Hacker News with Generative AI: Proof

A cute proof that makes e natural (poshenloh.com)
This webpage pulls out the part of the article which uses Pre-Calculus language to explain what is so natural about e, while intuitively connecting the following two important properties:

Mathematics, Proof, Number Theory

101 points by georgecmu 9 days ago | 43 comments

Mathematical Reasoning and Proofs [pdf] (alistairsavage.ca)

Mathematics, Proof, Academia

13 points by ibobev 11 days ago | 0 comments

Collatzeral damage: bitwise and proof foolish (soatok.blog)
Let’s talk about the Collatz Conjecture, which is like mathematicians’ original version of this programmer joke:

Mathematics, Proof, Programming

14 points by fanf2 41 days ago | 2 comments

Lemma for the Fundamental Theorem of Galois Theory (susam.net)
This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory (FTGT). Note that FTGT is not covered in this post. The focus of this post is on understanding and proving this lemma only. Here is the lemma from the book Galois Theory, 5th ed. by Stewart (2023):

Mathematics, Galois Theory, Proof, Education

134 points by susam 42 days ago | 37 comments

A Proof of the Collatz Conjecture (arxiv.org)
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.

Mathematics, Proof, Collatz Conjecture

6 points by doall 42 days ago | 3 comments

'Once in a Century' Proof Settles Math's Kakeya Conjecture (quantamagazine.org)
The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems.

Mathematics, Conjecture, Proof, Geometry

104 points by pseudolus 42 days ago | 29 comments

Experience with semi-formal proofs [video] (youtube.com)

Mathematics, Proof, Video

3 points by wwilson 52 days ago | 0 comments

How to prove false statements? (Part 1) (cryptographyengineering.com)
If you’ve read my blog over the years, you should understand that I have basically two obsessions. One is my interest in building “practical” schemes that solve real problems that come up in the real world. The other is a weird fixation on the theoretical models that underpin (the security of) many of those same schemes.

Cryptography, Security, Proof, Theoretical Models

90 points by feross 80 days ago | 8 comments

New Proofs Probe the Limits of Mathematical Truth (quantamagazine.org)
By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.

Mathematics, Proof, Unknowability

94 points by headalgorithm 81 days ago | 21 comments

How many real numbers exist? New proof moves closer to an answer (2021) (quantamagazine.org)
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

Mathematics, Infinity, Proof, Real Numbers

58 points by lisper 108 days ago | 60 comments

Proved my physics professor wrong with help from my 3D printer (reddit.com)
Vindicated after 25 years! Proved my physics professor wrong with help from my P1S! (v.redd.it)

Physics, 3D Printing, Education, Proof, Vindication

7 points by niceice 116 days ago | 1 comments

Ever wished you could time-travel just to say 'I told u so'? (tolduvault.com)
Save Your BrillianceProve You Were Right

Time Travel, Social Media, Proof, History

12 points by frankbdev 130 days ago | 15 comments

Fermat's Last Theorem – how it’s going (wordpress.com)
So I’m two months into trying to teach a proof of Fermat’s Last Theorem (FLT) to a computer. Most of “how it’s going” is quite tedious and technical to explain: to cut a long story short, Wiles proved an “R=T” theorem and much of the work so far has gone into teaching the computer what R and T are; we still have not finished either definition.

Mathematics, Computer Science, Proof

443 points by verbify 135 days ago | 210 comments

Math's 'Bunkbed Conjecture' Has Been Debunked (quantamagazine.org)
It was intuitive, even obvious. It was also wrong.

Mathematics, Conjectures, Proof

25 points by nhatcher 175 days ago | 3 comments

Euclid's Proof that √2 is Irrational (mathsisfun.com)

Mathematics, Proof, Irrational Numbers

172 points by thunderbong 247 days ago | 93 comments

A simple proof that pi is irrational [pdf] (1946) (ams.org)

Mathematics, Proof, History

66 points by pipopi 262 days ago | 55 comments

Monumental proof settles geometric Langlands conjecture (quantamagazine.org)