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Mathematics has changed not only what I notice,

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but also what I'm willing to ignore, at least

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for a while. This is the power of abstraction.

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When mathematicians study a problem, they often

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set aside details that do not matter for the

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question at hand. We may draw a triangle in blue

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ink, tilt it to one side, or place it in the

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corner of a page. These details are visible,

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but they are not relevant to whether the sum

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of the interior angles is 180 degrees in Euclidean

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geometry. Ignoring them allows us to concentrate

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on the structure beneath them. Abstraction can

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help us to see what very different situations

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have in common, but it also raises an important

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question. Which details are irrelevant? and which

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are essential? And that question becomes especially

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important when we move from mathematical objects

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to human beings. So, in the book X plus Y, mathematician

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Eugenia Ching uses abstraction to reconsider

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familiar ideas about gender and behavior. Rather

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than labeling certain qualities as masculine

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and others feminine, she proposes a different

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dimension. Ingressive and congressive. Ingressive

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behavior emphasizes the individual, asserting

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oneself, competing, and pursuing individual achievement.

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Congressive behavior emphasizes bringing people

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together, collaborating, connecting, and strengthening

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the community. Chang's point is not that one

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category belongs to men and the other to women.

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And once we set aside the gender labels, we can

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examine the behaviors themselves and ask which

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ones our institutions encourage and reward. That

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change in abstraction helps us to ask better

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questions. Rather than asking how many people

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can succeed within a competitive system, could

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become more congressive? Could success include

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helping other people flourish? Could education

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become less about demonstrating individual superiority

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and more about building understanding together?

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This has changed the way I think about fairness.

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Fairness is not always achieved by treating everyone

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the same, because people do not necessarily begin

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in identical circumstances. But at the same time,

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focusing on every difference can prevent us from

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seeing our shared humanity. We need the wisdom

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to know which differences matter in a particular

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situation and which ones are distracting us from

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the deeper structure. Mathematics does not automatically

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answer these questions. An abstraction can clarify.

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but it can also conceal. If we ignore the wrong

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detail, we may create a model that is elegant,

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but unjust. What mathematics gives me is a disciplined

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way to ask, what am I choosing to notice? What

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am I temporarily setting aside? What becomes

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clearer because of that choice? Who might disappear

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from view? Abstraction changes the way I see.

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Fairness asks me to use that changed vision responsibly.