How abstract mathematics can help us understand the world | Dr Eugenia Cheng | TEDxLondon

Main ideas and concepts

• Problem framing: The modern public sphere feels dominated by divisive arguments, including:

  • conflict
  • fake news
  • blame
  • prejudice/bigotry
  • “victimhood” contests
  • echo chambers

• Proposed tool: Abstract mathematics can help people understand and navigate these social conflicts—not by solving school-style equations for daily life, but by using mathematical-style thinking to:

  • structure arguments
  • build empathy

• Bridge from math to society: A math concept about factors and hierarchical structure is generalized into a model for interacting types of privilege.

Method / instructional structure (as presented)

Step 1: Start with a concrete math example (factors of 30)

• Define factors of 30 as the numbers that divide 30:

[ 1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30 ]

• Organize factor relationships visually:
  • Create a cube-like hierarchy/family-tree diagram showing which numbers divide which.

Step 2: Identify “levels” via prime factorization

• Bottom level: (1)

  • Framed as: “nothing divides them except themselves.”

• Prime level: (2, 3, 5) (primes)

• Next level: products of prime factors:

  • (6 = 2 \times 3)
  • (10 = 2 \times 5)
  • (15 = 3 \times 5)

• Top level: the whole number:

  • (30 = 2 \times 3 \times 5)

Step 3: Generalize the diagram to an abstract template

• Replace specific numbers with letters:

  • Treat prime factors as generic elements (a, b, c).

• Interpret the diagram structurally as an abstract cube of combinations:

  • Top: (a, b, c)
  • Middle: pairwise combinations
  • Lower: single elements
  • Bottom: none (empty set)

Step 4: Map abstract elements to social categories

• Example assignment (types of privilege):

  • (a, b, c) could represent rich, white, and male

• Use cube corners to represent groups defined by which privilege types they have.

• Add emphasis for inclusion:

  • Include non-male (for non-binary people) by explicitly adding adjective variants (e.g., “non-male”).

Step 5: Draw lessons from the structure

Lesson A (misinterpretation correction)

A common misunderstanding is:

“White privilege means all white people are better off than all non-white people.”

The model instead suggests a conditional/hypothetical claim:

• If someone (e.g., a super rich black sports star) had the same characteristics except whiteness, they would be expected to be better off.
• So the privilege is not a blanket “everyone beats everyone.”

Lesson B (inequality is uneven across rows/layers)

• Privilege combinations at the same “level” aren’t necessarily equal in outcome.
• Example reasoning:
  • Rich white women may be better off than poor white men.
  • Rich black men may fall somewhere between.

Therefore, the real-world effect is skewed, not perfectly symmetric.

Lesson C (interaction between privilege layers changes interpretation)

• Someone with fewer privilege types could still outperform someone with a different mix due to cross-layer interaction.
• Example given:
  • Michelle Obama / Oprah Winfrey are described as doing better than poor, white, unemployed, homeless men, even with different privilege combinations.

Lesson D (explaining anger without just counter-attacking)

The model helps explain why:

• some poor white men may feel anger

They can be “high” in a relative privilege structure (in the cube), but not feel absolute advantages.

• Suggested response: understand the root of that anger rather than reacting angrily.

Lesson E (context switching / multiple “tops”)

• The “top of the cube” changes when you restrict the context.
• For instance:
  • Broad society: “rich white men” occupy the analogous top position.
  • Restricted context (non-men only): “rich, white, non-men” would be the top in that restricted view.

This helps interpret why anger can be directed toward rich white women in some feminist discourse:

• They may perceive themselves as underprivileged compared to white men, while forgetting relative privilege versus non-white women.

Step 6: Use the model as a personal practice (pivoting)

• Everyone can pivot mentally between:
  • when they are more privileged
  • when they are less privileged

Example (as described by the speaker):

• As an Asian person, she feels less privileged than white people (due to white privilege),
• but also among the more privileged within non-white groups.

She also compares wealth positions:

• not super-rich, but better off than those struggling (e.g., unemployed or minimum-wage workers).

These pivots are used to understand others’ perspectives.

Step 7: Conclusion / desired social outcome

• Abstract mathematical thinking can support empathy and encourage people to work together instead of competing to “prove others wrong.”
• Hope stated: people understand one another more and collaborate.

Speakers / sources featured

• Dr Eugenia Cheng (speaker)
• TEDxLondon (event/context; not a distinct person in the subtitles)
• Examples referenced: Michelle Obama and Oprah Winfrey