TITLE: Was lattice theory central to mid-20th century mathematics?
QUESTION [24 upvotes]: Four years ago, I read a book on the history of mathematics up to 1970 or so. It was very interesting up until the end. The last few chapters, though, were on lattices. The author claimed that lattices were taking math by storm, and that soon lattices would be one of the central objects in mathematics, and many other such claims similar to those now made in reference to category theory.
I couldn't find the book online, but I found references to similar ideas in this post:Good lattice theory books?
Question 1: Was lattice theory central to mid-twentieth century mathematics?
Question 2: Is it central now?
Edit: A simpler question with more definite answers: did any mathematicians in the mid-1900s claim that lattice theory was vital or central to mathematics, and what arguments did they give?

REPLY [7 votes]: Answer to Question 1.  In "The Many Lives of Lattice Theory," Gian-Carlo Rota wrote of "Professor [I. M.] Gelfand's oft-repeated prediction that lattice theory will play a leading role in the mathematics of the twenty-first century."  So you'd better get on board now!
Von Neumann spent a few years working in lattice theory (writing "Continuous Geometry"), creating with Professor Birkhoff the logic of quantum mechanics. Nowadays there is the work of people like Fotini Kalamara Markopoulou of the Perimeter Institute, whom Scientic American "hailed as one of the world's most promising young physicists." She uses certain types of distributive lattices called Heyting algebras.
Going back to the middle of the last century, Horn also did work on Heyting algebras. (In fact, he had many papers dealing with lattices.)
I was introduced to lattice theory through "Algebra" by Birkhoff and Mac Lane, and I imagine many people who read that book over the decades were also somehow influenced, by that and Cohn's books, which took a universal algebraic approach.  Tarski did work with people like C. C. Chang dealing with general algebras which necessarily involved lattice theory and order theory. They also worked with Bjarni Jonsson; when I mentioned his name to an Icelandic mathematician I knew in graduate school, the latter got very excited...
You'll find a couple of papers dealing with lattice theory by people like Shannon; Turing Award winner Hartmanis's first papers were in lattice theory.  2012 Nobel laureate Al Roth's first paper was in lattice theory. 
Lurking behind what I heard was the most downloaded article on JSTOR, "College Admissions and the Stability of Marriage," by Gale and Shapley, is lattice theory; Conway proved that that the set of stable marriages forms a distributive lattice.
Dana Scott, another Turing Award winner, advanced the idea of "data types as lattices." 
You find lots of applications of lattice theory---for instance, in imaging, I was told by a prominent figure in mathematical morphology that the lattice theory is essential. Last summer I even found out that the police in Amsterdam are using lattice theory for terrorist profiling.  A group at Los Alamos National Laboratory was also using lattice theory in a terrorism context. Lattice theory (or order theory) has also been used in sociology, chemistry, epidemiology, linguistics.... Just to leave you with one example, you can look up a $749,226 Environmental Protection Agency grant from 2013 dealing with "Galois lattices."