Project:A comment on history of geometry, analysis and computer science

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One historical event triggers another, and in a long chain of cause and effect, the first event and the last event, in many cases, do not necessarily have a recognizable, substantial causal relationship; people call it a chance. The most famous and hypothetical example is a hurricane caused by a butterfly in South America. Unlike the flapping of a butterfly's wings, events in the history of mathematics have epistemological significance. In this case, is there an epistemological causal connection between the first event and the last event in the causal chain? This topic is what we mainly want to explore in this essay.

Our example is about analysis, geometry, and computer science history. In this short text, we will give a minimal retrospect on history and ask a question on the development of mathematics. Furthermore, we will discuss the learning problem in this context at the end.

A minimal retrospect

Babylonian mathematicians knew how to accumulate small changes to approximate a physical process[1]. Many early mathematicians, such as Eudoxus, Archimedes in ancient Greece, or later Liu Hui, Zu Chongzhi in ancient China, they significantly used infinitesimals to solve their mathematical tasks.

In the early 17th century, mathematicians like Barrow, Descartes, Fermat, they intensively investigate the concept of derivative. In 1637, Descartes published the groundbreaking La Géométrie. [2] Since then, a new toolset was developed and sharpened to combine the power of algebra and geometry. Descartes' work influenced to the creation of calculus in 1666 and 1684 by Newton and Leibniz.[3]

The elusive infinitesimal invoked a broad discussion; it required a rigorous foundation of real analysis.

The development of non-Euclidean geometries

Hilbert's program and Gödel's incompleteness theorems

The discovery of computability theory in 1930s

Our questions

The interdisciplinary position of computer science?

The learning problem

References

  1. Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484.
  2. Neovius, Sofia. “René Descartes’ Foundations of Analytic Geometry and Classification of Curves.” (2013).
  3. Grabiner, Judith V.. “Descartes and problem-solving.” Mathematics Magazine 68 (1995): 83-97.