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Paul Griffiths wrote on 2011 Feb 5:

Iannis Xenakis, the Greek-French composer who often used highly sophisticated scientific and mathematical theories to arrive at music of primitive power [...] These writings show how deeply he based his music on mathematics and logic.

Tom Service, PhD in music (Southampton) wrote on 2013 Apr 23:

And that's exactly what Xenakis would do, and was already doing - which is both one explanation of his music's shocking otherness (it was heard as "alien" even by the hipsters of the early 1950s; the 1955 premiere of Metastasis at the Donaueschingen Festival was one of the scandals of postwar music) and a revelation of this music's deep, primal rootedness in richer and older phenomena even than musical history: the physics and patterning of the natural world, of the stars, of gas molecules, and the proliferating possibilities of mathematical principles. Xenakis resisted the label of being a mere mathematician in music just as surely as he refused the idea of his music's political or social message, and it was of course how he used those scientific principles (outlined in his book, Formalized Music) to create pieces of shattering visceral power.

Professor Marcus du Sautoy OBE, The Secret Mathematicians, on 2014 May 21:

Actually, another composer who used a lot of sort of Schoenberg’s ideas, and went well beyond those actually I think, I have just discovered, is an Emeritus Professor at Gresham College, Iannis Xenakis. He was a Greek composer who was very obsessed with mathematical ideas. This piece here actually is a piece called Metastaseis – it is the score for that piece. But if you looked at that, you would, at first sight, say, well, that is a piece of geometry, looks like hyperbolic geometry, not a piece of music. Xenakis was very interested in symmetrical ideas, and in fact, he dedicated a piece called Nomos Alpha to one of my mathematical heroes, Evariste Galois, who developed a language in order to describe symmetry.

I'm not sure if Messiaen knew more than A-Level Math, but he affirms Xenakis's:

When Xenakis first approached Messiaen in Paris for composition lessons, the latter turned him down, because, “I think one should study harmony and counterpoint. But this was a man so much out of the ordinary that I said… ‘No, you are almost 30, you have the good fortune of being Greek, of being an architect and having studied special mathematics. Take advantage of these things. Do them in your music’.” That, he did.

  • I do remember reading somewhere that Xenakis used Brownian motion in a (possibly more than one) piece, but I cannot remember where. This is an explicit physics phenomenon, so you might want to look that up, as one would have to be familiar with mechanics to have come across the idea. – LSM07 Mar 19 '18 at 4:05
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    While these questions are kind of interesting, at some point you probably should stop asking "how much math did $COMPOSER$ understand" before doing a decent amount of research on your own. – Carl Witthoft Mar 19 '18 at 12:55
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His compositions show that he understood the basics of at least stochastics (probability distributions, Markov processes), group theory, linear algebra (vector spaces), logic (e.g., conjunctive normal form for his theory of sieves), and writing software. In other words, a decent undergraduate education. He applied this mathematics to music, but strictly within mathematics he didn't publish any papers or original research.

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