Who is credited with inventing the term "high dimensional data"? Title says it all, who is credited with inventing the term "high dimensional data"?
 A: I tried looking in Google Books high dimensional. Before 1970, I didn't noticed the term in the context of data but I might have missed some references. 
I found the 1973 book "A Method for the Selection of Variables for Classification of High-dimensional Data" by Larry Randolph Muenz from Department of Statistics, Stanford University. It was Muenz's dissertation.
So, it might not be the first occurrence but for sure the term was used by 1973.
A: Q: Who invented the term "high dimensional data." 
First of all, visualization of higher dimensional data, and models, was developed mathematically in the French language and developed in German. The notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen Kontinuität, Hamilton's 1843 discovery of the quaternions and the construction of the Cayley algebra marked the beginning of higher-dimensional geometry. Exemplis gratis, see footnote page 224 circa July 1893 referring to earlier work by the same author in German.
With the development of special relativity in 1905 by Albert Einstein, it was shown that only 4D spacetime $(x,y,z,t)$ is invariant, not 3D space $(x,y,z)$. This hit the public's imagination like a mindfire. Einstein’s four-dimensional universe, is conceptually different from four spatial dimensions. But the two kinds of four-dimensional world became conflated in interpreting the new art of the 20th century. Early Cubist works by Pablo Picasso that simultaneously portrayed all sides of their subjects became connected with the idea of higher dimensions in space, which some writers attempted to relate to relativity. 
The first person to add a fifth dimension to a theory of gravity was Gunnar Nordström in 1914, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. Nordström attempted to unify electromagnetism with his theory of gravitation, which was however superseded by Einstein's general relativity in 1919. Thereafter, German mathematician Theodor Kaluza combined the fifth dimension with general relativity, and only Kaluza is usually credited with the idea. In 1926, the Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions. One notable feature of string theories is that these theories require extra dimensions of spacetime for their mathematical consistency. In bosonic string theory, spacetime is 26-dimensional, while superstring theory is 10-dimensional and supergravity theory 11-dimensional. In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments.
Finally, although one can ascribe sign posts to past events, I agree with @Glen_b that Stigler's Law of eponymy, which given the chicken and egg phylogeny of an onion layered dialectal term, prohibits isolation of an ontological moment for origin of a thought. That is, there was never a first egg, or a first chicken, there was a continuum of proto-chickens that species drifted to become modern chicken. Likewise, higher dimensionality is something we understand without being told, we avoid future events when we avoid getting hit by a bus (4D spacetime), or put a coat on when it is cold out (5D spacetime + temperature). 
In statistics, it is hard to say when multi-dimensionality first occurred. For example, Mahalanobis n-space distance dates from 1936. However, Euclidean $n$-space distance (or Hilbert space distance) is just root sum squared, so that it has been around at least as long as a standard deviation.
As lessons in humility, when Newton was asked how it came to be that he conceived of so much, he reputedly responded that "If I have seen further, it is by standing on the shoulders of giants."  That thought (Latin: nanos gigantum humeris insidentes) is in turn attributed to Bernard of Chartres in the 12$^{th}$ century. When Einstein was asked how he came to be such a genius, he responded, "It's not that I am so smart. I just stay with problems longer." And one has to, to develop a dialectic.
A: The word 'high' can be subject to much argument as to what exactly constitutes high.  However the term, the 'curse of dimensionality' is due to Bellman.  It refers to the fact that in large dimensional spaces problems exist that don't exist in low dimension.  The quintessential example would be, for me, the fact that most of the points of a sphere $S^n$ are concentrated around the edge and the proportion grows with n.  Once one believes in 'the curse of dimensionality' , high dimension, and hence high dimensional data would be data point in $\mathbb{R}^n $ for which this becomes an issue. 
