The Frankensteinian Nature of Mathematics

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be-tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new goals. We want to stress that the same relation holds in mathematics. The special point about mathematics is that both the instruments and the goals are mathematics. The first mathematics, usually including definitions and notations, is invented by mathematicians; the second, including lemmas, theorems and results, is accordingly discovered. The point we want to make about the chain of concepts invented and discovered in mathematics is that some of the new beings (created or discovered) can get out of the control of mathematicians, and that this reveals an important aspect of the nature of mathematical science, which we call the Frankensteinian nature of mathematics.