After posting about Booker and Sutherland’s cool expression of 42 as a sum of three cubes, Drew Sutherland wrote to say that they found a new way to write 3 as a sum of three cubes:

$569936821221962380720^3 + (-569936821113563493509)^3 +  (-472715493453327032)^3 = 3$.

As explained below, this is both amazing and predicted.  Some earlier computer attempts turned up no new solutions from what Mordell had already found.  Nevertheless, Heath-Brown expected an infinite number of solutions, and even estimated their density.  However, it wasn’t until Booker and Sutherland had cracked the much harder nuts 33 and 42 that this new solution for 3 was found.  It sure helps to have access to half a million cores!

Sutherland gave me permission to quote his message, which tells the latest story well.

[Note: I made minor edits, including some formatting to work in WordPress.] Continue reading →

The number 42 is famous for its occurrence in The Hitchhiker’s Guide to the Galaxy. In 2032, Adele might come out with a new album with 42 as its title.  But today, the fame of the number 42 has to do with its representation as a sum of three cubes.  Continue reading →