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I'm running a time travel game, and I was wondering if there was any consensus on who the finest minds of the late 19th/early 20th century?

I'm looking to use a bunch of them in the game

Here are a few.

Albert Einstein (1879-1955), Marie Curie (1867-1934), Nikola Tesla (1856-1943), Sigmund Freud (1856-1939), Thomas Edison (1847-1931)

Seconding Shawn's list.

Srinivasa Ramanujan

Do not forget Marconi, Oppenheimer, Ressel, Willy Messerschmidt, Fokker and more.

There are great minds and also great engineers .

To answer the original question, no, there is no consensus. Picking the most brilliant minds of any time period is really more a matter of opinion and preference than of documented facts.

Personally, I think William James Sidis (pronounced /ˈsaɪ dɪs/; April 1, 1898 – July 17, 1944) fits the bill. Although not well known in history and never officially tested for an intelligent quotient, the man's incredible mastery of a wide variety of subjects deserves consideration. If he were alive today, he probably would have been considered a recluse genius suffering from some form of autism or another. I write 'considered' because he only suffered when he was in the limelight as a child celebrity. By the age of eleven, he was lecturing at Harvard University about 4th dimensional physics, writing papers about theoretical mathematics, and performing musical concerts. As an adult, he worked a series of manual labor jobs and lived a quiet life while authoring a book about streetcar ticket collecting and some articles. We don't really know how much he wrote because he what he did publish was under a series of different pen names. He was a historian (with a few particularly strange ideas), an astrophysicist (basically he predicted the discovery of dark matter, wrote about how the universe was probably eternal and thus disputing the big bang), linguist (spoke and wrote in 40 languages including Wampum and cited wampum belts as references in his history book of North America), psychologist (with his own theory of unconsiousness which disputed Sigmund Freud's theories), and political activist (greatly opposed World War I and protested against conscription for it; seems to have been a socialist as a young man but developed into more of a libertarian later in life).

I guess you can use me in your game if you really want to... though unfortunately my genius (like most brilliant minds) wont be realized until long after my death.