Historical Aspects of Mathematics  HAM

Instructor: Dr. András RINGLER

"The philosophy begins with the wonder, first about the simple things (about everyday things), then about the Sun and Moon, and then about the origin of the World."                                                                                             (Aristoteles)

"If we wish to foresee the future of mathematics our proper course is to study the history and present condition of the science".                             (Henry Poincaré)

The goal of the lectures: to follow and demonstrate the development of natural philosophy. The course is recommended to students (mathematicians, physicists and engineers), who are interested in natural sciences.

The lecturer will discuss those thoughts, ideas and discoveries that have changed the face of the natural sciences and have given direction to the development of technical progress. The thoughts, ideas and efforts of eminent scientists, the technical progress and the cultural institutions were born and were effective among particular historical and ideological circumstances. The knowledge of these past events is not only a part of general education, but acts as a compass to those persons who feel responsibility for the future of  humankind. The names Thales, Aristoteles, Pythagoras, Archimedes, Bruno, Copernicus, Galilei, Kepler, Descartes, Newton, Leibnitz, Watt, Volta, Faraday, Maxwell, Marie Curie, Einstein, Neumann etc. are not only simple names, but very "weighty", behind these names are very serious thoughts and discoveries, still influencing our everyday life. The results of the work of these persons - like the beacon from a lighthouse - illuminate the path of knowledge for subsequent generations.

Recommended books:

- Morris Klein: Mathematical thought from ancient to modern times, New York, Oxford University Press, 1972 (ISBN 0 19 501496 0)
- Jack Meadows, W. H. Brock and A. G. Keller: The history of scientific discovery, Phaidon Press Limited, Oxford, 1987.
- John Desmond Bernal: The extension of man, a history of physics before 1900, Weidenfeld and Nicolson, 5 Winsley street London W 1.

Content of the course:

1. Empirical experiences and its importance in the natural philosophy. The history of measurement. The SI system
2. The ancient civilisations. The development of simple everyday tools, weapons and agricultural implements
3. The origin of natural sciences. Mathematics in Mesopotamia (number symbols, arithmetic operations, algebra and geometry). Mathematics in Egypt. The Egyptian and Julianus calendar
4. The natural philosophy of classical Greek philosophers (Thales, Anaximandros, Pythagoras, Demokritos, Platon, Aristoteles, Archimedes, Ptolemaios)
5. The mathematics in Greece and Alexandria: the Pythagoreans, the Platonic and Aristotle’s school. The mathematical works of Euclid and Apollonius. Alexandrian activity in geometry
6. The discovery of compass. The mathematics of Hindus and Arabs. The natural philosophy in the medieval period
7. The technical development in the medieval period and in the renaissance. The appearance of cannons and the motion of cannon-balls
8. The development of astronomy and navigation in the late medieval period and in the  renaissance. Copernicus
9. Science and religion: Tycho Brahe, Giordano Bruno, Johannes Kepler, Galileo Galilei
10. Arithmetic and Algebra in the sixteenth and seventeenth centuries (The beginnings of coordinate geometry and the calculus, Descartes, Newton, Leibnitz)
11. The work of Newton. The development of light concept
12. The development of heat concept and the history of steam engine
13. The development of electricity and magnetism: generators and motors, electromagnetic waves
14. Radioactivity. The significance of radioactive isotopes. Nuclear powerstations. Energy production in stars