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I'm pretty sure it was less than 50 years ago that what are now called compact topological spaces were known as "bicompact", and "compact" meant what is now called "sequentially compact".


The statement that elliptic curves are modular was (I think) universally known as the Weil Conjecture back in 1970 or so when I first learned about it. Nowadays, it's generally known as the Shimura-Taniyama-Weil Conjecture (or, the Modularity Theorem). I don't know enough about the history to discuss the conditions responsible for the success of the proposed ...


A few examples: Regarding Grothendieck's theory of schemes: These were called preschemes at first, while the word 'scheme' was reserved for separated (pre)schemes. ( Preschemes and schemes). An example from (combinatorial) topology: Nowadays the terminology simplicial set is universally used for a bunch of sets indexed over the nonnegative numbers ...

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