In ancient times, so long ago that money was not yet available, people exchanged goods for goods to get what they wanted. For example, there were people who always traded 10 chickens for a pig. However, one day they had to exchange 15 chickens for a pig. At this point, if you cannot do the math, you are in trouble. Calculation is something that has been done by humans since ancient times. In other words, it is impossible to say exactly when and by whom they were made.
By the way, how long ago is this long time ago?　Not 100 or 200 years ago. It is said that about 3,800 years ago, arithmetic was already being taught in schools in what are now Iraq and Egypt. This means that calculation has existed since before that time.
However, the ancient people's calculation methods were quite different from those we learn in school. The method of calculation varied from country to country, but it seems that in many places they used something like an abacus.
The calculations we learn in school today are based on the calculation methods used by the Arabs about 800 years ago.