Based on above reading, write a short essay to answer following questions: ( ple

Question

Based on above reading, write a short essay to answer following questions: ( please type it )
1. From the point of view of a student of the history of mathematics, how do you judge Kline's characterization of the relationship between pure and applied mathematics? 2. How do you think mathematics of the distant and recent past would react to what marhemaricians do today? 3. Are there any changes we should make in how we do and teach mathematics? On On p. 247, Dunham quotes the late Morris Kline, who was a strong advocate of Johnny Can't the applications ofmathematics. Here is a quote "Why Add": ...most mathematicians of the past hundred years have broken away from science. They know no science, and what is more, are no longer concerned with the utilization of mathematical research in It is true that some, aware the noble tradition that motivated mathematical claim the past and that warranted the honor to men such as Newton and Gauss for potential scientific value for their mathematical work. They speak of creating models science. But in truth they are not concerned with this goal. In fact, since most modern mathematics professors know no science they can't be creating models. They are quite willing to of ne by reflection of the light shed by great mathematicians o the past and even justify support their present research by citing the accomplishments of their predecessors. Mathematics now happened inward; it feeds on itself; and is extremely unlikely, judge to the in the past, that most of modern mathematical research will ever contribute advancement of science. When confronted with this charge, the mathematicians deny it then defend their creations on the ground that they are beautiful. hether or not there i beauty in the creations need not be a here. The important point is that this value is used to justify the work.

Explanation / Answer

1.Pure math is a branch of mathematics which lays more focus on the discovery of the properties of numbers and applied mathematics is a branch which deals with the utilisation of the discoveries in mathematics in finding out the laws of nature or how everything around us function,primarily the utilisation of this branch in science and it's different branches.Kline is extremely skeptical and apprehensive about the relationship between pure and applied maths. The one of the primary reasons for this apprehension is the attitude of the mathematicians towards the application of their mathematical discoveries,their indifference towards the importance of science,their lack of concern towards the application of the mathematical discoveries in science,their false promises to create mathematical model for science,where in reality he's quite convince that they lack the sheer capabilities to do so primarily because they're not concerned with it and because he lack the scientific knowledge to do so. Kline is not completely at fault for drawing such conclusions and forming such opinions. Mathematicians tend to focus primarily on the nature of their mathematical research, the discovery of an anti particle by Paul Dirac, was due a mere anomaly in the calculations,he was only concerned with the math and least with what the result could actually prove,which luckily turned out to be a major discovery in the field of particle physics. There are quite an ample of instances where mathematicians paid no heed to the application of their work in science.

2.The mathematicians of the past (either distant or recent )should react quite postively with high hope to the mathematicians and mathematics of the present generation,today any mathematical discovery is not judged by the mere beauty of its properties but it's application either in science or in economics or finance or in computer science. The reaction of mathematics critique like Kline would be positive considering the attitude of the present day mathematicians. If on one hand we have a set of theoreticians discovering something worth the scientific importance on the other we have a team of experimentalists proving it. The discovery and the application is going hand in hand. Discovering something and then applying it to find solutions to the problems in science has become a unified project.Even the highest honour that is conferred on the scientist that is the Nobel prize has application of the proved theory as one of the criteria for awarding the same.

3. A lot can be said and argued about the nature of teaching in today's world,not only about mathematics. Since,the demands for jobs is skyrocketing, the schools are more concerned with imparting their pupil with as many modules as possible,so that they become competitive in the real world as they graduate so that they're guaranteed more number of jobs. Especially,in the field of mathematics which is quite high on demand everywhere from physics to Engineering,from economics to finance to neurobiology and etc, the focus on quality learning can be assumed to be decreasing since the focus of the students will always be only the completion of the syllabus for tests in order to fetch highest scores possible. We can either increase the duration of completion of a degree or reduce the amount of the syllabus to ensure quality learning with the aptitude for scientific research.

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