- By Jean-Paul Delahaye on September 21, 2020

Credit: Christina Hemsley

Deep Thought takes 7.5 million years to calculate the answer to the ultimate question. The characters tasked with getting that answer are disappointed because it is not very useful. Yet, as the computer points out, the question itself was vaguely formulated. To find the correct statement of the query whose answer is 42, the computer will have to build a new version of itself. That, too, will take time. The new version of the computer is Earth. To find out what happens next, you’ll have to read Adams’s books.

The author’s choice of the number 42 has become a fixture of geek culture. It’s at the origin of a multitude of jokes and winks exchanged between initiates. If, for example, you ask your search engine variations of the question “What is the answer to everything?” it will most likely answer “42.” Try it in French or German. You’ll often get the same answer whether you use Google, Qwant, Wolfram Alpha (which specializes in calculating mathematical problems) or the chat bot Web app Cleverbot.

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Since the first such school was created in France in 2013 there has been a proliferation of private computer-training institutions in the “42 Network,” whose name is a clear allusion to Adams’s novels. Today the founding company counts more than 15 campuses in its global network. The number 42 also appears in different forms in the film

The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out. For example:

In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins.

The marathon distance of 42.195 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens to announce victory over the Persians in 490 B.C. (The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing.)

Ancient Tibet had 42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.

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The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”

According to a March 6

In the binary system, or base 2, 42 is written as 101010, which is pretty simple and, incidentally, prompted a few fans to hold parties on October 10, 2010 (10/10/10). The reference to base 13 in Adams’s answer requires a more indirect explanation. In one instance, the series suggests that 42 is the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54.

Apart from allusions to 42 deliberately introduced by computer scientists for fun and the inevitable encounters with it that crop up when you poke around a bit in history or the world, you might still wonder whether there is anything special about the number from a strictly mathematical point of view.

The number is the sum of the first three odd powers of twothat is, 2

The number 42 is the sum of the first two nonzero integer powers of sixthat is, 6

Forty-two is a Catalan number. These numbers are extremely rare, much more so than prime numbers: only 14 of the former are lower than one billion. Catalan numbers were first mentioned, under another name, by Swiss mathematician Leonhard Euler, who wanted to know how many different ways an

Catalan numbers are named after Franco-Belgian mathematician Eugène Charles Catalan (1814–1894), who discovered that

For example,

All this is amusing, but it would be wrong to say that 42 is really anything special mathematically. The numbers 41 and 43, for example, are also elements of many sequences. You can explore the properties of various numbers on Wikipedia.

What makes a number particularly interesting or uninteresting is a question that mathematician and psychologist Nicolas Gauvrit, computational natural scientist Hector Zenil and I have studied, starting with an analysis of the sequences in the OEIS. Aside from a theoretical connection to Kolmogorov complexity (which defines the complexity of a number by the length of its minimal description), we have shown that the numbers contained in Sloane’s encyclopedia point to a shared mathematical culture and, consequently, that OEIS is based as much on human preferences as pure mathematical objectivity.

The problem is stated as follows: What integers

For the sum of cubes, some solutions may be surprisingly large, such as the one for 156, which was discovered in 2007:

For

Consider the example of 16, which is double the cube of 2. For p = 1, we get:

The research carried out thus far, which depends on the power of the computers or computer networks used, has produced an ever expanding body of results. This work leads us back to the famous and intriguing number 42.

In 2009, employing a method proposed by Noam Elkies of Harvard University in[[OR: by American mathematician Noam Elkies in 2000, German mathematicians Andreas-Stephan Elsenhans and Jörg Jahnel explored all the triplets

In a 2016 preprint paper, Sander Huisman, now at the University of Twente in the Netherlands, pressed on and found a solution for 74:

The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed:

The conjecture that solutions exist for all integers

The difficulty appears so daunting that the question “Is

The number 42 was difficult, but it is not the final step!