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Mathematical Musings
Marveling the mysteries of the universe
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Is it too late to learn Math?
Is it too late to learn Math?
Few people claim that they had terrible math education when they were young, and now they recoil whenever they see squiggly characters on a…
Freedom Preetham
Oct 17
Rocket Launch Path Optimization
Rocket Launch Path Optimization
High-School Math
Freedom Preetham
Oct 15
Advanced Mathematical Concepts Elevating AI Reasoning in Models like Strawberry
Advanced Mathematical Concepts Elevating AI Reasoning in Models like Strawberry
Capturing the Mathematical Essence Behind Planning
Freedom Preetham
Sep 18
Why Ignoring Algebra Could Doom Your Career in AI Research
Why Ignoring Algebra Could Doom Your Career in AI Research
Intersecting Functional Analysis, Algebra, and Formal Methods
Freedom Preetham
Sep 15
Tasking Open AI Strawberry To Solve a Complex Math Problem
Tasking Open AI Strawberry To Solve a Complex Math Problem
OpenAI Strawberry just got released, and I was wondering how it performs on math problems. As the latest advancement in AI language models…
Freedom Preetham
Sep 13
Comparing Complexity in Physics and Biology From a Math Perspective
Comparing Complexity in Physics and Biology From a Math Perspective
Over the weekend, I engaged in a discussion with postdoctoral math students about how to approach the inherent complexity in different…
Freedom Preetham
Aug 11
Exploring Nonlocal Interactions through Choquard Equations: An Easy Math Intro
Exploring Nonlocal Interactions through Choquard Equations: An Easy Math Intro
Partial differential equations (PDEs) are powerful tools that help us understand how various quantities evolve over space and time. From…
Freedom Preetham
Aug 9
AlphaProof and AlphaGeometry2 Wins Silver In International Math Olympiad
AlphaProof and AlphaGeometry2 Wins Silver In International Math Olympiad
Artificial intelligence has significantly advanced in various fields, and its potential to address complex mathematical problems is…
Freedom Preetham
Jul 27
The Timeless Elegance of Mathematics
The Timeless Elegance of Mathematics
“Why, oh why, do you use math equations in your writings?”
Freedom Preetham
Jul 15
Understanding Green’s Theorem: A Comprehensive Guide
Understanding Green’s Theorem: A Comprehensive Guide
Green’s Theorem is one of the cornerstone results in vector calculus, bridging the concepts of line integrals and double integrals. It…
Freedom Preetham
Jul 14
Mathematical Intuition for Gene Expression Modeling using Graph Dynamical Systems
Mathematical Intuition for Gene Expression Modeling using Graph Dynamical Systems
Gene expression analysis through the lens of graph dynamical systems offers profound insights into the complex interactions that govern…
Freedom Preetham
Jul 5
How Gaussian Distribution Maximizes Entropy — The Proof
How Gaussian Distribution Maximizes Entropy — The Proof
The normal distribution, often referred to as the Gaussian distribution, stands as a fundamental element in the realm of statistics and…
Freedom Preetham
May 4
Mathematical Bridge Between Softmax Functions and Gibbs Distributions
Mathematical Bridge Between Softmax Functions and Gibbs Distributions
The softmax function is an essential element in various neural networks, particularly those designed for classification tasks. It…
Freedom Preetham
Apr 25
Mathematical Insights into Multi-Class Cross-Entropy Loss
Mathematical Insights into Multi-Class Cross-Entropy Loss
The multi-class cross-entropy loss is an extension of the concept of entropy in information theory, applied to the context of machine…
Freedom Preetham
Apr 25
The Gaussian Distribution: A Mathematical Perspective
The Gaussian Distribution: A Mathematical Perspective
The normal distribution, often referred to as the Gaussian distribution, is pivotal in statistics, owing to its fundamental mathematical…
Freedom Preetham
Apr 24
Tensor Contraction and Dimensionality Reduction
Tensor Contraction and Dimensionality Reduction
Tensor contraction is a nuanced and potent mathematical operation employed extensively across various scientific disciplines, including…
Freedom Preetham
Apr 14
The Mathematical Foundation to Understand Human Genomic Variation
The Mathematical Foundation to Understand Human Genomic Variation
Despite 99.9% genetic similarity among humans, the phenotypic diversity we observe — ranging from physical appearance to disease…
Freedom Preetham
Apr 12
A Mathematical Exploration of the Computational Universe: A Critique of Wolfram’s Framework
A Mathematical Exploration of the Computational Universe: A Critique of Wolfram’s Framework
The concept of a computational universe as proposed by Stephen Wolfram posits that the universe’s complexity arises from simple…
Freedom Preetham
Nov 9, 2023
Part 6 — Tensor Algebra: Dissecting Multidimensional Genomic Interactions
Part 6 — Tensor Algebra: Dissecting Multidimensional Genomic Interactions
As we proceed in our voyage through the genomic universe, the spotlight now turns to Tensor Algebra, a potent mathematical framework that…
Freedom Preetham
Nov 5, 2023
Part 5 — Statistical Mechanics: Probing the Dynamic Behavior in Genomic Systems
Part 5 — Statistical Mechanics: Probing the Dynamic Behavior in Genomic Systems
The voyage into the genomic universe continues as we harness the powers of statistical mechanics to decipher the dynamic behavior…
Freedom Preetham
Nov 5, 2023
Differential Geometry: Unveiling the Geometric Structure of Genomic Grammar — Part 4
Differential Geometry: Unveiling the Geometric Structure of Genomic Grammar — Part 4
The venture into the genomic landscape further deepens as we employ the tools of differential geometry to delineate the geometric…
Freedom Preetham
Nov 3, 2023
Algebraic Topology: Charting the Topological Landscape of Genomic Grammar — Part 3
Algebraic Topology: Charting the Topological Landscape of Genomic Grammar — Part 3
The realm of genomics is a vibrant space of intricate interactions and multifaceted regulatory frameworks. The application of algebraic…
Freedom Preetham
Nov 3, 2023
Tensor Representations: Understanding the N-Dimensional Genomic Grammar — Part 2
Tensor Representations: Understanding the N-Dimensional Genomic Grammar — Part 2
Building upon the foundational discussion laid out in Part 1, “A Rigorous Mathematical Exposition on N-Dimensional Genomic Grammar vs…
Freedom Preetham
Nov 2, 2023
Part 1 — A Rigorous Mathematical Exposition on N-Dimensional Genomic Grammar vs One-Dimensional…
Part 1 — A Rigorous Mathematical Exposition on N-Dimensional Genomic Grammar vs One-Dimensional…
People ask why can’t we just point an LLM architecture to a DNA sequence and just decode the language of life! Just like how we did for…
Freedom Preetham
Nov 2, 2023
Mathematical Explanation of Chaos, Randomness, and Complexity in the Universe.
Mathematical Explanation of Chaos, Randomness, and Complexity in the Universe.
Freedom Preetham
Oct 1, 2023
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