Later, the “operational calculus” was used by engineers to solve problems in cable theory even though mathematicians kvetched about Heaviside’s lack of rigor when he invented it (eventually, of course, rigorous foundations based mostly on Taylor series expansions and Euler’s theorem were developed).

]]>FYI

http://nuit-blanche.blogspot.com/2013/05/sunday-morning-insight-200-year-gap.html

I have read claims that much of modern AI & machine learning can be seen as just this: algorithms invented decades ago, but only made useful with modern fast computers and large data sets. (One example in particular being the field of computer vision.) I don’t know how true this is, but it seems plausible for examples that I know of: garbage collection was invented back in the ’50s or something, and only in the ’90s did it really become standard issue for new languages to the point where contemporary programmers take it purely for granted; and Bayesian spam filters (mid 90s to early 00s?) are naive Bayesian classifiers and I wouldn’t be surprised if that was arguably centuries old.

]]>Cool post. I’d suggest you to add the gap between Rosenblatt’s introduction of the Perceptron

Rosenblatt, Frank (1958), The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain,

Cornell Aeronautical Laboratory, Psychological Review, v65, No. 6, pp. 386, 408. doi:10.1037/h0042519

and Novikoff’s proof that the Perceptron algorithm converges after a finite number of iterations if the data

set is linearly separable.

Novikoff, A. B. (1962). On convergence proofs on perceptrons. Symposium on the Mathematical Theory of Automata, 12, 615-622. Polytechnic Institute of Brooklyn.

All my best,

Zen.

]]>The counterfactual approach is described here

http://en.wikipedia.org/wiki/Rubin_causal_model

I don’t have a definition of “inventing a method.”

I had hoped I had made that clear in the post.

I don’t think this is really a “method”

]]>In this case there’s an eternal gap!

]]>I think convex optimization broadly has a very rich history of methods and gaps — but even restricting to LPs — they were first formulated by Kantorovich in the 30s (though people were solving linear systems long before), then Dantzig came up with the simplex method during WWII, and then Khachiyan came up with the Ellipsoid in the seventies, Karmakar in the 80s came up with interior point methods, and Spielman-Teng gave a smoothed analysis for the simplex in the 2000s.

Method: Simplex, Inventor: Dantzig (40s), Theoretical justification: Spielman-Teng (2000s)

(Theoretically good) Poly-time methods were known for a few years before they became practically useful.

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