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I don't think anyone can be more controversial than J. Robert Oppenheimer. 

Regarded as the Father of the Atomic Bomb, he recalls thinking the words, "Now I am become Death, the destroyer of worlds," when witnessing the first detonation of a nuclear weapon during the Trinity nuclear test, a month before atomic bombs that he and his team created were dropped in Hiroshima and Nagasaki.  

However, aside from leading the research that lead to the creation of the atomic bomb, what makes Oppenheimer really controversial are his postwar experiences which included, a meeting with President Truman that allegedly went badly and resulted in him infuriating the President and his critique of the US move from atomic weapons to the hydrogen bomb. 

Oppenheimer was also made more notorious as the subject of a controversial security hearing that stripped him of his Q clearance, saw him accused of everything from having Communist ties to being a Soviet spy, and heralded the end of the "messianic role of scientists" in postwar policies. In the end, Oppenheimer was exiled from his work and the academe.

Eventually, President. Kennedy moved to rehabilitate Oppenheimer's reputation and Oppenheimer was awarded the prestigious Enrico Fermi Award by President Johnson, following President Kennedy's assassination. 

Because of this, I would consider Oppenheimer as one of the most controversial scientists of our time. Not only did he lead the team that delivered the atomic bomb to the world, his professional struggles after the war was also rife with controversy and intrigue.

Source: 

J. Robert Oppenheimer. https://en.wikipedia.org/wiki/J._Robert_Oppenheimer

Richard Feynman was one of the most productive and famous physicists of the 20th century. Especially in relation to Manhattan Project - a very secret effort made by the United States to make atomic bombs.

However, he is also a fad and has a reputation as a troublemaker. When bored with the project he was working on at Los Amos, Feynman reportedly spent his spare time unloading locks and breaking into people's safes - not his money or property, but to show how easily a system was hacked.

And, that's not just the adventure. While developing the theory of quantum electrodynamics - which led him to the Nobel prize - he reportedly often mingled with Las Vegas dance girls, had time to study until he became a Maya language expert, learned Tuva's distinctive throat singing, and explained how the rubber seal of the O ring (O- ring) triggered the Challenger spacecraft explosion in 1986.

The nutty professor