The power of mathematical thinking: from Newton's laws to elections and the economy

The unreasonable effectiveness of mathematics

Seeing higher dimensions and symmetry

Understanding Ptolemy's enduring achievement

Kepler's 3 laws of planetary motion

Newton's powerful law of gravitation

Is Newton's law precisely correct?

Expansion and recurrence: Newtonian chaos!

Stable motion and central configurations

The evolution of the expanding universe

The winner is: determined by voting rules

Why do voting paradoxes occur?

The order matters in paired comparisons

No fair election rule? Arrow's theorem

Multiple scales: when divide and conquer fails

Sen's theorem: individual versus societal needs

How majority improvements go wrong

Elections with more than three candidates

Donuts in decisions, emotions, color vision

Apportionment problems of the U.S. Congress

The current U.S. apportionment method

The mathematics of Adam Smith's invisible hand

The unexpected chaos of price dynamics

Using local information for global insights

Toward a general picture of what can occur.

Disc 1. The unreasonable effectiveness of mathematics ; Seeing higher dimensions and symmetry ; Understanding Ptolemy's enduring achievement ; Kepler's 3 laws of planetary motion ; Newton's powerful law of gravitation ; Is Newton's Law precisely correct?

Disc 2. Expansion and recurrence: Newtonian chaos! ; Stable motion and central configurations ; The evolution of the expanding universe ; The winner is... determined by voting rules ; Why do voting paradoxes occur? ; The order matters in paired comparisons

Disc 3. No fair election rule? Arrow's theorem ; Multiple scales: when divide and conquer fails ; Sen's theorem: individual versus societal needs ; How majority improvements go wrong ; Elections with more than three candidates ; Donuts in decisions, emotions, color vision

Disc 4. Apportionment problems of the U.S. Congress ; The current U.S. apportionment method ; The mathematics of Adam Smith's invisible hand ; The unexpected chaos of price dynamics ; Using local information for global insights ; Toward a general picture of what can occur.