Finding out hidden rules of the mathematical, physical and natural systems using mathematics, computing, and machine learning toolkit.
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Einstein’s collected works at the Einstein Paper Project (LA)
Recently, I had an opportunity to visit the Einstein Papers Project (EPP), a centre that is currently compiling, organising, and publishing all the major and minor written works by the great 20th century theoretical physicist Albert Einstein. This centre is born out of the efforts from Einstein’s secretary Miss Helen Dukas and close friend Otto…
Congratulatory post – incoming Ph.D. student at the University of Edinburgh
This post is intended to congratulate Mr Adnan Mahmud, who is going to join the University of Edinburgh as a Ph.D. student and work on digital twins using Bayesian networks for real-time uncertainty quantification and predictive analysis. After supervising Adnan on the Fluid Mechanics course for Cambridge CE Tripos, we worked on a series of…
2-player games: Ergodic Theory and Ramsey Theory results
This post aims to summarise key results from the literature of two-player games, both finite (with an absorbing state) and infinite (without an absorbing state). Canonical examples include competitive or recreational games like chess, tic-tac-toe (including the ultimate version), and attacker-follower games (known as Stackelberg games in game-theoretic economics). On Math Stack Exchange, for over…
Fluid Dynamics, Computer Science, and Geometry – Barcelona 2024
After the June 2023 workshop organised in Royal Institution, London on “Navier-Stokes regularity, fluid computing, and machine learning”, which hosted the guest lecture by Prof. Eva Miranda, who was awarded the Hardy lecturer title, Eva, Daniel, and Ángel organised a first of its own kind workshop in Barcelona, in September 2024. Spanning almost a week,…
Euler’s (compiled) works in Bernoulli-Euler Zentrum, Basel
Recently, I had an opportunity to visit the University of Basel in Switzerland, which houses a fascinating archive centre in its University Library — the “Bernoulli-Euler Center (BEZ in German)”, founded in 2010. I was kindly hosted and given a brief tour of the archive centre by the researcher and archivist based in the centre,…
A few disjoint thoughts collating “numbers”
The spring of 2024 started with a new habit, that turned into a hobby, and eventually, a fascinating observation. Counting the number of veins in either half of the leaf, I found a repeated pattern that the number is more likely to be an odd or prime number than even number (there were significantly minor…
Mathematical model for computability using neural networks: Part 1 (RNN)
Prologue Ongoing advances in LLMs call for a mathematical model that can analytically model its computability. To do so, it is important to start with a basic model of LLM that captures the core properties, still allowing mathematical tractability. Let’s start with mathematical model for RNNs. Introduction Consider an RNN network 
Multitudes of beliefs in science
It is often said that science and scientists work objectively, and logic, rationalism governs science. While for the most part of the process it is true, except that the underlying axioms or beliefs dictate which thread of rationalism a particular scientist weaves through their career. This is an important question to consider, given that science…
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