Insights into Mathematics | Finite versus infinite and number systems | Sociology and Pure Mathematics | N J Wildberger @njwildberger | Uploaded 2 years ago | Updated 3 hours ago
A social scientist wanting to understand the culture of mathematics needs also to have at least some familiarity with the role of number systems throughout history. This is a rich and surprising topics, and in subsequence videos in the series we will be investigating quite different historical roles, starting with the fascinating Egyptian and Mesopotamian number systems and then move forward towards to modern European epochs and eventually the current difficulties that beset the so-called theory of "arithmetic with real numbers".

There are many important sociological questions that arise when looking at the almost deliberate attempt by the academy to ignore discussion of this crucial topic.

The rift between the realities of computational mathematics and the dreaming of pure mathematics in the direction of "real numbers", "infinite series" and "transcendental functions" (just to get started) is now so pronounced that it is become impossible to dismiss. One place to anchor the discussion in the difference between studying a finite discrete system, say a list or sequence , and the corresponding "infinite or unbounded" concepts --which are at their core quite different mathematical objects and need to be treating quite differently.

So let's start a wide ranging discussion about the role of numbers in mathematics, and how to explain the sociological forces that maintain the pretense that all is well despite obvious evidence to the contrary.

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Here are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained: youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: youtube.com/playlist?list=PLBF39AFBBC3FB30AF
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And here are some of the other Wild Egg Maths Playlists (some available only to Members!)

Solving Polynomial Equations: youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
Exceptional Structures in Maths and Physics via Dynamics on Graphs" youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
Triangle Centres: youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-