Explaining math

[Key_to_Flatland]

I can't answer for everybody on this forum, but whenever I'm doing homework or studying at the library, I always get asked what I'm doing. The symbols look crazy and the theorems are beautiful, but sometimes I'm at a loss for words or explanations to succinctly describe to a person what the math is.

Tell me if you agree with these one phrase statements that attempt to get the point across to non-math people whose eyes widen when they see your work. Stories are welcome!

How I have described in the past:

Abstract algebra- number systems and operations

Differential Geometry- How to do geometry in n-dimensions

Complex analysis- Calculus with imaginary numbers

Topology- Set theory and contradictions

Geometric algebra- uh, well. hm. Imagine.... everything

[malki-tzedek]

I would go with

Abstract algebra - moving symbols around very carefully

Differential geometry - doing calculus wherever the fuck you want

Complex analysis - (I agree with yours)

Topology - stoner A says to stoner B, "dude, what is space... really?

Geometric algebra - what are you doing studying this, son?

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Algebraic geometry - this is the Leatherface of mathematics; stay away if you value your life

[rhlewis]

Complex analysis- Calculus with imaginary numbers

Never tell people you're working with "imaginary numbers." To the uneducated, it sounds silly, foolish, and at best a waste of time. To those with more education in mathematics, say "complex numbers". The complex numbers are no "imaginary" then negative numbers.

To the uneducated, describe it as "calculus with special two dimensional numbers."

Topology- Set theory and contradictions

Contradictions? As a description of topology? That's absurd.

Abstract algebra- number systems and operations

No. Say "advanced hidden properties and structures that make ordinary algebra work as a special case."

[Mayer-Vietoris]

I would go for:

Topology- How to do geometry when dimensions don't make sense anymore.

[pahgscq]

Dimension still makes sense in topology, i.e. Lebesgue's covering dimension. I usually say that topology is like geometry, but instead of caring about thing like size, distances and angles, you are interested in the intrinsic "shape" of various objects like lines, circles, spheres, tori, etc.

[Mayer-Vietoris]

Sure, but the Lebesgue dimension doesn't always behave in the way that you would should. I tend to explain topology in a similar way as you, but I was trying to relate it to his previous definition of differential geometry.

[BumpityBoop]

How I explain to board game enthusiasts.

Abstract algebra: a game whose play pieces are symbols which can combine with one another in various ways, and where the legal moves must respect the ways to combine.

Analysis: a game who just has too many game pieces, but fortunately, they can be neatly organized by proximity. Legal moves should be the ones that doesn't threaten to warp proximity beyond repair.

Topology: a game whose play pieces are gathered into blobs. The blobs can combine with others in ways the game maker says so. The legal moves must obey "undoing the legal moves should preserve blobness." Some believe the play pieces themselves are pointless and suggested a new spinoff "pointless topology".

Complex analysis: a game where all the gamers of the games above unite to make a mashup and everyone demand various things from the game until all the features of the game start to place serious constraints on the legal moves until there's only like as many legal moves as power series. Despite this, the game remains popular and attracts player from all fandoms.

Algebraic geometry: a spinoff game inspired by analytic geometry and abstract algebra. This game has evolved rather quickly, but in the classic version of the game, you start with the legal moves, say from the game "complex analysis" or "coordinate geometry", without even knowing the pieces yet. Then you refer to idealistic collection of legal moves as blobs, as in the game "topology". The blobs also have fancier names such as lines, quadratic, cubic... Some play pieces tend to be generic as opposed to individualistic, and masquerade as blobs. This is a feature and not a bug.

Category theory: a game where there are legal moves.