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"In 1723, received his Master of Philosophy with a dissertation that compared the philosophies of Descartes and Newton. At this time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics.[5] Euler was at this point studying theology, Greek, and Hebrew at his father's urging, in order to become a pastor, but Bernoulli convinced Paul Euler that Leonhard was destined to become a great mathematician. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono." - From the English Wikipedia

At what age did Euler got his first PHD? Some sources say that it was the third time Euler promoted in 1726. This is really confusing.

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To my knowledge, Euler's only scientific thesis was "De Sono", and it was submitted in 1726, though some sources say it was in 1727, because he published it that year. He also submitted theses in other areas, but I don't think they awarded him the title of Doctor of Philosophy for those works. It's not even clear to me that he ever earned something called a Ph.D. at all. Anyhow, the whole origin of the Ph.D. system is quite archaic, and I don't think it would be proper to compare how academics earned degrees then, to how they earn them now.

I might note that you can find Euler's math genealogy page here, and if you have a PhD or are going to earn one soon in mathematics, with high probability you can find a way to trace your academic lineage (e.g. via your dissertation adviser, and then his/her adviser, and so forth) back to Euler.

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"you can find a way to trace your lineage back to him." - Sorry, but I don't understand this sentence. So, He was 18/19? –  user1095340 Feb 4 '13 at 22:59
    
I've made some changes to my answer. Based on a biography I checked out, his dissertation is considered to be equivalent to a modern day doctoral thesis, but it is implied it was not literally a Ph.D. –  Christopher A. Wong Feb 5 '13 at 0:36

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