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Mathematical Musings پولیا درباره فون نویمان
On October 3, 1947, I visited him (von Neumann) for the first time at the Institute for Advanced Study at Princeton. I remember trying to describe to von Neumann, as I would to an ordinary mortal, the Air Force problem. I began with the formulation of the linear programming model in terms of activities and items, etc. Von Neumann did something which I believe was uncharacteristic of him. ‘‘Get to the point,’’ he said impatiently. Having at times a somewhat low kindling-point, I said to myself ‘‘O.K., if he wants a quicky, then that’s what he will get.’’ In under one minute I slapped the geometric and algebraic version of the problem on the blackboard. Von Neumann stood up and said ‘‘Oh that!’’ Then for the next hour and a half, he proceeded to give me a lecture on the mathematical theory of linear programs.
At one point seeing me sitting there with my eyes popping and my mouth open (after I had searched the literature and found nothing), von Neumann said: ‘‘I don’t want you to think I am pulling all this out of my sleeve at the spur of the moment like a magician. I have just recently completed a book with Oscar [sic] Morgenstern on the theory of games. What I am doing is conjecturing that the two problems are equivalent. The theory that I am outlining for your problem is an analogue to the one we have developed for games.’’ Thus I learned about Farkas’ Lemma, and about duality for the first time.
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Mathematical Musings احتمال ۴ اومدن می شه ۱/۶ و ۴ نیومدن می شه ۵/۶. پس احتمال غلط بودن مقدم می شه ۵/۶ می شه. پس احتمال درست بودن گزاره می شه ۵/۶، یعنی گزینه اول جواب می شه.
Singular Thinker 📢 PhD position in Statistics & Deep Learning at the University of Bergamo 📢 The call is now open for a PhD position co-supervised by me and Stefano Coniglio, funded by BPER Banca, on: “Statistics and deep learning techniques for synthetic data generation…
Neurologue 🧠 ایشون، رکسانا زراعتی، کارهای جالبی انجام دادن و الان هم لب‌شون تازه باز شده و دوتا پی‌اچ‌دی میخوان بگیرن. با تیم IBL هم همکاری داشتن. I recently started my research group at the Max Planck Institute for Biological Cybernetics in Tübingen, Germany, and we…
Forwarded from Neurologue 🧠
Singular Thinker Thermodynamics Reveals the Generalization in the Interpolation Regime 1/n 🔗 Link of the paper: https://arxiv.org/abs/2510.06028 In the realm of overparameterized NNs, one can achieve almost zero training error on any data, even random labels, that yield…
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