Matching Games

Note: These are not designed to be student facing.

I make these notes available with the intent of making it easier to plan and/or take notes from class.

Student facing resources for each topic are all available at vknight.org/gt/.

Activity (20 minutes)

Student Instruction Sheet

You have been given a character card. Each card describes the personality,
strengths, and tendencies of a famous mathematician or physicist. A short
sentence also gives a fact about their historical contributions.

Your task is to imagine how your character would rank the members of the
opposite group.

  1. Read your card carefully.
  2. Think about which characters your own character would most like to work
    with, and which they would not.
  3. Write down a ranked list from most preferred to least preferred.
  4. Keep your preferences private until the matching begins.

We will then run the stable matching algorithm together. Be ready to:

  • Propose to other characters in the order you ranked them.
  • Accept or reject proposals depending on your list.

After the activity, we will discuss:

  • How the algorithm guarantees stability.
  • How the outcome changes depending on who proposes.
  • What this might mean in real-world applications of matching algorithms.

Teacher Instruction Sheet

Below are suggested preference orders for each character. These are based
on the biographies provided, but you can change them to keep the game fresh.
(Students can also invent their own lists if you want more variety.)

Mathematicians vs Physicists

Mathematicians

  • Gauss: Einstein > Curie > Newton > Feynman
  • Noether: Curie > Feynman > Einstein > Newton
  • Turing: Einstein > Feynman > Curie > Newton
  • Euler: Newton > Curie > Einstein > Feynman

Physicists

  • Einstein: Noether > Gauss > Turing > Euler
  • Curie: Noether > Euler > Turing > Gauss
  • Newton: Gauss > Euler > Noether > Turing
  • Feynman: Turing > Noether > Gauss > Euler

Past vs Present Mathematicians

Past Mathematicians

  • Euclid: Erdős > Lovelace > Turing > Noether
  • Archimedes: Noether > Lovelace > Erdős > Turing
  • Euler: Turing > Noether > Lovelace > Erdős
  • Newton: Noether > Turing > Euler > Erdős

Present Mathematicians

  • Noether: Archimedes > Euler > Newton > Euclid
  • Lovelace: Newton > Euler > Euclid > Archimedes
  • Turing: Euler > Newton > Noether > Euclid
  • Erdős: Euclid > Newton > Noether > Archimedes

Teaching Notes

  • Start with one group proposing (e.g., mathematicians to physicists).
  • Record the matching.
  • Reset, then swap proposers (e.g., physicists to mathematicians).
  • Compare the two outcomes and highlight who benefits in each case.

Use the discussion to connect to fairness, power, inclusivity, and real-world
matching systems like school admissions and residency matches.


Character Bios


Mathematicians vs Physicists

Carl Friedrich Gauss (1777–1855)
Gauss, often called the “Prince of Mathematics,” valued precision and elegance.
He preferred collaborators who respected rigor and quiet focus. He was less
interested in flashy ideas than in solid foundations.
Contribution: Gauss made fundamental contributions to number theory,
statistics, analysis, differential geometry, and electromagnetism.

Emmy Noether (1882–1935)
A pioneer of abstract algebra, Noether loved symmetry and generality. She
thrived with creative, inclusive collaborators and dismissed narrow or rigid
approaches.
Contribution: Noether’s theorem revealed the deep link between symmetries and
conservation laws in physics.

Alan Turing (1912–1954)
Visionary and analytical, Turing admired boundary-pushing ideas in logic and
computation. He was impatient with old-fashioned approaches but enjoyed
brilliance and playful creativity.
Contribution: Turing is considered a father of computer science and helped
crack the Enigma code in World War II.

Leonhard Euler (1707–1783)
Prolific and versatile, Euler thrived on solving many problems with boundless
energy. He liked enthusiastic colleagues and disliked skeptics or show-offs.
Contribution: Euler made groundbreaking contributions across mathematics,
including graph theory, analysis, and mechanics.

Albert Einstein (1879–1955)
Einstein valued bold, imaginative ideas and admired eccentric creativity. He
struggled with rigid, routine-based thinkers.
Contribution: Einstein developed the special and general theories of
relativity, revolutionizing physics.

Marie Curie (1867–1934)
Curie respected discipline, patience, and practicality. She admired
collaborators who balanced creativity with hard work, but avoided drama.
Contribution: Curie discovered polonium and radium, and pioneered research in
radioactivity.

Isaac Newton (1642–1727)
Intense and ambitious, Newton respected power and clear reasoning. He liked
determined collaborators but disliked rivals.
Contribution: Newton developed the laws of motion and universal gravitation,
and co-invented calculus.

Richard Feynman (1918–1988)
Playful and curious, Feynman thrived on excitement and fresh perspectives. He
disliked rigidity and self-importance.
Contribution: Feynman contributed to quantum electrodynamics and became known
as a brilliant physics communicator.


Past vs Present Mathematicians

Euclid (c. 300 BCE)
Euclid loved order, clarity, and logical systems. He admired systematic
thinkers and disliked chaotic approaches.
Contribution: Euclid wrote Elements, one of the most influential works in
the history of mathematics.

Archimedes (c. 287–212 BCE)
Archimedes was inventive and practical, preferring energy and cleverness. He
grew frustrated with endless theorizing without application.
Contribution: Archimedes advanced geometry, mechanics, and invented ingenious
machines such as war engines and pumps.

Leonhard Euler (1707–1783)
(Prolific and versatile, as above.) Euler enjoyed enthusiastic collaborators
and disliked obstruction or excessive skepticism.
Contribution: Euler bridged pure and applied mathematics, creating much of
modern mathematical notation.

Isaac Newton (1642–1727)
(Intense and ambitious, as above.) Newton demanded high standards and resisted
undermining of his authority.
Contribution: Newton’s Principia Mathematica laid the foundation for
classical mechanics.

Emmy Noether (1882–1935)
(Creative, symmetry-loving, as above.) She admired open collaboration and
avoided rigid hierarchies.
Contribution: Noether’s algebraic insights transformed mathematics and
physics alike.

Ada Lovelace (1815–1852)
Visionary and imaginative, Lovelace embraced the link between art and
mathematics. She admired forward-looking colleagues and disliked dismissive
critics.
Contribution: Lovelace is regarded as the first computer programmer for her
notes on Charles Babbage’s Analytical Engine.

Alan Turing (1912–1954)
(Logical and boundary-pushing, as above.) He admired curiosity about machines
and avoided conservative views.
Contribution: Turing formalized the concept of computation and proposed the
universal Turing machine.

Paul Erdős (1913–1996)
Restless and eccentric, Erdős loved endless collaboration and disliked
territoriality.
Contribution: Erdős published more papers than any other mathematician and
is celebrated for his collaborative spirit.


Example Gale–Shapley Run (Mathematicians Propose)

Round 1

  • Gauss proposes to Einstein (accepted).
  • Noether proposes to Curie (accepted).
  • Turing proposes to Einstein (Einstein prefers Noether to Gauss, but Gauss is
    better than Turing → Einstein keeps Gauss, rejects Turing).
  • Euler proposes to Newton (accepted).

Round 2

  • Turing, rejected by Einstein, proposes to Feynman (accepted).

Final Matching (Mathematicians propose)

  • Gauss ↔ Einstein
  • Noether ↔ Curie
  • Euler ↔ Newton
  • Turing ↔ Feynman

This outcome is mathematician-optimal. Repeat with physicists proposing to
see how the matches change.


Discussion (20 minutes)

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