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UK<a href="https://www.europesays.com/uk/80048/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.europesays.com/uk/80048/</a> Mathematicians Just Solved a 125-Year-Old Problem That Unites Three Major Theories of Physics <a href="https://pubeurope.com/tags/DavidHilbert" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DavidHilbert</a> <a href="https://pubeurope.com/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physics</a> <a href="https://pubeurope.com/tags/ProbabilityTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ProbabilityTheory</a> <a href="https://pubeurope.com/tags/Science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Science</a> <a href="https://pubeurope.com/tags/UK" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#UK</a> <a href="https://pubeurope.com/tags/UnitedKingdom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#UnitedKingdom</a>

Hacker NewsAn Introduction to Stochastic Calculus<a href="https://bjlkeng.io/posts/an-introduction-to-stochastic-calculus/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://bjlkeng.io/posts/an-introduction-to-stochastic-calculus/</a><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/StochasticCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#StochasticCalculus</a> <a href="https://mastodon.social/tags/Introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Introduction</a> <a href="https://mastodon.social/tags/MathFinance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathFinance</a> <a href="https://mastodon.social/tags/ProbabilityTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ProbabilityTheory</a> <a href="https://mastodon.social/tags/Education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Education</a>

Manuel Baltieri2025 is looking like a great year for work at the intersection of <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="tag">#categorytheory</a>, <a href="https://mathstodon.xyz/tags/systemstheory" class="mention hashtag" rel="tag">#systemstheory</a>, <a href="https://mathstodon.xyz/tags/controltheory" class="mention hashtag" rel="tag">#controltheory</a>, <a href="https://mathstodon.xyz/tags/machinelearning" class="mention hashtag" rel="tag">#machinelearning</a> and <a href="https://mathstodon.xyz/tags/probabilitytheory" class="mention hashtag" rel="tag">#probabilitytheory</a>, this thread will be a very biased collection of works (in no specific order) I'm hoping to read as soon as possible!Starting with: "Logical Aspects of Virtual Double Categories" <a href="https://mastoxiv.page/@arXiv_mathCT_bot/113921693949589956" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://mastoxiv.page/@arXiv_mathCT_bot/113921693949589956</a>

j_bertolottiGiven that I am surrounded by Mathematicians here, let me ask for help for what should be a simple problem I can't seem to be able to solve: Assume you have n fair dice with m faces (i.e. each can roll an integer from 1 to m with a uniform probability). You roll all n, and keep the k (with 0<k<=n) highest results. What is the probability that the sum of the k dice you kept is X? (If one keeps all the dice, probability-generating functions give the answer straightforwardly. If I roll 2 dice and keep 1 I can easily enumerate the outcomes and calculate the probabilities, but I am stumped by the general case).<a href="https://mathstodon.xyz/tags/ProbabilityTheory" class="mention hashtag" rel="tag">#ProbabilityTheory</a> <a href="https://mathstodon.xyz/tags/IShouldKnowHowToSolveThisButIDoNot" class="mention hashtag" rel="tag">#IShouldKnowHowToSolveThisButIDoNot</a> 😞

Michael MisamoreFun little exercise: prove that if two Bernoulli random variables are perfectly correlated then they must be equal. <a href="https://sigmoid.social/tags/probabilitytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilitytheory</a>

RanaldClouston<a href="https://fediscience.org/tags/FinishedReading" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FinishedReading</a> <a href="https://fediscience.org/tags/Boole" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Boole</a> 's Laws of Thought, whose final chapters partly shift attention from <a href="https://fediscience.org/tags/logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#logic</a> to <a href="https://fediscience.org/tags/probabilityTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilityTheory</a> and <a href="https://fediscience.org/tags/philosophyOfScience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#philosophyOfScience</a> . I don't have a strong sense of his historical standing in either discipline, although for probability there is <a href="https://en.m.wikipedia.org/wiki/Boole%27s_inequality" rel="nofollow noopener noreferrer" target="_blank">https://en.m.wikipedia.org/wiki/Boole%27s_inequality</a> . The attraction of probability is clear, with its range of values from 0 to 1, use of '1 -' for negation, multiplication for conjunction (of independent events) etc. There are rhymes here with his logic at least

