Gumbel specialised in mathematical statistics and, along with Leonard Tippett and Ronald Fisher, was instrumental in the development of extreme value theory, which has practical applications in many fields, including engineering and finance.

Born to a prominent Jewish family in Württemberg, Gumbel graduated in mathematics from the University of Munich, completing his doctoral thesis on the topic of population statistics shortly before the outbreak of the First World War.

[7] In January 1918, Gumbel took up a position with the electronics company Telefunken, researching sound transmitter waves, and he continued his political activities with the support of one of the firm's founders, Georg Count von Arco, a prominent member of the human rights movement.

He then moved to France, where he taught at the École libre des hautes études in Paris, and in Lyon, as well as continuing his political activities and helping other refugees, until the German invasion of 1940.

[6] During his time at the University of Munich (1910-1914), Gumbel was taught mathematics, economics and the social sciences by eminent scholars known to have liberal political views, including Alfred Pringsheim and Lujo Brentano.

[14] After the 1919 murder of prominent USPD member, Karl Liebknecht, who Gumbel greatly admired, there was strong criticism by journalist Kurt Tucholsky that the trial judge completely ignored evidence against the Nazi Brownshirts.