Section and page numbers are from the textbook The History of Mathematics: An Introduction by David Burton.
Lecture 1 (18.02.2026): Introduction, Syllabus
Lecture 2 (25.02.2026): Big history, Cosmic and biological evolution, Mathematics perception of animals, Examples from chicks, bees, ants, chimps, homo neanderthalensis, homo sapiens, Pre-history, Modes of industry in stone age, Number perception of humans and babies, Tally sticks, Parallel individuation system, Approximate number system (Sec 1.1).
Lecture 3 (11.03.2026): Mathematics in the Cradles of Civilization, Non-Eurocentric trajectory of history of mathematics, Americas: Inca and Quipu, Maya, Mayan astronomy and calendar, Mesopotamia: Sumer, Library of Ashurbanipal tablets and Behistun inscriptions, Babylonia, clay tablets, Plimpton 322 tablet, Egypt: Rhind, Moscow and Berlin papyrus, Rosetta stone, China: Yang Hui, India: Aryabhata, Brahmagupta, Sulbasutras, Jainist mathematics, Numerals: Maya, Egypt, Sumer, China, India (Chapter 2, Sec 5.3 pages 225-230, Sec 5.5 pages 251-263).
Lecture 4 (18.03.2026): History of ancient Greek, Macedon, Ptolemic Egyptian, Roman civilizations (kingdom, republic, empire), From mythos to logos, Pre-socratic philosophers: Milletian school, Pythagoras, Heraclitus, Anaxagoras, Empedocles, Democritus, Zeno, Peak of Greek philosophy: Socrates, Plato, Eudoxus, Aristotle, Hellenistic period: Euclid, Aristarchus, Archimedes, Eratosthenes, Apollonius, Hipparchus, Alexandrian Mathematics, Greek numerals, Roman empire: Ptolemy, Diophantus, Pappus of Alexandria, Hypatia, Roman architecture, Migration period and division of Roman empire, Byzantine mathematicians, Roman numberals, Roman, Julian and Gregorien calendars, Etymology and history of months and weekdays (Sec 3.1, 3.2, 3.3, Sec 4.1, 4.4, 4.5, Sec 5.1, 5.2)
Lecture 5 (25.03.2026): History of Islamic civilizations, Golden age of Islam, Science and philosophy in Islam, House of Wisdom, Madrasa, Observatories, Zijes, Trigonometry, Al-Fazari, Al-Mahani, Al-Khwarizmi, Al-Kindi, Thabit Ibn Qurra, Abu Kamil, Al-Battani, Ibn Al-Haytham, Fatima de Madrid, Lubna of Cordoba, Al-Ijliyyah, Al-Zarqali, Al-Idrisi, Ibn Rushd, Al-Samawal, Omar Khayyam, Sharaf al-Din al-Tusi, Nasir al-Din Al-Tusi, Al-Kashi, Influence of Islam on Europe, Toledo School of Translators, Hindu-Arabic numerals, Cities of Baghdad, Cordoba, Toledo, Cairo, Jund-i Shapur (Sec 5.5 pages 238-251, Sec 6.1, 6.2 pages 277-280)
Lecture 6 (01.04.2026): History of Europe, Recall of classical antiquity, Dark ages, 5th-16th centuries, Gerbert of Aurillac, The renaissance of the 12th century, Influence of Islam on Europe, Michael Scotus, Fibonacci, Renaissance, Italian algebra: Tartaglia, Cardano, Ferrari, Beginning of modern notation, Simon Stevin, John Naiper, Bernoulli family, Scientific revolution, Modern foundations of mathematics, 17-19th centuries (last three topics will be discussed in the future lectures in details) (Chapter 6, 7, Sec 8.1)
Lecture 7 (08.04.2026): Midterm
Lecture 8 (15.04.2026): History of Turkish civilizations: Beginnings, Kara-Khanid Khanate, Ghaznavids, Seljuk Empire, Mongol Ilkhanate, Timurid Empire, Al-Farghani, Divanu Lugati’t-Türk, Biruni, Madrasa and Nizam al-Mulk, Ulugh Beg and Zij-i Sultani, History of Anatolia (Asia Minor), Oghuz and Seljuk, Ottoman Empire: Al-Jazari, Qaḍi Zada al-Rumi, Mehmed the Conqueror, Ali Qushji, Piri Reis, Taqi ad-Din and Istanbul Observatory, Vidinli Tevfik Pasha, Mehmet Nadir Bey, Salih Zeki, Rasathane-i Amire and Kandilli Observatory
Lecture 9 (22.04.2026): Republic of Türkiye, Reforms of Atatürk, Letter reform, Agop Dilaçar, Geometry book of Atatürk, University reform, Albert Malche, German scholars, History of universities, Aydın Sayılı, Feryal Özel, Feza Gürsey, Erdal İnönü, Kerim Erim, Cahit Arf
Lecture 10 (29.04.2026): A very short history of philosophy, Kant, Analytical philosophy, A synthesis of history of mathematics, Set theory, ZFC set theory, Logic, Foundational crisis in mathematics, Logicism, Frege, Russell, Formalism, Hilbert program, Constructivism/Intuitionism, Brouwer, Brouwer-Hilbert controversy, Gödel, Cohen, Continuum hypothesis, Category theory (Sec 11.4 pages 646-650, Sec 12.2, 12.3)
Lecture 11 (13.05.2026): A brief history of numbers and algebra, Fermat's last theorem and Wiles' proof of Taniyama–Shimura–Weil conjecture, Number systems, Vidinli Tevfik Pasha, Cayley-Dickson construction, Polynomials, Ruffini, Abel, Galois, Gauss, Prime numbers, Twin prime conjecture and Goldston–Pintz–Yıldırım sieve, Cem Yıldırım (Sec 10.1, 10.2, 10.3, 11.4 pages 630-646, 13.1)
Lecture 12 (20.05.2026): A brief history of geometry, astronomy and laws of mechanics, Aristotelian laws and spacetime, Scientific revolution, Heliocentric universe model, Copernicus, Kepler's law, Galilean Spacetime, Newton's laws of motion and gravity, History of calculus, Descartes, Newton and Leibniz, Analysis and topology, Generalized Poincare conjecture, Selman Akbulut, Euclid's axioms, Fifth parallel axiom, Hyperbolic geometry, Elliptic geometry, Lobachevsky, Riemann, Electromagnetism and aether, Special and general relativity, Black holes and cosmology, Quantum gravity and search for a new geometry (Sec 8.1, 8.2, 8.3, 8.4, 11.1, 11.2)