Mathematics, physics and theoretical physics

Mathematics and physics in reality

Within the School of Engineering there are a number of researchers active in Mathematics and Theoretical Physics.

On a practical level, mathematics is fundamental for Engineering Science since all technology uses mathematics for description, understanding and computation. Physics (and Chemistry) constitutes the natural science foundation for all of modern technology. Without these fundamental sciences, our modern technological society would be impossible. Any school of engineering must keep an active contact with research in these basic areas of human knowledge.

Superficially, theoretical research might not appear to be very relevant to a University dedicated to professional science and education. Quite to the contrary, theoretical science is never far from the applications. Just because of its abstract and general nature, mathematics, theoretical physics and also theoretical computer science are very powerful tools when practical knowledge has to be systematised, structured and generalised. Indeed, ‘’theory’’ could be seen as empirical knowledge that one has ‘’made sense of’’. This can be underlined by an historical example. The great ancient cultures had a lot of practical knowledge in mathematics, geometry and astronomy as well as practical technology. Undoubtedly all this knowledge played a great role in the functioning of these societies. It could well be argued that ancient civilisation would not have been possible without the mathematics of those days. But not until the advent of the Greek civilisation was a theoretical science born including mathematics and natural philosophy that during the long rediscovery period from the 12th century onwards finally during the 16th and 17th centuries gave rise to natural science and technology in the modern sense.

During the last two centuries science and technology has grown together in a symbiotic interaction. It is hardly possible, nor meaningful to try to disentangle them. New discoveries within natural science soon find technological applications, and new improved technology facilitates new discoveries and better measurements. New areas of technology such as logistics use theories from mathematics and computer science.

The nature of mathematics and physics

Modern Mathematics and Theoretical Physics are two scientific disciplines with both similarities and differences. They are characterised by somewhat different scientific cultures, and it is rare that one and the same person is active in both fields although it is not that uncommon to be interested in the other discipline. At the same time there is much that unites the fields, and they certainly share a lot of concepts and techniques.

Physics has historically, during certain periods and in certain contexts, been a source of inspiration for the development new mathematics. On the other hand, mathematics that initially was thought to have no application, have turned out to be useful in physics, technology and computer science. Indeed, it is remarkable to note that almost all of mathematics has applications in natural science and technology. During the past decades both disciplines has started to interact closely with theoretical computers science.

Mathematics is a logical, deductive science characterised by a very high standard of rigour in definitions, theorems and proofs. Inner consistency, simplification, abstraction and generalisation are strong forces behind progress in mathematics.

In theoretical physics, advanced mathematical tools are used for description of physical phenomena, predicting results of experiments and observations, but mainly for building a number of theoretical structures which together encompass all of the known physics from the largest cosmological distances down to the smallest submicroscopic scales.

Both disciplines are characterised by a very high level of abstraction and the main resource needed in order to carry out research in them is time, time to reach the frontier of research and time to be able to get something done once there.