Problems with the Calculus | Math History | NJ Wildberger

We discuss some of the controversy and debate generated by the 17th century work on Calculus. Newton and Leibniz's ideas were not universally accepted as making sense, despite the impressive, even spectacular achievements that the new theory was able to demonstrate.

In this lecture we discuss problems with the differential calculus (i.e. derivatives), integral calculus and the nature of curves, the role of imaginary numbers, and a conundrum involving probability theory, called the St. Petersburg paradox.

Amongst the critics were members of the Bernoulli family, a Dutch physician, and an English bishop. The debate was very important historically--it motivated 18th century mathematicians, notably Euler and Lagrange, to try to put the calculus on a more logical algebraic foundation, and led also to 19th century work on limits and the nature of the continuum, along with 20th century axiomatic approaches to real numbers, and Robinson's non-standard analysis.

Arguably, a lot of these essential difficulties have not been fully dealt with, even by modern axiomatic approaches. The problems of the calculus form part of a trajectory going back to the ancient Greeks, and are still very much with us now in the 21st century.

************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

   • MathHistory: A course in the History ...  
   • WildTrig: Intro to Rational Trigonometry  
   • Math Foundations  
   • Wild Linear Algebra  
   • Famous Math Problems  
   • Box Arithmetic  
   • Elementary Mathematics (K-6) Explained  
   • Year9Maths  
   • Ancient Mathematics  
   • Wild West Banking  
   • Sociology and Pure Mathematics  
   • Sociology and Pure Physics  
   • Old Babylonian Mathematics  
   • Probability and Statistics: an introd...  
   • Boole's Logic and Circuit Analysis  
   • Universal Hyperbolic Geometry  
   • Differential Geometry  
   • Algebraic Topology  
   • MathSeminars  
   • Playing Go  
   • Diffusion Symmetry: A bridge between ...  

Here are the Wild Egg Maths Playlists (some available only to Members!)

   • Algebraic Calculus One  
   • Classical to Quantum (Members only)  
   • Algebraic Calculus Two  
   • Advice for mathematics exploration (M...  
   • Solving Polynomial Equations (Members...  
   • The Hexagrammum Mysticum (Members only)  
   • Algebraic Calculus and dCB curves (Me...  
   • Dynamics on Graphs (Members only)  
   • Плейлист  
   • Triangle Geometry  
   • Explorations with q-series (Members o...  
   • Six: An elementary course in Pure Mat...  
   • Maxel Inverses and Orthogonal Polynom...  
************************