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Why Euler?

Walter Gautschi's Leonhard Euler: His Life,the Man,and His Works remarks how Euler was apt to share in the joy of discovery and give credit to others, writing (pg 30):

Feelings of rancor, due to either priority issues or unfair criticism, were totally foreign to Euler. When Maclaurin, for example, discovered the well-known summation formula which Euler obtained six years earlier, Euler did not object, let alone complain, when for some time the formula was generally referred to as the "Maclaurin summation formula." It may even have pleased him that others hit upon the same fortunate idea. In due time, of course, the formula became justly known as the Euler-Maclaurin summation formula. Another example is Maupertuis's claim for the principle of least action (cf. section 2.3), which Euler had already enunciated before, much more clearly and exhaustively; yet Euler remained supportive of Maupertuis. Euler's forgiving way of reacting to Robins's criticism of the Mechanica has already been mentioned in section 3.3.1.

Sharing ideas with others and letting others take part in the process of discovery is another noble trait of Euler. A case in point is the way he put on hold his already extensive work on hydrodynamics, so that his friend Daniel Bernoulli, who was working on the same topic, could complete and publish his own Hydrodynamics first! It became a classic.

As for Euler's qualities as expositor and thinker, he had what Vladmir Arnold called "the Russian approach" always in mind. Gautschi continues (pg 31, emphasis mine)

Euler's writings have the marks of a superb expositor. He always strove for utmost clarity and simplicity, and he often revisited earlier work when he felt they were lacking in these qualities. Characteristically, he will proceed from very simple examples to ever more complicated ones before eventually revealing the underlying theory in its full splendor. Yet, in his quest for discovery, he could be fearless, even reckless, but owing to his secure instinct, he rarely went astray when his argumentation became hasty. He had an eye for what is essential and unifying. In mechanics, Gleb Konstantinovich Mikhailov [20, p. 67] writes, "Euler possessed a rare gift of systematizing and generalizing scientific ideas, which allowed him to present large parts of mechanics in a relatively definitive form." Euler was open and receptive to new ideas. In the words of André Weil [30, pp. 132-133],

...what at first is striking about Euler is his extraordinary quickness in catching hold of any suggestion, wherever it came from [...]. There is not one of these suggestions which in Euler's hands has not become the point of departure of an impressive series of researches[...]. Another thing, not less striking, is that Euler never abandons a research topic, once it has excited his curiosity; on the contrary, he returns to it, relentlessly, in order to deepen and broaden it on each revisit. Even if all problems related to such a topic seem to be resolved, he never ceases until the end of his life to find proofs that are "more natural," "simpler," "more direct."

I find these qualities very admirable.