# 42 is the answer to the question

## Finally: The mystery of the number 42 has been solved

The number 42 owes its fame to the science fiction classic "The Hitchhiker's Guide to the Galaxy" by Douglas Adams. In the cult book by the English author, 42 is the simple answer that the planetary supercomputer Deep Thought spits out after 7.5 million years of computing time to the question "about life, the universe and everything else". This answer made history, the band name Level 42 is one of its pop-cultural precipitations.

Until recently, the number 42 itself posed a tricky number-theoretical puzzle. Mathematically formulated halfway exactly, it is about a Diophantanian equation, which is nothing more than a polynomial function with integer coefficients and integer solutions, as every number theorist knows.

### Not difficult to understand

That sounds complicated, and in terms of number theory it is too. But the concrete problem that has been researched since 1956 is quite easy to understand: A whole number (in the concrete case 42) should simply form the sum of three whole cube numbers, so we are looking for x^{3}, y^{3} and Z^{3}. Two simple examples to illustrate this

2, for example, can be described as 0^{3} + 1^{3} + 1^{3} represent.

6 in turn is the sum of

2^{3} + (-1)^{3} + (-1)^{3}

You can also use negative numbers like -1, -2, -3.

This becomes quite complicated with some two-digit numbers, for some there is basically no solution: namely for numbers that divide by 9 result in the remainder 4 or 5. These are, for example, 13, 14 and 22. At 33 (does not fall under the exclusion criterion) the mathematicians bit their teeth for a long time before the British Andrew Booker (University of Bristol) was only successful at the beginning of this year, as DER STANDARD reported . Booker's solution:

33 = 8866128975287528^{3} + (-8778405442862239)^{3} + (-2736111468807040)^{3}

Since then, the number 42 has been the smallest number (and also the only one under 100) for which there was still no answer. Booker (or a computer network at MIT) has now cracked 42, as the great YouTube math channel Numberphile recently reported:

By the way, it was also a Numberphile video that a few years ago pointed out to the mathematician these special equations, the still unsolved numbers and a new possible new approach to a solution. And of course there was also a numberphile clip to solve 33.

### A good million math hours

Booker succeeded in the solution In cooperation with MIT mathematician Andrew Sutherland and supported by MIT's own computer network, because 42 needed significantly more computing power than 33. After more than a million computing hours, the supercomputer spat out the quite impressive answer for that number which itself is actually the answer. Booker received it in the form of an email that was little different from what you can read on the next line:

42 = (-80538738812075974)^{3} + 80435758145817515^{3} + 12602123297335631^{3}

The smallest solvable number, which is still waiting for a solution, is now 114 - a number that, in terms of pop culture, of course completely drops off compared to 42.

PS: The answer to the question of how Douglas Adams came up with the number 42 is "very simple", as the author himself explained: "It was a joke. It had to be a number, a very ordinary, rather small number [. ..] I sat at my desk, stared out into the garden and thought: '42 fits'. I typed it in. That's all. "

PPS: If you haven't tried it yet: Enter "the answer to life, the universe and everything" in the Google search field. The solution will (not) surprise you! (tasch, 12.9.2019)

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