j_bertolottiThere are many situations in the real world where small initial differences can easily grow into very large differences just out of pure chance. Since we are on a social network, let's create a toy model* where a number of posts all have the same probability to be reposted/shared/boosted by any person seeing them. Since the more people see a post, the more people have a chance of boosting it, the posts with more visibility are also the ones that are likely to gain more visibility. So small initial fluctuations (just one or two extra boosts at the beginning) can lead a post to skyrocket in popularity, even though it is not intrinsically "better" than any of the other. If we simulate this process numerically and make a histogram of the result, we see that the distribution of how many boosts a post had rapidly grows a tail, with most posts having no visibility whatsoever, and a few having a LOT more than the average. <a href="https://mathstodon.xyz/tags/ITeachPhysics" class="mention hashtag" rel="tag">#ITeachPhysics</a> <a href="https://mathstodon.xyz/tags/ProbabilityTheory" class="mention hashtag" rel="tag">#ProbabilityTheory</a> <a href="https://mathstodon.xyz/tags/ToyModel" class="mention hashtag" rel="tag">#ToyModel</a>* In the <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="tag">#Physics</a> jargon, a "toy model" is a very simple (often unrealistic) model, which nevertheless capture the essence of the problem, without being burdened by all the real world complications. If you ever heard about spherical cows in vacuum, that is a toy model!

Christos Argyropoulos MD, PhDWhile waiting for a meeting to start, I decided to revisit one of the classics <a href="https://mstdn.science/tags/graphicalmodels" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graphicalmodels</a> <a href="https://mstdn.science/tags/probabilityandstatistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilityandstatistics</a> <a href="https://mstdn.science/tags/probabilitytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilitytheory</a> <a href="https://mstdn.science/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://mstdn.science/tags/DAG" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DAG</a>

Mohammad HajiaghayiNow (7pm ET Wed) watch <a href="https://youtu.be/QS0VmCD9YLU" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://youtu.be/QS0VmCD9YLU</a>(FEEL FREE TO SUBSCRIBE TO YOUTUBE @hajiaghayi FOR FUTURE LESSONS) Lesson 14: Introduction to Algorithms by Mohammad Hajiaghayi: We talk about <a href="https://mathstodon.xyz/tags/Probability" class="mention hashtag" rel="tag">#Probability</a> (Part 2) useful for designing <a href="https://mathstodon.xyz/tags/randomized" class="mention hashtag" rel="tag">#randomized</a> <a href="https://mathstodon.xyz/tags/algorithms" class="mention hashtag" rel="tag">#algorithms</a> <a href="https://mathstodon.xyz/tags/algorithms" class="mention hashtag" rel="tag">#algorithms</a>, <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="tag">#design</a>, <a href="https://mathstodon.xyz/tags/induction" class="mention hashtag" rel="tag">#induction</a>, <a href="https://mathstodon.xyz/tags/recursive" class="mention hashtag" rel="tag">#recursive</a>, <a href="https://mathstodon.xyz/tags/randomizedalgorithms" class="mention hashtag" rel="tag">#randomizedalgorithms</a>, <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="tag">#probability</a>, <a href="https://mathstodon.xyz/tags/randominput" class="mention hashtag" rel="tag">#randominput</a> , <a href="https://mathstodon.xyz/tags/probabilitytheory" class="mention hashtag" rel="tag">#probabilitytheory</a>, <a href="https://mathstodon.xyz/tags/randomvariables" class="mention hashtag" rel="tag">#randomvariables</a>, <a href="https://mathstodon.xyz/tags/expectations" class="mention hashtag" rel="tag">#expectations</a>, <a href="https://mathstodon.xyz/tags/variance" class="mention hashtag" rel="tag">#variance</a>, <a href="https://mathstodon.xyz/tags/Bernoulli" class="mention hashtag" rel="tag">#Bernoulli</a>, <a href="https://mathstodon.xyz/tags/Binomial" class="mention hashtag" rel="tag">#Binomial</a>, <a href="https://mathstodon.xyz/tags/Poisson" class="mention hashtag" rel="tag">#Poisson</a>, <a href="https://mathstodon.xyz/tags/Normaldistribution" class="mention hashtag" rel="tag">#Normaldistribution</a>, <a href="https://mathstodon.xyz/tags/Gaussian" class="mention hashtag" rel="tag">#Gaussian</a>, <a href="https://mathstodon.xyz/tags/Python" class="mention hashtag" rel="tag">#Python</a>, <a href="https://mathstodon.xyz/tags/numpy" class="mention hashtag" rel="tag">#numpy</a>.random, <a href="https://mathstodon.xyz/tags/scipy" class="mention hashtag" rel="tag">#scipy</a>.stats, <a href="https://mathstodon.xyz/tags/correlation" class="mention hashtag" rel="tag">#correlation</a>, <a href="https://mathstodon.xyz/tags/Pearson" class="mention hashtag" rel="tag">#Pearson</a>, <a href="https://mathstodon.xyz/tags/spearman" class="mention hashtag" rel="tag">#spearman</a>, <a href="https://mathstodon.xyz/tags/geeksforgeeks" class="mention hashtag" rel="tag">#geeksforgeeks</a> , <a href="https://mathstodon.xyz/tags/hackerrank" class="mention hashtag" rel="tag">#hackerrank</a>, <a href="https://mathstodon.xyz/tags/leetcode" class="mention hashtag" rel="tag">#leetcode</a>, <a href="https://mathstodon.xyz/tags/cs" class="mention hashtag" rel="tag">#cs</a>, <a href="https://mathstodon.xyz/tags/computerscience" class="mention hashtag" rel="tag">#computerscience</a>

