Jenga is a game where you start with a tower of wooden pegs and take turns removing pegs until someone makes the tower collapse. A style of mathematics analogous to Jenga reached the height of its popularity about 40 years ago and then fell out of fashion. I use the phrase “Jenga mathematics” to refer to generalizing a well-known theorem by weakening its hypotheses, seeing how many pegs you can pull out before it falls.
Many 20th century mathematicians spent their careers going over the work of 19th century mathematicians, removing every hypothesis they could. Sometimes a 20th century mathematician would get his name tacked on to a 19th century theorem due to his Jenga accomplishments.
Taken to extremes, Jenga mathematics turns theorems inside-out and proofs become hypotheses. Natural hypotheses are replaced with a laundry list of properties necessary to make the proof work. Start with some theorem of the form “Let X be a widget. Then X has a foozle.” Go back over the proof and see just what features of a widget are needed for the proof. Then restate the theorem as “Let X have the following apparently arbitrary list of properties necessary for my proof to work. Then X has a foozle.” Never mind whether anybody can think of anything other that a widget that satisfies the hypotheses of the new theorem.
Jenga mathematics is no longer fashionable. Mathematicians still value removing unneeded hypotheses, but they’re not as willing to go to extremes to do so. They are more interested in building new towers than in removing every piece possible from old towers.