Індивідуальне читання за фахом

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René Descartes made many notable contributions to mathematics. In 1618 Descartes journeyed to Holland, where he met Isaac Beeckman, a thirty year-old student of medicine who was astounded at the range of Descartes' scientific curiosity. Over the next few weeks Descartes showed Beeckman how to apply algebra and mathematics to many problems. He proposed algebraic formula to determine the raise in water level when a heavy object was placed in water, drew a geometric graph that showed how to predict the accelerating speed of a pencil falling in a vacuum at any time during a two hour period, and showed how a spinning top stays upright and how this could be used to help man become airborne. Beeckman's journal showed us that by the end of 1618, Descartes was already applying algebraic equations to solve geometric problems, and that it was then, not later as many sources say, that he invented analytical geometry.

One day during the winter while he was in the army, Descartes decided to escape the cold by shutting himself up in a stove. While there he had dreams with flashing lights and thunder, in which it seems some spirit was revealing to him a new philosophy. This was the way that a geometric proposition can be transferred into algebraic terms, using a vertical axis, a and a horizontal axis, b. Any position to the left or right of the vertical axis can be shown as some function on a and b. This let the geometric equations be manipulated in new ways that were impossible using a mass of geometric tangents. Five days before his twenty-third birthday Descartes wrote a letter to Beeckman in which he told him that there was no problem in geometry that cannot be expressed using axes, lines and curves.

Before Descartes all of the sciences and mathematical fields had been thought of as separate entities. He had seen that if math was a "science of discontinuous quantities", and geometry was a "science of continuous quantities" the barriers that had been perceived to separate them collapse, creating analytical geometry. Descartes also realized that arithmetic and algebra were not just sciences of numbers, but sciences of propositions, which justified the use of irrational numbers and opened up vast new mathematical possibilities. After this Descartes universalized this principle in the first of his "Rules for Guidance of the Mind": Descartes said that math and all of the sciences were interrelated and are easier to treat as a whole than break apart and learn individual little pieces. Descartes reinforced the commonness of all the sciences in his fourth rule, in which he stated that mathematics can be applied to all measurable things : "Without its mattering that this measure be sought for in numbers, figures, stars, sounds or any other object, and thus one observes that there must be some general science explaining everything that one can look for regarding order and measurement without application to a particular matter, and that this science is called universal mathematics." The universal mathematics that Descartes described has since been applied to optics, astronomy, meteorology, acoustics, chemistry, architecture, physics, engineering, accounting, and warfare, all of which Descartes foresaw, plus electronics, cybernetics, microbiology, genetics, economics, and even politics, which he didn't.

General understanding

Answer the questions in written form:

1. Why was Isaac Beeckman do astounded at Descartes’ personality?

2. What inventions were made by Descartes by 1618?

3. In what circumstances did the new philosophy come to Descartes?

4. What were the main principles of this philosophy?

5. What epithet did Descartes use for his mathematics? Why did he use namely that word?