In this note, I develop my personal view on the scope and relevance of symbolic computation in software science. For this, I discuss the interaction and differences between symbolic computation, software science, automatic programming, mathematical knowledge management, artificial intelligence, algorithmic intelligence, numerical computation, and machine learning. In the discussion of these notions, I allow myself to refer also to papers (1982, 1985, 2001, 2003, 2013) of mine in which I expressed my views on these areas at early stages of some of these fields. It is a great joy to see that the SCSS (Symbolic Computation in Software Science) conference series, this year, experiences its 9th edition. A big Thank You to the organizers, referees, and contributors who kept the series going over the years! The series emerged from a couple of meetings of research groups in Austria, Japan, and Tunisia, including my Theorema Group at RISC, see the home pages of the SCSS series since 2006. In 2012, we decided to define "Symbolic Computation in Software Science" as the scope for our meetings and to establish them as an open conference series with this title. As always, when one puts two terms like "symbolic computation" and "software science" together, one is tempted to read the preposition in between - in our case "in" - as just a set-theoretic union. Pragmatically, this is reasonable if one does not want to embark on scrutinizing discussions. However, since I was one of the initiators of the SCSS series, let me take the opportunity to explain the intention behind SC in SS in this note. Also, this note, for me, is a kind of revision and summary of thoughts I had over the years on the subject of SCSS and related subjects.

This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021. Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs, representations of algebraic objects, etc.). Powerful algorithms have been developed during the past decades for the major subareas of symbolic computation: computer algebra and computational logic. These algorithms and methods are successfully applied in various fields, including software science, which covers a broad range of topics about software construction and analysis. Meanwhile, artificial intelligence methods and machine learning algorithms are widely used nowadays in various domains and, in particular, combined with symbolic computation. Several approaches mix artificial intelligence and symbolic methods and tools deployed over large corpora to create what is known as cognitive systems. Cognitive computing focuses on building systems that interact with humans naturally by reasoning, aiming at learning at scale. The purpose of SCSS is to promote research on theoretical and practical aspects of symbolic computation in software science, combined with modern artificial intelligence techniques. These proceedings contain the keynote paper by Bruno Buchberger and ten contributed papers. Besides, the conference program included three invited talks, nine short and work-in-progress papers, and a special session on computer algebra and computational logic. Due to the COVID-19 pandemic, the symposium was held completely online. It was organized by the Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz on September 8--10, 2021.