This web site developed and maintained by Tim S Roberts Email: timro21@gmail.com |