Jerome PI@pgrepds I thought I coudn't understand <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="tag">#probability</a>. Thanks to a teacher, I understand better the relationship between <a href="https://mathstodon.xyz/tags/probabilitytheory" class="mention hashtag" rel="tag">#probabilitytheory</a>, <a href="https://mathstodon.xyz/tags/settheory" class="mention hashtag" rel="tag">#settheory</a> and <a href="https://mathstodon.xyz/tags/topology" class="mention hashtag" rel="tag">#topology</a>. Now, I think I will be able to work these different fields together.

DataPacRatI get an extra layer of humor here by being amongst the LessWrong crowd...<a href="https://mastodon.xyz/tags/Peanuts" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Peanuts</a> <a href="https://mastodon.xyz/tags/Lucy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lucy</a> <a href="https://mastodon.xyz/tags/CharlieBrown" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CharlieBrown</a> <a href="https://mastodon.xyz/tags/Odds" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Odds</a> <a href="https://mastodon.xyz/tags/NeverTellMeTheOdds" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeverTellMeTheOdds</a> <a href="https://mastodon.xyz/tags/LessWrong" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LessWrong</a> <a href="https://mastodon.xyz/tags/Rationality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Rationality</a> <a href="https://mastodon.xyz/tags/Rationalism" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Rationalism</a> <a href="https://mastodon.xyz/tags/ProbabilityTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ProbabilityTheory</a>

Lika<a href="https://mathstodon.xyz/tags/Introduction" class="mention hashtag" rel="tag">#Introduction</a> time!I'm Lika, a data analyst. I have an organic chemistry background. Hope to join an academic program focused on modern aspects of <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="tag">#combinatorics</a> in the near future.<a href="https://mathstodon.xyz/tags/highereducation" class="mention hashtag" rel="tag">#highereducation</a> <a href="https://mathstodon.xyz/tags/linearalgebra" class="mention hashtag" rel="tag">#linearalgebra</a> <a href="https://mathstodon.xyz/tags/machinelearning" class="mention hashtag" rel="tag">#machinelearning</a> <a href="https://mathstodon.xyz/tags/mathteaching" class="mention hashtag" rel="tag">#mathteaching</a> <a href="https://mathstodon.xyz/tags/neuralnetworks" class="mention hashtag" rel="tag">#neuralnetworks</a> <a href="https://mathstodon.xyz/tags/probabilitytheory" class="mention hashtag" rel="tag">#probabilitytheory</a> <a href="https://mathstodon.xyz/tags/statistics" class="mention hashtag" rel="tag">#statistics</a> <a href="https://mathstodon.xyz/tags/documentaryfilms" class="mention hashtag" rel="tag">#documentaryfilms</a> <a href="https://mathstodon.xyz/tags/boardgames" class="mention hashtag" rel="tag">#boardgames</a> <a href="https://mathstodon.xyz/tags/rocksinging" class="mention hashtag" rel="tag">#rocksinging</a>Fun fact: This year I had experience as a museum tour guide. I was telling about Andrei Sakharov: his study and research in the field of theoretical physics.

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