Short answers, pulled from the story.
Hilary Putnam is best known for the hypothesis of multiple realizability, introduced in key papers published in the late 1960s. The hypothesis argues that mental states such as pain can be realized by entirely different physical states in different organisms, challenging type-identity theory. Putnam also originated machine-state functionalism, which became the dominant theory of mind in philosophy for much of the late 20th century.
The Twin Earth thought experiment, first laid out in Meaning and Reference (1973) and expanded in The Meaning of "Meaning" (1975), imagines a planet identical to Earth except that its water is made of XYZ rather than H2O. Because an earthling and his Twin Earth counterpart use the same word "water" to refer to chemically different substances, Putnam concluded that meaning cannot be determined solely by what is in a speaker's head, a position he called semantic externalism.
The Quine-Putnam indispensability argument holds that because quantification over mathematical entities is indispensable to science, we are committed to accepting the existence of those entities. Putnam presented what became the locus classicus of the argument in his 1971 book Philosophy of Logic, attributing the core argument to Willard Van Orman Quine. The Stanford Encyclopedia of Philosophy has described it as considered by many in the field to be the best argument for mathematical realism.
The Davis-Putnam algorithm, developed by Hilary Putnam and Martin Davis in 1960, determines whether a Boolean expression can be made true by some assignment of truth values to its variables. In 1962, Putnam, Davis, George Logemann, and Donald W. Loveland refined it into the DPLL algorithm. It remains efficient and still forms the basis of most complete SAT solvers in use today.
Putnam's brain in a vat argument holds that one cannot coherently suspect one is a disembodied brain whose experiences are generated by a mad scientist's computer. Because words refer to what their users or their ancestors actually encountered, a brain in a vat would have no words that genuinely refer to brains or vats, making the self-description incoherent. Putnam stated that his real target was metaphysical realism, not skepticism.
Hilary Putnam died on the 13th of March, 2016, at his home in Arlington, Massachusetts. At the time of his death he held the title of Cogan University Professor Emeritus at Harvard University.
Putnam received the Rolf Schock Prize in 2011 and the Nicholas Rescher Prize for Systematic Philosophy in 2015. He was elected a Fellow of the American Academy of Arts and Sciences in 1965, a Corresponding Fellow of the British Academy, and was elected to the American Philosophical Society in 1999. He also served as president of the American Philosophical Association in 1976.