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- 01:00 CRD Babylonians. From 3000-200BC. Before Islam. Corn yields. Digging canals. Astronomy. Algorithmic. Base 60: hence 60 seconds, 360 degrees.
- 04:20 CRD Indians. 800BC-1200AD. Astronomy and religion. Interest in v big numbers. Often handed down in poetical / oral phrases.
- 05:30 JAK Omayyads early: not v scholarly. Abbasids C8: Persian, Indian, Greek texts started obsession with learning. Baghdad biggest city in world. Also lines in Qu’ran re learning.
- 08:31 House of Learning in Baghdad at time of Al-Ma’mum. Little archaeological evidence. JAK compares with library of Alexandria.
- 11:00 PP translation. Pythagoras and Euclid household names also in Islamic world. Textbook was Euclid’s Elements.
- 13:00 PP Babylonian, Greek, Indian interrelations. Solon says “Greeks like children, all knowledge from Egyptians”. Euclid sources unknown.
- 14:30 CRD Greek maths geometric, but it pioneered idea of proof. Algebra solving probs of area and volume; not provable thing. Early algebra written in prose. Full symbolism not until 1600s-1700s, but sense of algebra comes in it being an area of study.
- JAK More on algebra in prose. Symbols not until Descartes. Greeks and Babylonians looked at specific examples. Al-Kwarizmi book looked at general algorithms first and specifics at end of book. Book for wider public: solve taxation etc.
- 18:50 PP Greeks solved problems, Arabs equations. Opens up solving quadratic and cubic equations – solving problems requiring greater levels of abstraction.
- 23:00 CRD Six different types of quadratic equation (not happy with -be numbers or zeros yet); topic on pen right worth classifying so anything involving squares, roots and things can be solved.
- 24:00 CRD Our tens + units type system Indian. Making itself through to Arab world by 600s. Better than Roman numerals (horrendous for division) or Babylonian.
- 25:30 JAK Indian decimals (base 10). Arabs using mix of Babylonian base 60 (sexuagesimal), Greek letters, reluctant to use decimals. Europeans also sceptical. Took centuries to catch on.
- 27:00 Distinction between decimals abs decimal fractions.
- 29:00 PP Spread of paper in C9 Baghdad. Mathematicians in Andaluce as well as Baghdad. Afghan / Uzbekistan. Texts travel.
- 30:45 MB Omar Khayyam known to us as poet, but …
- CRD classifies cubic equations. Can’t give algebraic solution but gives geometric solutions intersecting curves. Gives approx solutions. Sets 4-5C race to solve cubics.
- 32:00 JAK Myth they invented 0. Au contraire. Symbol / Placeholder: Babylonian (also Mayan). Concept / Nothingness: Aristotle – philosophical, not mathematical. Number: Indians – Ariavata (C6), Rama Gupta; inherited as package with 1-9. Infinity much later, as did number line stretching either side of -1/+1. Arabs did not acknowledge zero as an answer.
- 35:00 PP C12/13. Robert of Chester translating Al-Kwarizmi. Latin takes over from Arabic as language of learning. Hit or miss what was translated.
- 36:20 CRD Fibonacci. Travelled. Learned Hindu numerals and algebra. Wrote Book of Abacus. Use of Indian numerals for trade.
- 37:30 JAK Belittling (not necessarily insidious) of Arab contribution. Copernicus acknowledges Islamic astronomers. But Galileo/Kepler/Newton v rapid development almost inevitable roots forgotten. Fragmemtation of Abassid empire into kingdoms, fiefdoms, caliphstes. No printing press in Arab world; scribes as part of culture.
- 40:00 PP Not downhill C13+, exchange doesn’t stop.
- 41:00 JAK Legacy. Algebra, trigonometry.
- Extra time not catalogued.

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