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Hopper was born on December 9, 1906 in New York City. She was the oldest in a family of three children. She was curious as a child, a lifelong trait – at the age of seven she decided to determine how an alarm clock worked, and dismantled seven alarm clocks before her mother realized what she was doing (she was then limited to one clock).For her pre-school education, she attended the Hartridge School in Plainfield, New Jersey. She was rejected  for early admission to Vassar College at age 16 (her test score in latin were too low), she was admitted the following year. She graduated Phi Beta Kappa from Vassar in 1928 with a bachelor's degree in mathematics and physics and then earned her Master's degree at Yale University in 1930.
In 1934, she earned a Ph.D. in mathematics from Yale under the direction of Øystein Ore. Her dissertation, New Types of Irreducibility Criteria, was published that same year. Hopper began teaching mathematics at Vassar in 1931, and was promoted to associate professor in 1941.
She was married to New York University professor Vincent Foster Hopper (1906–1976) from 1930 until their divorce in 1945. She never remarried, and she kept his surname.

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