There was no depth to mathematics in Euler's time, he made the depth. He arguably didn't understand analysis on a technical level as well as a modern undergraduate; as I recall, he was confident that all smooth functions are analytic. He had incredible intuition and was able to make great progress by trusting it, but playing around with tools you don't understand stops being effective once a field is past its infancy.
There was no depth to mathematics in Euler's time, he made the depth. He arguably didn't understand analysis on a technical level as well as a modern undergraduate; as I recall, he was confident that all smooth functions are analytic. He had incredible intuition and was able to make great progress by trusting it, but playing around with tools you don't understand stops being effective once a field is past its infancy.