From Rolf Jeltsch’s colloquium in the Mathematics Department are the following:
 Euler was probably one of the earliest mathematical modellers: for example, he turned the Koenigsburg bridge problem into one of graph theory; and, apparently, he is also the first one to consider control volumes in fluid dynamics while the other hydrodynamicists were looking at the entire fluid under different circumstances and tried to describe its behaviour.
 Euler was pretty open by the then scientific standards; while his contemporaries were trying to keep their discoveries secret, apparently, he wrote expository pieces and circulated them, and, never indulged in priority disputes.
I have read great things about Euler through his great admirer (probably the greatest) Clifford Truesdell. After learning about his open science approach, I am more impressed.