We can elegantly prove Gödel's 1st and 2nd incompleteness theorems using the language of computation. In this blog post, I present it in a way so that things follow intuitively from Cantor's work. And the concept of self-referencing emerges from a more basic principle. Link below
On the one hand, 3SAT has a surprising and very clever subexponential-time algorithm.
On the other hand, no polynomial-time approximation algorithm for MAX-3SAT can do better than flipping a coin for each variable (unless P = NP).
In math, is there still a point in communicating a full proof among ourselves, or should we just communicate the proof idea? (Assuming a machine can fill in the details.)
I talked to Anupam Gupta @anupamg about his research area, theoretical computer science in general, advice for students, and more... He is one of the kindest and smartest people you'll ever meet.
https://t.co/ICi4M7XZGC
We can elegantly prove Gödel's 1st and 2nd incompleteness theorems using the language of computation. In this blog post, I present it in a way so that things follow intuitively from Cantor's work. And the concept of self-referencing emerges from a more basic principle. Link below
An inspiring talk (at a personal and a scientific level) by the great Bernhard Haeupler at CMU; do watch at least the first 5 minutes!
https://t.co/FFJ776zKty
🎉¡¡¡¡¡Anil Ada is putting his lectures for CS 251 (Great Ideas in Theoretical Computer Science) online!!!!!
I can GUARANTEE you will never find awesomer explanations of the fundamentals of CS Theory. These lectures are PURE GOLD, seriously!!
https://t.co/r1otWprSJB
Algorithms model any process evolving via simple, local steps. So insights from theory of computation are relevant far beyond CS. With that as motto & inspired by Avi W's "math & computation", @Anil_Ada_ & I'll teach "The Computational Lens" in Spring'22 https://t.co/z3kmaTEjdI
@RichardDawkins That being said, there is really no alternative to evaluating and trying to understand nature using logic. And in this sense, it will always be mathematical.
@RichardDawkins I think what people really mean is that elegant/simple math theories are surprisingly powerful at modeling the universe.
As an analogy, you might say the source code of the universe is short and elegant as opposed to being an endless sequence of conditionals.
Had a great time being on @Anil_Ada_'s (new?) podcast. He asked me mostly about quantum computing...
https://t.co/o2VvRiu6U2
Eagerly awaiting to see who he interviews next... :-)