Section and page numbers are from the textbook The History of Mathematics: An Introduction by David Burton.
Lecture 1 (27.02.2025): Introduction, Big history, Mathematics perception of animals, Examples from chicks, bees, ants, chimps, Number perception of humans and babies, Tally sticks, Parallel individuation system, Approximate number system (Sec 1.1).
Lecture 2 (06.03.2025): Mathematics in the Early River Valley Civilizations, Non-Eurocentric trajectory of history of mathematics, Americas: Inca, Maya, Mayan astronomy and calendar, Quipu, Mesopotamia: Sumer, Babylonia, clay tablets, Egypt: Rhind papyrus, Rosetta stone, China: Yang Hui, India: Aryabhata, Brahmagupta, Sulbasutras, Jain mathematics (Chapter 2, Sec 5.3 pages 225-230, Sec 5.4 pages 251-263).
Lecture 3 (13.03.2025): History of ancient Greek, Macedon and Roman civilizations, 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, From Hellenistic to Dark: Ptolemy, Diophantus, Pappus of Alexandria, Hypatia (Sec 3.1, 3.2, 3.3, Sec 4.1, 4.4, 4.5, Sec 5.1, 5.2)
Lecture 4 (20.03.2025): History of Islamic civilizations, Golden age of Islam, Science and philosophy in Islam, House of Wisdom, Madrasa, Observatories, Zijes, 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 (Sec 5.5 pages 238-251, Sec 6.1, 6.2 pages 277-280)
Lecture 5 (27.03.2025): 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, 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, Republic of Türkiye, Reforms of Atatürk, University reform, Aydın Sayılı, Feryal Özel, Feza Gürsey, Erdal İnönü, Kerim Erim, Cahit Arf
Lecture 6 (17.04.2025): 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 (08.05.2025): 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, Peano axioms, Constructivism/Intuitionism, Brouwer, Law of excluded middle, Brouwer-Hilbert controversy, Gödel, Cohen, Continuum hypothesis, Axiom of choice, Category theory (Sec 11.4 pages 646-650, Sec 12.2, 12.3)
Lecture 8 (15.05.2025): A brief history of numbers, Fermat's last theorem and Wiles' proof of Taniyama–Shimura–Weil conjecture, Number systems, Vidinli Tevfik Pasha, Cayley-Dickson construction, Polynomials, Ruffini, Abel, Galois, Wantzel and old problems: Angle trisection, doubling the cube, squaring the circle, Gauss and fundamental theorem of algebra, Prime numbers, Euclid, Eratosthenes, Ibn al-Haytham, Al-Marrakushi, Mersenne, Germain, Ramanujan, Euler, Euler-Riemann zeta function, 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 9 (22.05.2025): A brief history of geometry, astronomy and laws of mechanics, Aristotelian laws and spacetime, Ptolemy and epicycles, Scientific revolution, Heliocentric universe model, Copernicus, Kepler's law, Galileo, Newton's laws of motion and gravity, History of calculus, Eudoxus, Archimedes, Al-Haytham, Sharaf al-Din al-Tusi, Descartes, Newton and Leibniz, Analysis and topology, Generalized Poincare conjecture, Selman Akbulut (Sec 8.1, 8.2, 8.3, 8.4)
Lecture 10 (29.05.2025): History of geometry in detail, Euclid's axioms, Fifth parallel axiom, Newtonian mechanics, Hyperbolic geometry, Elliptic geometry, Lobachevsky, Bolyai, Gauss, Riemann, Thurston geometrization conjecture (now theorem), Metric-affine geometry, Electromagnetism and aether, Lorentz transformations, Special and general relativity, Black holes and cosmology, Quantum gravity and search for a new geometry (Sec 11.1, 11.2)