I had a lot of fun chatting with Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about:

- Whether advanced math requires AGI
- What careers should mathematically talented students pursue
- Why Grant plans on doing a stint as a high school…

In this video we'll talk about Padé approximants: What they are, How to calculate them and why they're useful.

Chapters:
0:00 Introduction
0:33 The Problem with Taylor Series
2:11 Constructing Padé Approximants
4:50 Why Padé Approximants are useful
5:45…

Attached: 1 image

Continuing to make progress on my #Lean4 formalization project. Thanks to a tip from a follower here, I was able to complete the proof that the derivative of a polynomial that splits of the reals, also splits over the reals, and as such…

There's often a lot of emphasis in math on generalizing concepts beyond the domains where they were originally defined, but what are the limits of this process? Let's take a look at a small example from complex analysis where we actually have the tools to…

A fundamental principle of derived deformation theory is that a formal “space” (i.e. formal moduli problem) can be encoded by a differential graded Lie algebra, or more generally, an $l…

In my last post, I told you how to encode the zero locus of a polynomial function $latex f: V \to E &fg=000000$ in terms of an $latex L_{\infty} &fg=000000$-algebra structure on $latex L = …

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sources and references, in temporal order:

Nature paper on the decline in disruptive science:
https://pubmed.ncbi.nlm.nih.gov/36599999/

Gordon Shepherd's book on the revolutionary 1950s "Creating Modern Neuroscience":
https://www.amazon.com/Creating-Modern…

Mathematics is about finding better ways of reasoning. But for many applied mathematicians, the primary mission is to shape their minds in a way that gets them closer to the truth. The calculations are secondary, the real question is: how we can better understand…

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If you would like help with your studies:
https://drive.google.com/file/d/1…

In this lecture, part of the celebration event for the tenth anniversary of the Andrew Wiles Building, home to Oxford Mathematics, Andrew himself traces the background to the one of the most famous series of conjectures in modern mathematics, starting in…

Let $latex {S}&fg=000000$ be a non-empty finite set. If $latex {X}&fg=000000$ is a random variable taking values in $latex {S}&fg=000000$, the Shannon entropy $latex {H[X]}&fg=00000…

Solutions to the wave equation preserve energy, and so, in some sense, they maintain their regularity over time. Nevertheless, there is a paradoxical local smoothing phenomenon: When measured in certain aspects, waves can become significantly smoother in…

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

My Courses: https://www.freemathvids.com/ || We go over one math book for every single math subject. Below are the list of math subjects covered in this video in the order that they appear in the video.
***************MATH BY SUBJECT*****************
Beginning…