Pi is Transcendental/Historical Note

Historical Note on $\pi$ is Transcendental
The transcendental nature of $\pi$ (pi) was investigated without success by in $1844$, at around the time he conjectured that Euler's number $e$ was likewise transcendental.

His ideas contributed towards work done by, who proved in $1873$ that Euler's number $e$ is transcendental, but had not noticed that it was a short step from there, via Euler's Identity $e^{i \pi} + 1 = 0$, that $\pi$ is transcendental:


 * I shall risk nothing on an attempt to prove the transcendence of the number $\pi$. If others undertake this enterprise, no one will be happier than I at their success, but believe me, my dear friend, it will not fail to cost them some effort.
 * --, in a letter to a friend

That final step was made by, who finally achieved this proof in $1882$.

Many people believed that was a grossly inferior mathematician to, and that he achieved this result by pure luck, and that it should have been  who gained the credit for it.

However, be that as it may, it was indeed and not  who made that actual step of reasoning, and the result falls fair and square at his feet.