Foundations of Mathematics Buried in School Garbage (Southern Mesopotamia, Early Second Millennium BCE)

2019 ◽  
pp. 1-25
Author(s):  
Christine Proust
Keyword(s):  
Foundations Of Mathematics ◽  
Second Millennium Bce

Category Theory and Foundations

2018 ◽  
Author(s):  
Michael Ernst
Keyword(s):  
Category Theory ◽  
Mathematical Thinking ◽  
Mathematical Practice ◽  
Foundations Of Mathematics ◽  
Ongoing Debate ◽  
Technical Adequacy ◽  
Theoretical Foundations

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.

Indo-Europeans

2012 ◽  
Author(s):  
H. Craig Melchert
Keyword(s):  
Eastern Europe ◽  
Traditional View ◽  
Asia Minor ◽  
European Languages ◽  
Linguistic Evidence ◽  
Second Millennium Bce

This article presents an overview of the arrival and florescence of the Indo-European languages in Anatolia, the most famous of which is Hittite. The weight of current linguistic evidence supports the traditional view that Indo-European speakers are intrusive to Asia Minor, coming from somewhere in eastern Europe. There is a growing consensus that the differentiation among the Indo-European Anatolian languages begins at least by the mid-second millennium BCE and possibly earlier. It is likely, but not strictly provable, that this differentiation correlates with the entry of the Indo-European speakers into Anatolia and their subsequent dispersal. Nothing definitive can be said about the route by which the Indo-European entry took place.

Carl Friedrich Gauss. Inaugural Lecture on Astronomy and Papers on the Foundations of Mathematics

1938 ◽  
Vol 12 (6) ◽  
pp. 314
Author(s):  
Martin A. Nordgaard ◽  
G. Waldo Dunnington
Keyword(s):  
Foundations Of Mathematics ◽  
Inaugural Lecture

Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus

2010 ◽  
Vol 23 (2) ◽  
pp. 151-186 ◽  
Author(s):  
Fabio Acerbi
Keyword(s):  
Present Article ◽  
Foundations Of Mathematics ◽  
Previous Issue ◽  
Greek Mathematics ◽  
Set Up ◽  
Key Characters

ArgumentThis article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.

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