Dance with Symbols?

Early 70ies. I started my math studies at JKU in Linz. Great luck that Bruno Buchberger started to teach there. He was (one of) the most influencing researchers of Symbolic Computation. It fit perfect into my interest: Algebra.

In brief SC deals with the manipulations of symbols, like mathematical expressions, geometrical objects, logical expressions, molecule structures, electronic circuits ... or even programs by computers. Bruno's Groebner bases are a perfect example of the requirement to dance with symbols: you solve a linear system by manipulating the base and bring it into a convenient form ("triangulation"). Manipulation by arithmetic. Bruno generalised this for polynomial rings (instead of base vector, he needed to deal with special ideals and complex elimination properties). Manipulate means transforming algebraic symbols. 

In non Mickey-Mouse cases, finding such a base without a computer is "impossible". Bruno: Mathematics is (only) essential, if you can do it by computer. I say, PLUGGED. 

Mathematics and computer science? Abstract data types are related to universal algebras. In a Ring (R, +,*), +,* are operations which results stay in-house. They encapsulate. All instances inherit Ring properties. And implementations of  +, * are independent of the interface (polymorphism). In my master thesis I studied "Free Algebras". They represent the language aspect of Algebras. The interface.

After my studies I made a career in factory automation. 1987 Bruno founded RISC . Factory automation deals with geometry, machine operations, robot tasks, operation, production and risk management, .. technical objects which are manipulated by programmable technical systems. I cooperate with RISC from the beginning. 

This influenced not only my problem solving capacity but my way of thinking. And finally my business life.