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17
two had a scandalous, rocky affair. The basic problem was that they
were both too passionate about their work to give it up for the other.
Maxim's work took him away from Stockholm and he wanted Sofia to
give up her hard-earned positions to simply be his wife. Sofia flatly
rejected such an idea but still could not bear the loss of him. She re-
mained in France with him for the summer and fell into another one of
her frequent depressions. Again, she turned to her writing. While she
was in France, she finished Recollections of Childhood.
In the fall of 1889, she returned to Stockholm. She was still mis-
erable at the loss of Maxim even though she frequently travelled to
France to visit him. She eventually became ill with depression and
pneumonia. On February 10, 1891, Sofia Kovaleskaya died and the
scientific world mourned her loss. During her career she published ten
papers in mathematics and mathematical physics and also several liter-
ary works. Many these scientific papers were ground-breaking theories
or the impetus for future discoveries. There is no question that Sofia
Krukovsky Kovalevskaya was an incredible person. The President of
the Academy of Sciences, which awarded Sofia the Prix Bordin, once
said: "Our co-members have found that her works bear witness not
only to profound and broad knowledge, but to mind of great inventive-
ness".
18
1. Read and translate the text
Topic 3
The Nature of Mathematics
Mathematics reveals hidden patterns that help us understand the
world around us. Now much more than arithmetic and geometry,
mathematics today is a diverse discipline that deals with data, meas-
urements, and observations from science; with inference, deduction,
and proof; and with mathematical models of natural phenomena, of
human behavior, and of social systems.
As a practical matter, mathematics is a science of pattern and or-
der. Its domain is not molecules or cells, but numbers, chance, form,
algorithms, and change. As a science of abstract objects, mathematics
relies on logic rather than on observation as its standard of truth, yet
employs observation, simulation, and even experimentation as means
of discovering truth.
The special role of mathematics in education is a consequence of
its universal applicability. The results of mathematics – theorems and
theories – are both significant and useful; the best results are also ele-
gant and deep. Through its theorems, mathematics offers science both a
foundation of truth and a standard of certainty.
In addition to theorems and theories, mathematics offers distinc-
tive modes of thought which are both versatile and powerful, including
modeling, abstraction, optimization, logical analysis, inference from
data, and use of symbols. Experience with mathematical modes of
thought builds mathematical power – a capacity of mind of increasing
value in this technological age that enables one to read critically, to
identify fallacies, to detect bias, to assess risk, and to suggest alterna-
tives. Mathematics empowers us to understand better the information-
laden world in which we live.
During the first half of the twentieth century, mathematical
growth was stimulated primarily by the power of abstraction and de-
duction, climaxing more than two centuries of effort to extract full
benefit from the mathematical principles of physical science formu-
lated by Isaac Newton. Now, as the century closes, the historic alli-
ances of mathematics with science are expanding rapidly; the highly
two had a scandalous, rocky affair. The basic problem was that they 1. Read and translate the text
were both too passionate about their work to give it up for the other. Topic 3
Maxim's work took him away from Stockholm and he wanted Sofia to
The Nature of Mathematics
give up her hard-earned positions to simply be his wife. Sofia flatly
rejected such an idea but still could not bear the loss of him. She re- Mathematics reveals hidden patterns that help us understand the
mained in France with him for the summer and fell into another one of world around us. Now much more than arithmetic and geometry,
her frequent depressions. Again, she turned to her writing. While she mathematics today is a diverse discipline that deals with data, meas-
was in France, she finished Recollections of Childhood. urements, and observations from science; with inference, deduction,
In the fall of 1889, she returned to Stockholm. She was still mis- and proof; and with mathematical models of natural phenomena, of
erable at the loss of Maxim even though she frequently travelled to human behavior, and of social systems.
France to visit him. She eventually became ill with depression and As a practical matter, mathematics is a science of pattern and or-
pneumonia. On February 10, 1891, Sofia Kovaleskaya died and the der. Its domain is not molecules or cells, but numbers, chance, form,
scientific world mourned her loss. During her career she published ten algorithms, and change. As a science of abstract objects, mathematics
papers in mathematics and mathematical physics and also several liter- relies on logic rather than on observation as its standard of truth, yet
ary works. Many these scientific papers were ground-breaking theories employs observation, simulation, and even experimentation as means
or the impetus for future discoveries. There is no question that Sofia of discovering truth.
Krukovsky Kovalevskaya was an incredible person. The President of The special role of mathematics in education is a consequence of
the Academy of Sciences, which awarded Sofia the Prix Bordin, once its universal applicability. The results of mathematics – theorems and
said: "Our co-members have found that her works bear witness not theories – are both significant and useful; the best results are also ele-
only to profound and broad knowledge, but to mind of great inventive- gant and deep. Through its theorems, mathematics offers science both a
ness". foundation of truth and a standard of certainty.
In addition to theorems and theories, mathematics offers distinc-
tive modes of thought which are both versatile and powerful, including
modeling, abstraction, optimization, logical analysis, inference from
data, and use of symbols. Experience with mathematical modes of
thought builds mathematical power – a capacity of mind of increasing
value in this technological age that enables one to read critically, to
identify fallacies, to detect bias, to assess risk, and to suggest alterna-
tives. Mathematics empowers us to understand better the information-
laden world in which we live.
During the first half of the twentieth century, mathematical
growth was stimulated primarily by the power of abstraction and de-
duction, climaxing more than two centuries of effort to extract full
benefit from the mathematical principles of physical science formu-
lated by Isaac Newton. Now, as the century closes, the historic alli-
ances of mathematics with science are expanding rapidly; the highly
17 18
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