TOK situations in mathematics
Knowledge of abstract structure established by proof from stated assumptions. Mathematics offers the nearest thing to certainty available to a knower, and raises the sharpest questions about what its objects are and why so much of it turns out to describe the world.
- The Middle East and North Africa
The book that named algebra
Al-Khwarizmi's ninth-century treatise systematised equation-solving for inheritance shares and trade, and its title gave algebra its name while his own gave us…
Enduring · Mathematics
- Explanation
- Culture
- East Asia
Move 37
In its 2016 match against Lee Sedol, AlphaGo played a move professional commentators initially called a mistake and later called beautiful, a line no human…
Enduring · Mathematics
- Interpretation
- Explanation
- South Asia
The third umpire and the ball that never arrived
A batter is given not out. The fielding side reviews. On the big screen, a tracking system reconstructs the ball's flight, and then continues it past the point…
Enduring · The natural sciences · Mathematics
- Evidence
- Certainty
- Interpretation
- Global
The proof no human has read
The 1976 proof of the four colour theorem relied on computer checking of hundreds of case configurations that no mathematician could verify by hand, and parts…
Enduring · Mathematics
- Certainty
- Justification
- India
Calculus before Newton, in Kerala
Mathematicians of the Kerala school, beginning with Madhava in the fourteenth century, derived infinite series for pi and trigonometric functions centuries…
Enduring · History · Mathematics
- Truth
- Perspective
- Global
The first woman to win the Fields Medal
Maryam Mirzakhani, Iranian-born and educated through Tehran's olympiad system, became in 2014 the first woman awarded mathematics' highest honour, in a…
Enduring · Mathematics
- Perspective
- Culture
- India
Binary patterns in Sanskrit prosody
Pingala's ancient treatise on Sanskrit poetic metre enumerates syllable patterns in ways that parallel binary representation and combinatorial rules formalised…
Enduring · Mathematics
- Explanation
- Culture
- The Middle East and North Africa
Finding the direction of prayer
Determining the qibla from any city is a problem in spherical trigonometry, and medieval Islamic mathematicians developed sophisticated solutions and…
Enduring · Mathematics
- Explanation
- Culture
- Latin America
Records tied in knots
Inca administration ran on quipus, cords whose knots encoded census and tribute data and possibly narrative, and Spanish authorities destroyed many precisely…
Enduring · History · Mathematics
- Interpretation
- Culture
- India
Ramanujan's unproven theorems
Srinivasa Ramanujan filled notebooks with thousands of results, many stated without proof and attributed by him to intuition or the goddess Namagiri.…
Enduring · Mathematics
- Interpretation
- Justification
- Global
The purest mathematics, weaponised for privacy
Number theorists studied primes for centuries as the discipline's most ornamental corner, celebrated precisely for uselessness, until public-key cryptography…
Enduring · Mathematics
- Values
- Explanation
- India
The textbook called Vedic Mathematics
The calculation shortcuts published in the twentieth century as Vedic Mathematics are useful and teachable, but historians of mathematics find no source for…
Enduring · History · Mathematics
- Power
- Justification