Does practicing math make us more intelligent in other areas as well?

I always come back to the same question, 'What is intelligence?'. For personal experience, practising math makes you better at math. Mindless computation just makes you better at mindless computation. Abstract thinking however, that has a deep impact on the way you see the world. Students from my university, are jokingly known in my country as 'cuadraditos', which I can faithfully translate as 'square-ish guys'. This means our mathematical training in abstract thinking makes us see the world and other topics (not necessarily science-related) always in a structured, analytical way, adjectives anyone would use to describe mathematical techniques or anything math related. This is of course, not always a good thing, but I think it answers in some way your question. No, mathematics doesn't make you any more intelligent. However you can export certain techniques and abilities from mathematics to almost every other field. That may be for good or for ill.

My answer is based on a distinction between "practicing math" (word problems that are in fact practical problems) versus drills. I think there are 6 key skills one learns through mathematics (besides the overall habits of mind like curiosity, grit, and persistence): Dealing with Data/Statistics (Spreadsheets) Problem-solving (perhaps even multiple ways to get to a solution for the same problem) Logic (particularly using proofs in Geometry) Abstract thinking & Critical analysis of problems (breaking things down) Patterns (Relationships, Nuance, and Pattern Seeking) Personal economics Other possible reasons http://www.math.uakron.edu/~norfolk/why223f03.pdf  (Warning this is roughly 25 pages long written by college students presumably in a math class) This organization claims there are at least 40 careers in math: http://weusemath.org/?q=careers  (these are 40 different types of thinking arguably) Further, here is a list of math organizations, which can provide further reasons one might want to study math: http://www.tntech.edu/math/whymath/ The question begs the issue of how mathematics is taught (ie what kinds of practical applications and problems are being taught).  With more specificity on this point, you can focus the types of value created by studying math.  For instance, math overlaps with a lot of subjects and human knowledge, but learning those skills isn't intrinsic to studying math.  For instance, science, cooking/culinary arts, programming. and design all have math as a key component.  But learning those ways of thinking isn't intrinsic to the studying or practicing of math.  Almost anything with data or money or numbers as component....can potentially be used as a tool to learning more about math and life.

I don't know of any hard research on this particular topic and, as usual, the devil is in the  details when it comes to making any type of statements about quantified  intelligence. My opinion, however, is that there are certain skill sets that one would build and  enhance during the study of mathematics (or anything for that matter)  that can be applied to other areas of life as well. Critical thinking,  abstract reasoning, pattern recognition, internalizing information, generalization, problem solving techniques etc...These are not only vital to the study of mathematics, but also make you a more adept citizen of an increasingly complex world. Does this make one more intelligent? It depends how you define it.

It depends. When developing the One Child Policy the Chinese state relied on rocket scientists to calculate the effects of the policy on the population. At first glance, that makes perfect sense - they certainly know how to plot growth trajectories. At second glance, that's completely insane. Thinking about society in terms of numbers, and not of complex social interactions might help you generate accurate population estimates. But it doesn't in any way enable you to understand the social consequences of those population figures - such as elderly unable to rely on large numbers of children for support in their retirement. So, the ability to think in abstract terms encouraged by math can make you dumber if you apply it to areas which are ill suited to it.

If you think of math as computation and solving homework, then mostly not much. But studying mathematics as problem solving techniques and what is the problem that lead to those solution will help for sure, eventually every topic in mathematics is a solution to some problem. For example read about the history of quadratic equation solving and see the ideas that lead to solving those problems. At last solving a lot of mathematical problem with out knowing the intuition behind them will only make you a slow calculator.

There is this interesting line from Book VII of Plato's The Republic:And have you further observed, that those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been.

Yes, practicing math makes you more intelligent in other areas.  But not in ways that are special to math.  Any practice that requires problem solving skills will help you become a better problem solver.  By understanding how to dissect a problem, find causes, and imagine solutions, you can get to the meat of the matter and find a solution that fits all the constraints. Also, mathematics teaches humility.  This might sound wrong to the many people who see math geeks as arrogant alpha-nerds, but no matter how good you are, you will find a problem you can't solve.  Even if you do eventually find a solution, it will probably be by making a lot of mistakes, and figuring out why you were wrong, and how to fix it.  In short, you will come to realize that you are wrong a lot. The results-oriented nature of mathematics can also teach important lessons in "management".  For example, I have personally gained a lot of "personal" insight into the practice of "decision science" -- how to make decisions, while taking account the consequences of being wrong about our assumptions.  And I earned this insight by reading some formal definitions (easy), and making lots of mistakes in the course of some 4 years, in an environment where mistakes are tolerated, as long as they get fixed.  As I said, there is a cost in making mistakes, since we have to take the time to fix them.  So, given that I want to get a problem solved as quickly as possible, and don't have any strong intuition to prefer either of  two alternative solutions, how do I choose?  Personally, I choose the one that is least costly to fix if I'm wrong. None of these lessons are unique to math.  Math teaches them because it is problem and results-oriented, abstract, and so on.  In particular, results oriented fields will teach the same results-oriented lessons.  Other abstract fields will teach the same abstract lessons, and so on.

Mathematics is the art of describing and modeling systems which may or may not exist. Having the ability to see models around you gives you an extra sense and intuition of the systems around you which can be useful and help in many many areas of life...Just look how many areas it is the core of already.

I highly recommend the reading this article by the Mathematician Paul Halmos.  : http://math.slu.edu/~srivastava/Halmos.pdf It tells you what a mathematician does for a living and why he enjoys doing it. "What is mathematics ? Different people would give different answers. A student in elementary school would probably say that it was about adding, subtracting, multiplying and dividing. Oh yes - and about fractions and decimals too. A student in high school would say that it is about learning rules and formulas to solve equations. Oh-yes-and learning rules and formulas of geometry. I am afraid that all too many students of calculus would also say that mathematics is about rules and formulas and impossible word problems and getting the right answer by the right method. Then, since most people lose contact with mathematics after high school, or after calculus, the average citizen keeps a limited view of mathematics for a lifetime. That is too bad, because those answers are not complete and we should not carry around in our head any more delusions or distorted views of reality than we have to. Talk to a painter and talk to a mathematician, and you'll be amazed at how similarly they react. Almost every aspect of the life and of the art of a mathematician has its counterpart in painting and vice-versa. Every time a mathematician hears "I could never make my checkbook balance" a painter hears " I could never draw a straight line" -- and the comments are equally relevant and equally interesting. The invention of perspective gave the painter a useful technique, as did the invention of 0 to the mathematician. Old art is as good as new; Old mathematics is as good as new..." I think for me, with the little of maths I tend to do, I feel if there is one thing I am surprised by, it is the subtlety of it all. Meaning a slightly different assumption can have such huge ramification. Your initial intuitions are often wrong, you struggle for quite sometime and then have a view of looking at things, which then seems to work, at least for a while. Now to whether mathematics makes as more intelligent : Its a very loaded questions. It is in some sense the equivalent of asking if mountaineering makes us better in an long arduous journey. Sure it improves certain aspects, like our grit for analysis. Practicing math we already know or learning : Both. Partly because you might not know everything you think you already know. When I say practice, I don't mean dumb repetition of steps, but pondering over those steps, asking questions about it, finding connections from one problem to other, keeping track of what you can prove from what you can't etc.   PS: I was asked to answer this question. Thought for a very long time whether to answer or not and then decided.