In Number Theory, Logic, and Cryptography
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.
December 2020: Thanks to the extra space enabled by HostPapa, files from contributors can now be up to 10MB in size. Also, I have found room on the site for some of my short vignettes, and for some of my IQ-test-like quiz contests from the past year.
November 2020: The Unsolved Problems web site is now hosted by HostPapa. Please let me know of any difficulties or glitches in navigating the site!
June 2020: Because of space limitations, several older contributions have been removed from the UP we site. Prizes for correct solutions to most of the problems listed now stand at US$1,500 and a bottle of champagne.
October 2019: Since Yahoo! has decided to cease hosting groups, the companion discussion group is now at https://groups.io/g/UnsolvedProblems/topics. Postings can be sent to UnsolvedProblems@groups.io.
March 2018: A bottle of champagne is on offer for a neat closed-form approximation to the Apery Constant. For details, please see here
February 2018: Nineteen contributions were published on the site in 2017. Hopefully some will prove useful to those looking at one or more of the problems. Prizes for any correct solution remain at US$2,500 and a bottle of champagne!
July 2017: All fees for publication and donations to the UP site received between 24th July and 31st August 2017 will be donated to the Against Malaria Foundation (AMF).
March 2017: A proposed proof of the non-existence of a Perfect Cuboid by Dr William Wyss has been found to have flaws and has been withdrawn.
October 2015: Contributions published during the period 1st October 2015 to 31st December 2015 will be eligible for prizes of US$5000.
August 2015: New contributions this month include one addressing the search for a Perfect Cuboid, and another looking at some of the puzzles behind Elgar’s Enigma Variations.
April 2015: The problem of finding a semi-magic square of cubes has been added to the site. Any fees received for articles published on the Solutions page between 5th April and 25th June 2015 will be donated to the Make-A-Wish Foundation.
March 2015: Brocard’s Problem has been added to the site. Thanks to Scott Hampton for the suggestion.
February 2015: Eight of the last ten contributions have been related to the Perfect Cuboid problem. They can be found on the Solutions page. Following further testing, the new lower bound for the odd side of a perfect cuboid has been raised to 25 trillion.
July 2014: Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Richard Taylor, and Terence Tao are the recipients of the first Breakthrough Prize in Mathematics. Each of the five mathematicians will receive US$3 million. For more details see here.
April 2014: Several items this month. First, there are several new contributions on the Solutions page, including one which raises the lower bound for the odd side of a perfect cuboid to 8*1012. Second, the developer of this web site is now offering US$1000 for valid solutions to 19 of the 22 problems listed - details on the Prizes page. Third, thanks to various contributors, A$329 is being donated to the Make-A-Wish Foundation.
March 2014: Contributions to the Rational Distance problem and the Perfect Cuboid problem, and revised versions of the papers relating to the decryption of the Dorabella Cipher, have been added to the Solutions page.
December 2013: All fees received between 1st October 2013 and 31st March 2014 will be donated to the Make-A-Wish Foundation. Additionally, the rules governing the $500 prizes have been relaxed so that prior publication on some other sites will not render the author(s) ineligible, and the time limit for acceptance has been extended to 18 months.
July 2013: The Rational Distance problem has been added to the site.
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.
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.
Some earlier items have now been removed
This web site developed and maintained by
Tim S Roberts