# Description of the RISC logo

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The RISC logo was not chosen randomly, just to please the eye, but it symbolizes the invention of the theory of Gröbner bases: the reduction relation modulo polynomial sets is symbolized by the arrows. This relation, in general, does not possess the "confluence property" (also called Church-Rosser property) that is symbolized by the divergence and, then, convergence of the arrows. By finding a Gröbner basis for a given set, the polynomial reduction (w.r.t. that basis) becomes confluent. This is being characterized in the RISC logo by the diverging white arrows (they symbolize the reduction relation w.r.t. the polynomial set given initially) and the blue arrow that is available only in the polynomial reduction w.r.t. to a corresponding Gröbner basis! The black dots symbolize polynomials (or more generally, ring elements in rings that allow a Gröbner basis theory).

Gröbner bases theory, invented by Buchberger in 1965, was an essential starting point for the research of the newly established chair of Buchberger at the Johannes Kepler University in 1974. It was also a basis for the international reputation of the working group CAMP (Computer-Aided Mathematical Problem Solving) initiated by Buchberger in 1982. Gröbner bases theory was also the reason why Buchberger in 1985 was asked by Academic Press to act as initiator and editor-in-chief of the Journal of Symbolic Computation. Furthermore, Gröbner bases theory was an essential basis for the foundation of RISC in 1987. Therefore, it was natural to symbolize Gröbner bases theory in the RISC logo.

In the creation of the RISC logo, Buchberger was also led by another thought: Starting from two diverging points (the left and the right dot in the logo), one often must walk "against the direction of the arrow" (i.e. against first intuition) in order to eventually arrive from something "seemingly more complicated", "the union / unification of contradicting poles" (the upper dot) at a convergence, a "simplification" (the lower point). In the case of Gröbner bases, the left and right dots are two arbitrary polynomials and the upper dot is the "S-polynomial of the two given polynomials" (the essential invention in the theory of Gröbner bases) for which one has to construct convergence by "completion" by the blue arrow. This principle, first doing something more complicated in order to arrive at something simpler, is a general and essential idea in the heuristic of mathematics - in particular for solving difficult problems - and thus, the RISC logo stands also for the (algorithmic) solving process in mathematics in general.

Even more generally, the principle symbolized in the RISC logo can also be seen as a manifestation of the fact that difficult problems in management, politics, economy, society, etc, are often "chicken and egg problems". Two seemingly contradicting things (chicken and egg), two things that depend on each other with neither of them existing at the beginning, create a dead-lock, and decisive progress can only be achieved, if a creative mind is able to establish "against the direction of the arrow", "against first intuition" a unification of contradiction (the upper dot) from which both items can be derived and brought to a convergence. RISC was and is the driving force of the Softwarepark Hagenberg and a number of other creative developments for economy, science, politics, and society in Upper Austria, Austria, and in the world. Again and again such "chicken and egg problems" had to be solved in order to "create new things out of nothing". The logo is also a symbol and liability for this role of RISC!

The RISC logo is, therefore, a stimulation and liability for RISC, to always play this creative role (nationaly and internationally) in the small area of Symbolic computation, of mathematics as a whole, and in the "innovation chain" of science and economy and in the society in general.

Bruno Buchberger, February 2010