Tools from other disciplines useful to mathematics research? Obviously, mathematics provides essential tools for physicists, biologists, economists, engineers and many others to use in their research. Equally obviously, physics, biology, economy and engineering provide the inspiration for research topics and directions in mathematics. But this isn't what this question is about. Instead, I'm wondering about tools provided to mathematicians by other disciplines.
Are there any examples of tools (excluding software) from another discipline that you personally have used in your mathematical research?
E.g., I find dimensional analysis (as in assigning dimensionfull units to variables) a very useful tool from physics, which can greatly help in finding errors during algebraic manipulation of equations.
 A: The William G. Pritchard Fluids Lab conducts experiments–actual, physical experiments with messy, wet fluids–in the Penn State Math Department. Perhaps this counts as drawing on laboratory techniques of physics, engineering, etc.
I haven't personally used this in my research, though. So I'm marking this answer as community wiki.
A: Two books in my library (but, sadly, as yet unread) claim to use physical methods (i.e., methods of physics, specifically, mechanics) to solve - or suggest a way of solving - mathematical problems:
The Mathematical Mechanic: Using Physical Reasoning to Solve Problems (Levi, 2009)

INTRODUCTION
...the book does exact revenge—or maybe just administers a pinprick—agsinst the view that mathematics is a servant of physics. In this book physics is put to work for mathematics, proving to be a very efficient servant (with apologies to physicists). Physical ideas can be real eye-openers and can suggest a strikingly simplified solution to a mathematical problem. ...

Some Applications of Mechanics to Mathematics (Uspenskii, 1961) - a slim volume, reproducing a lecture to (Russian) high school students:

FOREWORD
The applications of mathematics to physics (in particular, to mechanics) are well-known. We need only open a school text-book to find examples.  The higher branches of mechanics demand a complex and refined mathematical apparatus.
There are, however, mathematical problems for whose solutions we can succeessfully use the ideas and laws of physics. A number of problems of this kind, soluble by methods drawn from mechanics (namely, using the laws of equilibrium) were given by the author in his lecture ...

A: I hope I correctly got what you mean by "tools". Google maps is a great tool for some applications of graph theory, optimization and even topology. I have seen several papers that use the map tools for developing optimal or sub-optimal algorithms on finding the shortest routes or statistical analysis etc.
For example, a brief search leads to this paper and a handful of others.
A: Since this is now CW, I can just as well add some answers.
As Matt F. mentioned in comments, language skills are often useful in mathematical research (e.g. for accessing literature written in French or Russian, or indeed in English in the case of second-language speakers), and those can certainly be considered tools from another discipline.
A: Since you mentioned dimensional analysis, you might enjoy the book Street-Fighting Mathematics:  The Art of Educated Guessing and Opportunistic Problem Solving
by Sanjoy Mahajan.  From the book description: "Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy."
A: I have built physical models (wood, paper, brass, plastic) of geometric objects (polyhedra, dissections, tensegrities) that have helped me see and prove theorems.
Steinhaus's Mathematical Snapshots is an inspiration. Dover offers the ebook. Better: find a used hard copy.
A: I find that thinking about types (as in object-oriented programming) is really helpful. This can help clarify things (and in particular, help students).
For example, one cannot usually add a matrix-type and a partition-type.
I suppose this is closely connected to category theory and/or type theory,
but one does not need any background in those fields, in order to think about types; perhaps this is similar to the "units"-connection mentioned in a different answer.
A: Sorry to post yet another self-answer, but this is completely separate from my other answer.
Polymath-style projects or sites like MathOverflow are tools for mathematical research that could be considered applications of social science to mathematics research. This is especially true if incentive systems like reputation scores or badges are being used, which are ultimately based on insights from psychology and/or economics (which can to some extent be understood to be the study of incentives).
A: It's not clear how useful this would actually be, but the idea of using "citizen science" (a somewhat sociology-based notion which has been developed into a useful tool for — primarily observation-based ­— scientific research by astronomers, botanists and zoologists, among others) for mathematics research has been floated here on MO: Can pure mathematics harness citizen science?. It would be nice to know whether any of the projects proposed in answers to that question ever came to fruition.
