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## Thursday, October 27, 2011

### Rene Descartes

In the book 'Problem Solving and Number Theory' I read
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.

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

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)