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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Planets evenly spaced on log scale
The distances to the planets are fairly evenly distributed on a logarithmic scale, not only in our solar system but in extrasolar systems as well.
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Matrices and Graph
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
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Bezier Curves and Picasso
Pablo Picasso Simplicity and the Artist Some of my favorite of Pablo Picasso’s works are his line drawings. He did a number of them about animals: an owl, a camel, a butterfly, etc. This piece called “Dog” is on my wall: Dachshund-Picasso-Sketch (Jump to interactive demo where we recreate “Dog” using the math in this…
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The Case for Bayesian Deep Learning
The Case for Bayesian Deep Learning Andrew Gordon Wilson Abstract Bayesian inference is especially compelling for deep neural networks. The key distinguishing property of a Bayesian approach is margin
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The Beauty of Roots (2011)
Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4:
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Algorithmic symphonies from one line of code
Lately, there has been a lot of experimentation with very short programs that synthesize something that sounds like music. I now want to sha...
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A lazy way to solve differential equations
Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them.
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Data diffs: Algorithms for explaining what changed in a dataset (2022)
tl;dr: part 1 explains what an explanation algorithm is, and part 2 describes an open source SQL data differ.
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Building a constraint programming solver in Julia
How to build a constraint programming solver in Julia. Part 1: Solving Sudoku using backtracking
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Generating Voronoi diagrams using Fortune's algorithm
This article is about using Fortune’s Algorithm to generate Voronoi Diagrams in O(nlogn) time. If I’d known how hard it would be I wouldn’t have started it. If you are intending to implement it with the intent to actually use it, rather than as an exercise, I would recommend not using Fortune’s. Unless you are doing a…
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How Slide Rules Work
The survival of our species owes much to our brain, specifically, its ability to observe, analyse, and plan. Planting crops and storing grains for the winter were some of the earliest uses of these abilities. Measuring and calculating are foundational elements of observation, analysis, and planning. Computation, upon…
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If 1+x is 1, how much is 1-x?
► Versión en Español (The title should be "if (= (+ 1 x) 1), how much is (- 1 x)?", but ...) Toy floating point Mathematically, if we...
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Solving Every Sudoku Puzzle (2006)
Every square has exactly 3 units and 20 peers. For example, here are the units and peers for the square C2 :
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A proof that Unix utility sed is Turing complete
Many people are surprised to learn that `sed`, a seemingly simple text filtering program, is actually Turing complete. This realization prompts the question: how can a text processing utility achieve such computational power? The answer lies in sed's fundamental operations. Essentially, sed functions as a miniature...
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What’s the difference between statistics and machine learning?
I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am …
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Sphere Eversion
Topology is the study of the properties of geometric objects which aren’t changed by continuous deformation. A standard low-grade math joke is that toplogists consider a coffee mug and a doughnut equivalent because they’re both torii—(pauses for laughter)—one can be continuously deformed into the other, called a…
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Gaussian integration is cool
Brief discussion on gaussian quadrature and chebyshev-gauss quadrature
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The Irish Logarithm
From the highly eclectic blog of Mark Dominus
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So you still don't understand Hindley-Milner? (2013)
I was out for drinks with Josh Long and some other friends from work, when he found out I "speak math." He had come across this …
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GPT-4 gets a B on my quantum computing final exam
Update (April 14): On the suggestion of my TA Justin Yirka, I gave GPT-4 problem 2 from the final exam, along with its own answers and my and Justin’s grading comments, and asked it whether i…
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Finally getting two's complement
A different view on two's complement math.
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What the Four Color Theorem Can Teach Us About Writing Software
A visual exploration of what The Four Color Theorem can say about software complexity.