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I am the third most famous member of the talented mathematicians bearing my "family-name."

After getting a doctorate in medicine, I became a Professor of Mathematics at the new St. Petersburg Academy...but eventually quit due to the primitive conditions.

My primary mathematics fame is due to my work involving differential equations (especially related to vibrating strings), though I also was a pioneer in the use of trigometrical series.

In a treatise on probability, I introduced the idea of "moral expectation."

In addition to working with mathematicians such as my dad, uncle, and brothers, I had the good fortune of working with Goldbach and Euler.

Answer: Daniel Bernoulli (1700 - 1782)