The law of quadratic reciprocity was discovered for the ﬁrst time, in a complex form, by L. Euler who published it in his paper entitled “Novae demonstrationes circa divisores numerorum formae $xx + nyy$.
Was there no notation for exponents in the time of the great Euler? I did not know how to formulate a query for Google, so I asked a question at Math/StackExchange.
I found out that Descartes introduced the notation for $x^2$. Descartes is famous for his quote "Cogito ergo sum", "Je pense donc je suis" or in plain English "I think, therefore I am". Descartes was my favourite mathematician in secondary school because he invented analytic geometry, one of the milestones in the development of mathematics. Before Descartes geometry was done strictly in the Euclidean way, by compass and ruler. Thanks to Descartes' quadrant and coordinates, geometric shapes like lines and circles could be respresented by algebraic equations. They become objects to do calculations with.
So far about Descartes.
Also, thanks to kind repliers I discovered the bookset "A History of Mathematical Notations, vols 1 and 2., by Florian Cajori". A real gem if you like the history of mathematics. Because the copyright expired one is allowed to freely download the original version. See the comments below the original question at StackExchange for a link to the full version of the book.
- Question at StackExchange