Can Mathematicians Code? The Intermediate Value Theorem
The IVT is introduced in every first-year differential calculus course, and gives a way of proving the existence of solutions to various equations... but does it say anything about how we can algorithmically find such a solution? Mathematicians don't program, they prove... but can we extract algorithms from proofs? __________ Timestamps: 00:00 - I want to apologise 00:43 - What is the IVT? 01:52 - Elementary proof 04:19 - Algorithm I 04:45 - Objections to the proof 05:03 - Abstract proof 05:20 - Step 0: Continuity (in detail) 06:28 - Step 1: Connectivity 07:42 - Step 2: The abstract IVT 08:18 - Step 3: Intervals are connected 09:18 - Algorithm II 09:51 - The truth about proof II 10:50 - Conclusion 11:00 - Thx 4 watching
▶︎
The beauty of Fixed Points
▶︎
What is a Monad? – Math vs Computer Science
▶︎
Topology: Why Mathematicians Say A Cup Is A Doughnut (The Math Behind Topology Ep1)
▶︎
Prelude to Galois Theory: Exploring Symmetric Polynomials
▶︎
A shallow grip on neural networks (What is the "universal approximation theorem"?)
▶︎
What does BLAZINGLY FAST even mean??
▶︎
Can programmers do math? What is a real number, really?
▶︎
A 50-Year Theorem Just Fell | The Square Root ShortCUT
▶︎
What is a Hilbert Space?
▶︎
We're 99.9% sure this pattern is true, but no one can prove it
▶︎
Solving one of the logic puzzles of all time!
▶︎
MIT Godel Escher Bach Lecture 1
▶︎
Why AI Can Never Escape Turing's 1936 Proof
▶︎
Solving a finite number problem using infinities
▶︎
WTF is Sheafification??
▶︎
What is a Comonad? – Comath and Mputer Science
▶︎
What's the big deal with the Yoneda Lemma?
▶︎
Putting Algebraic Curves in Perspective
▶︎
The Theoretical Limit of Image Compression
▶︎