- Person
- Abraham Wald
- Lived
- 1902–1950
- Field
- Statistics
- From
- Hungarian-American
The story
Abraham Wald was born in 1902 in Kolozsvár, then in Hungary and now Cluj-Napoca in Romania. In 1927 he went to the University of Vienna to study with the mathematician Karl Menger, and in 1931 he earned his doctorate in geometry. He became a star of Menger's mathematical seminar, publishing 21 papers on geometry between 1931 and 1937, work Menger described as deep, beautiful and of fundamental importance.
Talent was not enough. Vienna in the 1930s offered almost no academic posts, and none to a young Jewish scholar. To support himself, Wald became mathematics tutor to Karl Schlesinger, a leading Austrian banker and economist who hired him in 1932. The economist Oskar Morgenstern also created a position in economics for him. Menger's seminar itself was forced to stop in 1936 after it was attacked for its Jewish contributors.
The detour proved remarkably fruitful. Schlesinger was interested in the mathematics of the Walrasian system, the set of equations describing how prices, production and demand across a whole economy fit together. In papers written for Menger's seminar, Wald proved the existence of a solution to the competitive economic model, and he went on to prove the existence and uniqueness of solutions for extended forms of the Walrasian equations of production. These were among the first rigorous proofs that a competitive economy can have a consistent equilibrium.
Between 1931 and 1937 Wald published ten papers on economics and econometrics. His work also covered approximate formulas for economic index numbers, indifference surfaces and the Cournot duopoly problem. In 1936 he published a monograph on removing seasonal variation from economic time series, in which, Morgenstern wrote, he developed techniques superior to all others.
In 1938 the Cowles Commission for Research in Economics invited him to the United States, and he left Austria that summer, months after the Nazi annexation. In America his economic interests continued. In 1939 he published a new formula for the cost-of-living index in Econometrica, and in 1943, with Henry Mann, he wrote a much-used paper on stochastic difference equations. His statistical work soon became his main focus, but his equilibrium proofs remained a landmark in the effort to put economic theory on a precise mathematical footing.
Why it matters
Wald's proofs showed that the classic picture of a balanced competitive economy could be made mathematically rigorous, a foundation that later economists built on.
About Abraham Wald
Refugee mathematician who founded sequential analysis and statistical decision theory, and whose wartime study of damaged bombers became the classic lesson in survivorship bias.
More about Abraham Wald
- Abraham Wald invented the test that can stop earlyDuring the Second World War, Abraham Wald created sequential analysis, a way to check evidence after each test and stop as soon as it is conclusive, often with far fewer observations.
- Abraham Wald fled the Nazis and helped America win the warAbraham Wald escaped Austria in 1938; of nine relatives left behind, all but one were murdered at Auschwitz. In America he put his mathematics to work for the Allied war effort.
- Abraham Wald turned statistics into a science of decisionsIn a 1939 paper and his 1950 book Statistical Decision Functions, Abraham Wald recast statistics as the problem of making decisions under uncertainty when mistakes have costs.
- Abraham Wald taught the world about survivorship biasDuring the Second World War, statistician Abraham Wald showed how to judge bomber damage from planes that returned, a classic lesson in survivorship bias.
- Statisticians use Abraham Wald's tools every dayThe Wald test, the Wald–Wolfowitz runs test, Wald's equation and the Wald distribution are among the everyday statistical tools that bear Abraham Wald's name.
Sources
- Abraham Wald MacTutor History of Mathematics, University of St Andrews
- Abraham Wald Wikipedia
- Karl Schlesinger Wikipedia
Another act of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.