Mathematics as a Tool

1. Introduction: Mathematics as a Tool
Johannes Lenhard, Martin Carrier

Part I. Organizing Science

2. Rational and Empirical Cultures of Prediction
Ann Johnson

3. Mathematization in Synthetic Biology: Analogies, Templates, and Fictions
Tarja Knuuttila, Andrea Loettgers

4. Trigonometry, Construction by Straightedge and Compass, and the Applied Mathematics of the Almagest

Ido Yavetz

5. Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystals
Henrik Kragh Sørensen

Part II. Conceptual Re-evaluation

6. Boon and Bane: On the Role of Adjustable Parameters in Simulation Models
Hans Hasse, Johannes Lenhard

7. Systems Biology in the Light of Uncertainty: The Limits of Computation
Miles MacLeod

8. The Vindication of Computer Simulations
Nicolas Fillion

9. Empirical Bayes as a Tool
Anouk Barberousse

Part III. Reflections on the Tool Character

10. On the Epistemic and Social Foundations of Mathematics as Tool and Instrument in Observatories, 1793–1846
David Aubin

11. Approaching Reality by Idealization: How Fluid Resistance Was Studied by Ideal Flow Theory
Michael Eckert

12. Idealizations in Empirical Modeling
Julie Jebeile

13. Forcing Optimality and Brandt’s Principle
Domenico Napoletani, Marco Panza, Daniele C. Struppa

14. Object Oriented Models vs. Data Analysis – Is This the Right Alternative?
Jürgen Jost

Keywords: Environment, Math. Appl. in Environmental Science, History of Science, Philosophy of Science, History of Mathematical Sciences