- Snapshots of modern mathematics
- Pierre de Fermat and Andrew Wiles in Czech Republic stamps
- Stefan Banach (March 30, 1892 – August 8, 1945)
- Guessing the Numbers
- What is mathematics for Ehrhard Behrends
- What is mathematics for Krzysztof Ciesielski
- The Three Ducks Trick
- What is mathematics for Franka Brueckler

# The ultimate question

If you are a reader of the *Hitchhiker’s guide to the galaxy*, you probably know that 42 is the answer to the *Ultimate Question of Life, the Universe, and Everything*. The choice of the number by **Douglas Adams** was quite random, excluding the simple fact that the number liked the writer. Yet the 42 was the protagonist of a recent news related to one of the open problems of mathematics:

Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes?

To find an answer to this question, mathematicians used numerical methods. In particular, **Andreas-Stephan Elsenhans** and **Jorg Jahnel** ^{[2]} using a particular vector space ^{[1]}, searched solutions of the following diophantine equation:

for with . This method was later developed by **Sander Husiman** ^{[3]} to . In the end all numbers, except for 33 and 42, below 100 that are not 4 or 5 module 9 have solutions.

The cubic decomposition of these two numbers come in 2019. In both cases, the protagonist was **Andrew Booker** ^{[4]}. In the case of 33 the solution arrives in march:

It’s interesting to observe that Booker, in abstract, write that he was inspired by a *Numperphile*‘s youtube video:

The solution for 42 arrived at the beginning of september:

In this case Booker obtains his result in collaboration with **Andrew Sutherland**: in this way the list of all numbers less than 100 that are not 4 or 5 module 9 is completed.

Now, in the list of numbers between 100 and 1000, the numbers without a cubic decomposition are: 114, 165, 390, 579, 627, 633, 732, 921, e 975.

- Forgive me for the excessive simplification. ↩
- Elsenhans, Andreas-Stephan; Jahnel, Jörg (2009), New sums of three cubes,
*Mathematics of Computation*, 78 (266): 1227–1230, doi:10.1090/S0025-5718-08-02168-6 ↩ - Huisman, Sander G. (2016), Newer sums of three cubes, arXiv:1604.07746 ↩
- Booker, A.R. Cracking the problem with 33.
*Res. number theory*(2019) 5: 26. doi:10.1007/s40993-019-0162-1 (arXiv) ↩

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