Why does Truman feel obligate to break with the tradition of sharing scientific breakthroughs with the world ?

Truman decided to keep the results of the Project Manhattan in secret, because the atomic bomb was a very important part of the American strategy at the end of World War II.

Explanation:

If Truman had shared the development of the Atomic Bomb, enemy countries like Japan could have developed their own atomic bombs very quickly, and use them against the United States.

As we know, what happened was exactly the opposite: the United States was for a while the only country with nuclear weapons, and used two atomic bombs against the Japanese cities of Hiroshima and Nagasaki, which eventually led to the unconditional surrender of Japan, and the end of the war.

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