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Module 6 Unit 1

Mathematics

Mathematics differs from the other sciences in that its subject is not nature. Progress in mathematics is usually not directly realized by the public since its results are so abstract and often isolated from every-day experience that they are difficult to understand. However, occasionally some mathematical news becomes visible to a broader public. One example is the application of large prime numbers for encryption purposes. Sometimes a result in pure mathematics also catches public attention like the recent proof of Fermat’s last theorem, which resisted the best efforts of mathematicians for more than three and a half centuries.

But mathematics is more than just peculiar theorems and occasional popular achievements. Because of its precision and accuracy, it is an essential tool for all of the sciences. There are many examples from the history of science in which the development of new mathematical methods allowed scientists to formulate fundamentally new theories and to achieve revolutionary conceptual breakthroughs. One of the most spectacular cases in this century was Einstein's use of the non-Euclidian geometry developed by Riemann in the 19th century to formulate the general theory of relativity.

The last part of the 20th century saw spectacular advances in mathematics, especially in the theory of dynamical systems and in stochastic analysis*. A combination of analytical and geometrical ideas has been characteristic of these developments. One example is the use of diffusion-reaction equations* to understand biological pattern formation*. Another example is the advances in our understanding of turbulence, in particular in the context of weather forecasting.

In the middle of the 20th century mathematics was examining its own foundations. Today we see a different trend, which is strongly influenced by recent advances in computing technology. Mathematical modelling, the development of algorithms, and scientific computing have become powerful tools for all the sciences. They promise to play a crucial role in future progress.

*stochastic analysis - вероятностный анализ

*diffusion-reaction equations - уравнение реакции диффузии

*biological pattern formation - формирование биологического рисунка

Chemistry

The chemical sciences have made breath-taking advances during the last five decades. They have provided innumerable benefits through an extremely wide range of applications. These include not only new materials, food additives, pharmaceuticals, and pesticides, but also new analytical tools for the study of living matter as well as the environment. The structures of many molecules were determined and this has provided the basis for their synthesis and production on an industrial scale. Notable examples are vitamins, which complement many biochemical reactions in the human body, and antibiotics, which have saved many lives.

In addition to characterising and synthesising a vast number of natural products, chemists have also designed absolutely new compounds. Major progress was also made in the synthesis of tailor-made polymers*, composite materials, and ceramics which is capable of superconduction.

Organic chemistry was instrumental to the great advances in understanding the structure and function of biomolecules. This has had an enormous impact on the bio-medical sciences. For instance, in 1954, the first naturally occurring protein hormone was analysed and then synthesised. For the first time, it was shown that an artificially produced protein has exactly the same properties as those naturally produced. The synthesis of insulin, a life-saving protein for diabetics, followed shortly thereafter. In 1959, the three-dimensional structure of haemoglobin (the oxygen-transporting molecule that makes blood red) was determined at atomic resolution*. Since then, the structures of thousands of biologically important molecules have been described. This knowledge plays a vital role in the development of new diagnostics and therapeutics. Aided by fast computers, medicinal chemists increasingly use the knowledge of bio-molecular structures to design small compounds with very specific pharmacological properties and make significant contributions both to our understanding of life processes and to medicine.

The chemical sciences are also contributing to the environmental sciences. For example, they provide new materials and contribute to the development of new means to crop protection, as well as animal and human health.

*tailor-made polymers - полимеры с заданными свойствами

*at atomic resolution - на уровне атомов

Astronomy

Over the last fifty years, our own solar system and its origins have become much better known. Many new satellites and rings around planets have been discovered and the nature of comets has been disclosed. One of the main reasons for this development was the beginning of the space age. All of these innovations were made possible by new observation instruments. Fifty years ago, the largest telescope was a 5-metre optical telescope, whereas modern telescopes are four times larger and more powerful. Furthermore, in 1990, the Hubble space telescope was sent into orbit. It has provided a lot of new information about our universe, as the radiation it collects does not have to pass through the Earth's atmosphere.

From the early 1960s on, communication satellites were sent into orbit, making wireless communication possible all around the world. Landings on the Moon and the planets by probes of ever-increasing sophistication started in the mid-1960s and continue today. Some of them have brought back samples making an in-depth chemical analysis of their composition possible. In 1969, the first man set foot on the moon, only twelve years after the first satellite was launched.

Another example is the development of weather satellites, which have become indispensable for tracking hurricanes and other violent storms. While these storms are still potentially dangerous, timely warning of their approach has saved many lives and helped to avoid vast property damage. There are also the Earth resource satellites which have become an integral part of geological data collection and provide us with a better means of assessing the Earth's resources. In addition, these satellites supply information about forest growth and crop diseases*.

*crop diseases - заболевания сельскохозяйственных культур

(Adapted from “Science for the Twenty-First Century: A New Commitment”, by Paul Hoyningen-Huene, Marcel Weber, and Eric Oberheim)