# How can you prove the 2 + 2 4?

## Aha : Why is 2 + 2 = 4?

Can you divide any large number by a second? Equipped only with paper and pencil? Such calculations have become more and more difficult for me since I have been relying on calculators or computers in everyday life. Now that the World Association of Mathematicians has opened its headquarters in Berlin, it is time for me to think about mathematics again. But how? In the bathroom there is a tear-off calendar with German poems from the past centuries: language education day after day. Why are there no calendars with arithmetic skills from the past centuries?

You could get on with Gottfried Wilhelm Leibniz. We owe him the first calculating machine for multiplications and divisions and a new intellectual penetration of mathematics. Leibniz begins with the basics: with the establishment of the unity, the one. If one repeats the one successively, the unity becomes multiplicity. There are different names for this: 1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4 and so on. For this type of addition one only needs to know what the definition of the numbers that follow one another is. The actual arithmetic only begins when you no longer add one, but two. Why is 2 + 2 = 4 and not about 5?

The proof that Leibniz gives is short: According to the previous definitions, 2 + 2 is the same as 2 + 1 + 1. From here we can now easily climb the number ladder, because according to the reading we already know: 2 + 1 + 1 = 3 + 1 = 4.

Math is that easy! Ultimately, all additions and subtractions are based on such general principles. Leibniz's four-species calculating machine also only had to add and subtract, because all multiplication and division can be traced back to it. That made the construction of the device easier and should help me again in the future with arithmetic with paper and pencil. Incidentally, Leibniz's machine got stuck in the same places for 40 years as with me: when storing the intermediate results correctly and carrying over tens. *Thomas de Padova*

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