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"Kolmogorov also started as a nonmathematician--he was studying history. His first paper, written when he was seventeen, was reported at a seminar given by Bakh

"Kolmogorov also started as a nonmathematician--he was studying history. His first paper, written when he was seventeen, was reported at a seminar given by Bakhrushin at Moscow University. Kolmogorov came to some conclusion based on an analysis of medieval tax records in Novgorod. After his talk, Kolmogorov asked Bakhrushin whether he agreed with the conclusions. 'Young man,' the professor said, 'in history, we need at least five proofs for any conclusion.' Next day, Kolmogorov switched to mathematics. The paper was rediscovered in his archive after his death and is now published and approved by historians." --V.I. Arnold, "An Interview with V.I. Arnold," Notices of the AMS, 44(4).

wwweston 12y ago
> 'Young man,' the professor said, 'in history, we need at least five proofs for any conclusion.' Next day, Kolmogorov switched to mathematics. Makes sense. In math, you only need one (solid) proof. :) The relative demand actually makes a lot of sense. When you're constructing a picture by interpolating a story around some points of evidence, overfitting is going to be a hazard, possibly inevitable. And you can't even re-run an experiment. You'd have to be as careful as a scientist, more thorough than a lawyer in discovery, and pretty creative.
MyHypatia 12y ago
"In this work, he used mathematical arguments to answer the following question: was it (i) a village that was taxed in the first place, and then the tax as divided between households, or (ii) the other way around, where it was a household that was originally taxed, and then the sum represented the total to be paid by the village?... Because the total received were always an integer number of (changing) monetary units, Kolmogorov proved that it was rule (ii) that was adopted" -Probability and Statistics by Example, Volume 1. I guess the households that paid their tax either always paid it in full, or if they paid a portion it was always an integer value? While you're definitely more likely to get integer values in the end if everyone is taxed $1,000 rather than $999.30. It still makes me wonder how they always ended up with integers in the end. I guess if I have to write a check to pay off a portion of an amount I'm more likely to pay $400 than 399.90. But maybe it also had something to do with how their monetary system was set up.

wwweston 12y ago

> 'Young man,' the professor said, 'in history, we need at least five proofs for any conclusion.' Next day, Kolmogorov switched to mathematics. Makes sense. In math, you only need one (solid) proof. :) The relative demand actually makes a lot of sense. When you're constructing a picture by interpolating a story around some points of evidence, overfitting is going to be a hazard, possibly inevitable. And you can't even re-run an experiment. You'd have to be as careful as a scientist, more thorough than a lawyer in discovery, and pretty creative.

MyHypatia 12y ago

"In this work, he used mathematical arguments to answer the following question: was it (i) a village that was taxed in the first place, and then the tax as divided between households, or (ii) the other way around, where it was a household that was originally taxed, and then the sum represented the total to be paid by the village?... Because the total received were always an integer number of (changing) monetary units, Kolmogorov proved that it was rule (ii) that was adopted" -Probability and Statistics by Example, Volume 1. I guess the households that paid their tax either always paid it in full, or if they paid a portion it was always an integer value? While you're definitely more likely to get integer values in the end if everyone is taxed $1,000 rather than $999.30. It still makes me wonder how they always ended up with integers in the end. I guess if I have to write a check to pay off a portion of an amount I'm more likely to pay $400 than 399.90. But maybe it also had something to do with how their monetary system was set up.