New book breaks barrier between students and modern research in mathematics
In recent years mathematicians, armed with global internet (which simplifies collaboration), and powerful computers (used for numerical simulations, hypothesis testing, routine algebraic manipulations, etc.), have achieved some amazing breakthroughs in essentially all areas of pure and applied mathematics. Many questions and conjectures that bothered mathematicians for centuries are now resolved, new powerful techniques are developed, new theories unifying different areas of mathematics are created.
However, mathematicians are much less successful in another task of the highest importance: communicating their results and the power and the beauty of mathematics to the public. Most mathematical papers, surveys, and books are either too complicated or specialised in some specific areas and give no overall picture of current research in the whole of mathematics. As a result, even educated people often treat modern mathematics as something that a small group of mathematicians are doing for each other, with no or little impact on the outside world. Even students in mathematics departments learn mostly theorems proved over 100 years ago and have little or no understanding of what is going on in the current mathematical research. Moreover, even on the PhD level, the students often learn only their highly specialised area in depth, with very limited knowledge about recent mathematical discoveries in all other areas.
This situation can now change. Bogdan Grechuk, Lecturer from School of Mathematics and Actuarial Sciences of the University of Leicester, has made a terrific effort in analysing all the papers published at the beginning of the 21st century in the Annals of Mathematics, which is one of the greatest mathematical journals. He then selected 106 mathematical theorems of the highest quality, and explained their formulation and importance in the language accessible to undergraduate and postgraduate students. His book Theorems of the 21st Century breaks barrier between students and modern research in mathematics. It is also invaluable for general educated people who would like to learn about current mathematical research, and even for mathematicians who are interested in what is going on in mathematics outside of their area of expertise. This book may therefore become an important milestone in the process of popularisation of mathematics, making its beauty and importance more appreciated by the general community.
Dr Bogdan Grechuk says: "I fell in love with mathematics from early childhood. From high-school time and forever, I am interested in current mathematical research. However, most of recent mathematical papers are very difficult to understand. I always had a dream to have a book in which the greatest current mathematical theorems are explained in an accessible way. Because I could not find the book of my dreams, I finally had to write it myself."
Bogdan Grechuk won a golden medal at the World Mathematical Olympiad in 1997. He works in Leicester since 2011.
Professor Alexander Gorban, Chair in Applied Mathematics at the University of Leicester says: "In my youth, the book of Polya and Szergo, Problems and Theorems in Analysis opened the door into the nice collection of theorems for advanced undergraduate and postgraduate students. I remember the happiness of solutions of these problems when we feel congenial to the great mathematicians of the past. Dr Grechuk makes the 'past' much closer to our time: he collected very recent great theorems and explained them in simple but rigorous words. His book is the treasure box for all math lovers."