Bipolar disorder is not so much discovered as it did exist throughout time. Dated back to Ancient Greece where Aretaeus of Cappadocia, who was a physician and philosopher in the time of Nero or Vespasian (first century AD) had observed patients that would dance and play all night for days even. Then without notice change to dull and somber and weeping.

It has always been there, just not yet labeled as such. 
In the early nineteen hundreds the term was called “Manic Depressive” in order to give a term to the manic side of mania and its counterpart depression

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 In 1854, Jules Baillarger (1809–1890) and Jean-Pierre Falret (1794–1870) both presented psychiatric terms and writing about the illness called ~dual insanity ~ 

It was In the early 1900s the eminent German psychiatrist Emil Kraepelin (1856–1926) coined the term that would be used to describe what we know as bipolar today. He called it ~manic depression~ 

It was not until the 1950’s that the terms for the illness went between using ~manic depressive~ to bipolar affective disorder ~ it was proposed by German psychiatrist Karl Leonhard in 1957.

So it truly has always been an illness, like all other illness that has also been around for ages. There is no definitive answer to exactly when it was discovered. Much like diabetes and cancer.. I don’t think we know who exactly discovered those either.