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The Music of The Shattered Spheres
The Music of The Shattered Spheres
That Mathematics can see its own limitations is part of its Sublimely Perfect Imperfection, and this arises in the restricted possibilities…
Selena Routley
Jul 17
The Sublime Perfection and Beauty of Imperfection
The Sublime Perfection and Beauty of Imperfection
Kurt Gödel and the loneliness and joy of being a Platonist in a smug world convinced of Human Omnipotence and that Man is the Measure of…
Selena Routley
Jul 17
Trisecting Angles and Higher Dimensional Numbers
Trisecting Angles and Higher Dimensional Numbers
Why can the Reals only be extended to Number "Fields" of dimension 1, 2, 4 and 8? And what has this to do with the Ancient Greek problem of…
Selena Routley
Jul 15
The Magnificent Octonions: When Do Equations Lose Information?
The Magnificent Octonions: When Do Equations Lose Information?
… and the amazing woman, Ruth Moufang, who answered an important part of this profound question
Selena Routley
Jul 8
Statistics: Time Series Analysis — Compilation of the fundamental concepts
Statistics: Time Series Analysis — Compilation of the fundamental c...
Gentle introduction of time series analysis basics with visualization and detailed mathematical derivation
Yuki Shizuya
Jul 5
50 Challenging Problems in Probability [Part 31]: Birthday Pairings
50 Challenging Problems in Probability [Part 31]: Birthday Pairings
Can you solve this interesting puzzle? What is the least number of persons required if the probability exceeds 1/2 that two or more of them
Shelvia
Jun 22
Brain Teaser 32: Coin Split Problem
Brain Teaser 32: Coin Split Problem
Can you solve this interesting puzzle? You split 1000 coins into two piles and count the number of coins in each pile. If there are x coins
Shelvia
Jun 22
Topological Magic: Bizarre Twists in Space
Topological Magic: Bizarre Twists in Space
The exquisitely beautiful Hopf Fibration and the generalization of a Cartesian Product to a fiber bundle
Selena Routley
Jun 25
Topological Magic: Formal Tricks to Increase our Mathematical Imagination
Topological Magic: Formal Tricks to Increase our Mathematical Imagi...
Quotient Spaces, Fiber Bundles and Covers produce simple and profound examples in topology, and give you powers of visualization that you…
Selena Routley
Jun 25
50 Challenging Problems in Probability [Part 30]: Evening the Sales
50 Challenging Problems in Probability [Part 30]: Evening the Sales
Can you solve this problem? A bread salesman sells on the average 20 cakes on a round of his route. What is the chance that he sells an…
Shelvia
May 9
How Do You Find the Red Angle?
How Do You Find the Red Angle?
The following problem is quite fun; as far as I know, it can’t be solved with trivial angle chasing. Meanwhile, it also helps to better…
Bekhruz Niyazov
Jun 17
Novel insights into fluorescent ‘dark states’ illuminate ways forward for improved imaging
Novel insights into fluorescent ‘dark states’ illuminate ways forwa...
When an excited electron in the fluorophore relaxes, it emits light after a delay, causing the molecule to glow (fluoresce). However…
Tunahan
Jun 17
The Final Countdown: Understanding General Relativity
The Final Countdown: Understanding General Relativity
The Magnificent Elegance and Beauty Behind Einstein's General Theory of Relativity
Selena Routley
Jun 16
Maths as a language
Maths as a language
Do you consider math a language we could use for communication? How could we use it in this manner?
Tobi Aikulola
Jun 15
The Universe's Binary Code
The Universe's Binary Code
The deep meaning of metric signature in defining geometries pertinent to cosmology through Sylvester's Law of Inertia
Selena Routley
Jun 14
Where is the Equivalence Principle in the Mathematics of General Relativity?
Where is the Equivalence Principle in the Mathematics of General Re...
It's so deeply baked into the equations of General Relativity that it is almost impossible to see
Selena Routley
Jun 13
Gentle introduction of Bayesian Linear Regression
Gentle introduction of Bayesian Linear Regression
Mathematical background behind the Bayesian linear regression with Gaussian prior and practical implementation
Yuki Shizuya
Jun 7
Archaic Mathematicians and Death By Ox!
Archaic Mathematicians and Death By Ox!
Please, please be ruthless in your culling of jargon when teaching our children!
Selena Routley
Jun 6
Mongolian 2024 Number Theory Problem
Mongolian 2024 Number Theory Problem
Can you figure out this problem from the 2024 Mongolian Mathematical Olympiad?
Wojciech kowalczyk
Jun 4
Can you solve this problem from the 2024 Japanese Preliminary Olympiad?
Can you solve this problem from the 2024 Japanese Preliminary Olymp...
A problem from the 2024 Japanese Preliminary Olympiad!
Wojciech kowalczyk
Jun 4
Bangladesh Mathematical Olympiad 2024 Problem 1
Bangladesh Mathematical Olympiad 2024 Problem 1
An interesting Diophantine equation from Bangladesh!
Wojciech kowalczyk
Jun 1
Understanding L1 and L2 regularization with analytical and probabilistic views
Understanding L1 and L2 regularization with analytical and probabil...
Derive L1 and L2 regularization via analytical and probabilistic solution
Yuki Shizuya
May 25
Sailing on the Vast Seas of Lie Groups
Sailing on the Vast Seas of Lie Groups
Avast Ye, Ye Bilge Sucking Scurvy Dogs! Weigh Anchor and Hoist the Mizzen!!
Selena Routley
May 23
The Photon’s Tale: Exploring Chemical Signatures in Exoplanet Atmospheres
The Photon’s Tale: Exploring Chemical Signatures in Exoplanet Atmos...
Let’s learn how photons — one of the messengers of the universe — help us understand an exoplanet’s atmosphere.
Hardik Medhi
May 20
Gentle introduction of Continuous Optimization for machine learning
Gentle introduction of Continuous Optimization for machine learning
This blog will introduce the basics of continuous optimization, gradient descent for unconstrained optimization, and Lagrange multiplier…
Yuki Shizuya
May 13
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