3Blue1Brown·2yA cute probability fact (part 2)
Discusses a probability concept using random values chosen from a uniform distribution within the interval of 0 to 1. It explains how to visualize pairs of these values as points in a two-dimensional space and examines conditions for the maximum value of the pair to be a specific number.
Daily Dose of Data Science | Avi Chawla | Substack·2yThe Mathematical Intuition Behind the Curse of Dimensionality
The curse of dimensionality refers to the surprising phenomena that arise in high-dimensional data spaces, affecting areas such as distance metrics and model generalization in machine learning and data science. Understanding its mathematical foundations can provide deeper insights and improve performance in high-dimensional datasets. The concept was first introduced by Richard Bellman in 1961.
Hacker News·2yWhy Physics Is Unreasonably Good at Creating New Math
Physics has begun to play an unexpectedly pivotal role in advancing mathematics, reversing the traditional dynamic where mathematics primarily served physics. Historical figures like Archimedes and Newton exemplified this interplay, but in the 20th century, the collaboration waned until recently. Pioneers like Michael Atiyah and developments in string theory have reignited this synergy. Insights from physics are revealing deep, unforeseen connections in fields of mathematics, facilitating significant breakthroughs. The inherent relationship between physical principles and mathematical structures continues to intrigue mathematicians and philosophers, suggesting that the language of the universe may indeed be mathematical, enriching both disciplines in the process.
Hacker News·2yThe centrality of stupidity in mathematics
Feeling stupid is a natural and essential part of learning mathematics. The essay underscores that periods of confusion and difficulty indicate deep learning. Overcoming these mental hurdles often results in sudden, profound comprehension. Teachers should recognize and validate these feelings while assuring students that they are a normal part of the learning process in mathematics.
Hacker News·2yOpen Mathematics Depository
The Open Mathematics Depository aims to provide access to valuable mathematical texts in PDF format that are either in the public domain or under an open license. Contributions of useful and helpful texts are encouraged, with a focus on English-language materials until curators for other languages volunteer. The project also outlines steps to follow for copyright owners to request the removal of their works.