In my house, we have a saying: “Never send a dynamicist to do a geometer’s job.” I usually say it while pretending to re-holster my finger guns after sweeping through and correcting the inefficient, and borderline offensive, way my spouse had loaded the dishwasher. My dishwasher loading exploits are the stuff of legend around here.
My spouse and I are both mathematicians. We have a lot in common in how we think about math, but we specialized in different fields. They aren’t exactly on opposite sides of the grand map of mathematics. I studied geometry—shapes, how they’re put together, what happens when you stretch them— and he studied dynamical systems—how mathematical spaces get jumbled up when you transform them. We joke that my geometrical background is the reason I’m so much better than he is at loading the dishwasher. In contrast, his dynamical systems background makes him better at mixing drinks and scrubbing the toilets. (We want the scum to be uniformly removed from the porcelain, after all, and sometimes you have to mix chemicals to do it.) Never fear; he does not perform these chores simultaneously.
Our family joke got me wondering what household chores are best for mathematicians in other disciplines. There is sometimes a belief that mathematicians have their heads in the clouds and don't do well with practical work. Nonsense! It's all a matter of finding the right chore for the particular branch of math. Here are a few of my recommendations. Disclaimer: Roots of Unity takes no responsibility for damage to persons or property based on hiring mathematicians to do household work instead of professionals who are actually experts in the task at hand.
Algebra: Algebra is the study of symmetries and structure, of the relationships between objects and transformations that obey a set of rules. Algebraists are naturally suited to interior design and carpentry.
Algebraic geometry: Algebraic geometry is a very hot field right now. As the name sort of suggests, they use algebraic tools to study geometry, often looking at problems relating to where the zero sets of certain polynomials are. You will often find algebraic geometers discussing fields and sheaves because they secretly wish they were farmers. They love being outside doing some raking, mowing, or gardening.
Analysis: In mathematics, analysis is a large field that roughly refers to souped-up calculus in its many different forms. Analysts are good at vacuuming, sweeping, and mopping.
Combinatorics: This is the study of discrete structures and configurations. How many people do you have to invite to a party in order to know that three mutual acquaintances or three mutual strangers will be there? Combinatorialists know how to find the answer. They’re good at designing seating charts or deciding who should walk with whom on the way to school in order to maximize social mixing or other questions about how to arrange people or things, so consider them for event planning. (Be warned, though: they might take 150 years to do it.) In addition, they often learn to juggle or do magic tricks, so they make pretty good babysitters.
Complex analysis: Complex analysts work in the complex plane. They often look at the way functions of complex variables behave, as opposed to functions of real variables. They are predisposed to ironing and sewing. After all, what is sewing but imposing a not-too-stretchy 2-dimensional structure, perhaps with a few singularities for seams or darts, around each point in a garment?
Dynamical systems: Dynamicists like my spouse look at how spaces get mixed up when you perform the same transformation over and over. They are well-suited to mixing drinks, making soup, and baking. They’re good at cleaning large, uniform surfaces. Think scrubbing toilets, sinks, and floors, not dusting. Use caution if you ask them to watch your pet.
Functional analysis: Functional analysts like analysis so much they do analysis to their analysis. Or at least that’s a flippant way to think about functionals and the calculus of variations. In addition to the vacuuming skills you can expect from all analysts, they make good navigators.
Geometry: As discussed above, geometers like yours truly are great at loading the dishwasher. They are also good at assembling flat-pack furniture and performing minor household repairs.
Logic: Mathematical logicians work on formal logic, examining proofs, and the foundations of mathematics. Their careful approach to reasoning through a problem can be invaluable when it comes to plumbing and electrical work. Be careful if you ask them to look at your foundation, though. You might not like it if they report that its structural integrity is undecidable.
Number theory: Naturally, number theorists deal with numbers. Specifically, they often focus on the distribution of prime numbers. They are meticulous and precise, and their problems are often easy to state and understand but extremely difficult to solve. Contrary to popular belief, you don’t necessarily want them to be balancing your budget or calculating a tip, but they are excellent at dusting. They are no strangers to time-consuming, frustrating tasks, so they won’t even bat an eye at dusting the baseboards and crown molding.
Partial differential equations: A person who studies PDEs (should we call them partial differentiators?) looks at equations involving multiple variables and their derivatives. They often know a lot about equations describing heat, wave patterns, acoustics, and electricity. They can be useful for working on your HVAC system, plumbing, electrical wiring, or sound systems, but you must approach them carefully. The first time you talk to them, they might just tell you whether or not a solution exists and, if so, whether it is unique. If you ask for specifics, they’re likely to tell you the problem can’t be solved exactly. But if you press them, they might pull out some numerical analysis and give you a solution that will be good enough for whatever you need it for.
Probability: Sometimes confused for combinatorialists or statisticians, probabilists analyze how likely certain outcomes are given certain beginning probabilities and initial conditions. They're probably good at everything. (Har!) Ask them for help with budgeting and investing. They also make the best couponers, so you should send them to do the grocery shopping.
Statistics: Statisticians are mostly good for telling you you’re doing everything wrong.
Topology: Topology is sometimes called rubber sheet, or postmodern, geometry. Topologists aren’t quite as meticulous as geometers when it comes to the exact shapes and sizes of objects, so you probably don’t want to put them on dish duty. Their flexibility really shines when it comes to cooking and decorating. They host creative and enjoyable dinner parties.
How'd I do? Did I get the chore right for your favorite area of math? Do you love a branch of mathematics or a chore I neglected? Feel free to send your suggestions to me on Twitter or Facebook.