## New answers tagged convention

9

Roger Penrose's abstract index notation for tensors is a relatively modest example, but I think it fits all the criteria of the question. Around 1952, Penrose invented a personal graphical notation for tensors and tensor operations such as contraction and covariant derivatives. It's been described as "fornicating ostriches;" variations on it are referred to ...

31

Although just beyond your 50-year scope, this may be of interest. Among the series $\mathsf A_n, \mathsf B_n, \mathsf C_n, \mathsf D_n$ in the Cartan-Killing classification of simple Lie groups, everyone (I believe) always agreed to call $\mathsf A_n$ the special linear group, $\mathbf{SL}(n)$, and $\mathsf B_n$ and $\mathsf D_n$ the special orthogonal ...

18

An example of a failure to change notation is the movement by Eilenberg, Jacobson, Herstein and others to replace function notation $f(x)$ with $xf$ and then have the composition $fg$ mean first do $f$ and then $g$. The notation has the advantage that diagrams $X\xrightarrow{f}Y\xrightarrow{g} Z$ don't have to be flipped around. It also has the property ...

8

In most cases that I am familiar with, successful changes to terminology were accompanied by other more basic innovations. E.g. Grothendieck's language became standard in algebraic geometry in the late 1950's, because he successfully rewrote the foundations of the subject.
An example of a proposed change for its own sake is the word "contrahomology" for ...

24

The subject known for decades as recursion theory, studying the class of recursive functions and the recursively enumerable (r.e.) sets and degrees, is now known almost universally, especially amongst the newer generation, as computability theory, studying the computable functions and the computably enumerable (c.e.) sets and degrees. This change, led by ...

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