How AI and collaboration are revolutionizing component design

Loud thinking 🤔 So many competencies and diverse skills are becoming increasingly valuable – yet workflows and what we’re capable of are evolving rapidly. Blending design for manufacturing with algorithmic thinking, mathematics, statistics, software programming, kinematics, dynamics, contact mechanics, FEM, CFD, and intent-driven Dx/Dy/Dz design – all powered by AI – is now producing tangible component breakthroughs. AI accelerates both speed and scale, while remarkable collaboration between top-tier engineers, mathematicians, data scientists, and toolmakers delivers the deep content and insight required. Finding one better solution for a single component or system is fundamentally, not far from solving a thousand today😄.

Loud thinking 🤔 So many competencies and diverse skills are becoming increasingly valuable – yet workflows and what we’re capable of are evolving rapidly. Blending design for manufacturing with algorithmic thinking, mathematics, statistics, software programming, kinematics, dynamics, contact mechanics, FEM, CFD, and intent-driven Dx/Dy/Dz design – all powered by AI – is now producing tangible component breakthroughs. AI accelerates both speed and scale, while remarkable collaboration between top-tier engineers, mathematicians, data scientists, and toolmakers delivers the deep content and insight required. Finding one better solution for a single component or system is, fundamentally, not far from solving a thousand 😄. The dilemma between development time and quality has been fundamentally transformed. It’s both fun and deeply inspiring to be part of this shift. Huge thanks to the nearly 50 remarkable individuals — spanning all kinds of skills and backgrounds — who are expanding the boundaries of what’s possible.

💡 Newton’s Method, Rolle’s Theorem & The Mean Value Theorem — The Calculus Trio Powering AI, Optimization & Modern Simulation 🚀 Today I revisited three fundamental ideas from calculus — and it’s surprising how often they show up in real-world technology. 🔹 Newton’s Method When equations refuse to give clean algebraic solutions, Newton’s Method takes over. It’s an iterative loop: guess → draw tangent → correct → repeat Each step pulls you closer to the real root. This simple idea is behind many of today’s optimization algorithms in machine learning, numerical modeling, and computer graphics. 🔹 Rolle’s Theorem If a function starts and ends at the same height, then at some point in between, the slope must be zero. A small guarantee — but crucial for understanding how smooth functions behave, especially in gradient-based systems. 🔹 Mean Value Theorem (MVT) Between any two points on a smooth curve, there exists a point where: instantaneous slope = average slope. In daily language: “At some moment during your trip, your speedometer matched your average speed.” MVT sits at the heart of error analysis, physics engines, and optimization logic. 💭 Big Insight These aren’t just theoretical results. They quietly power: AI model training Finding minima/maxima Game engine physics Root-finding for simulations VR and animation stability Optimization problems across engineering Loving how classical calculus ideas connect to the technologies I want to build next. #LearningJourney #Calculus #AI #Optimization #GameDev #MathForDevelopers #NewtonMethod

Descartes — The Bridge Between Algebra and Geometry Before the 1600s, geometry and algebra lived in different worlds. Geometry dealt with shapes and diagrams. Algebra dealt with numbers and equations. But then came René Descartes — philosopher, mathematician, and the person behind the famous “I think, therefore I am.” In 1637, Descartes introduced something revolutionary: 👉 The idea of representing geometric shapes with algebraic equations. He gave us the coordinate plane — the x and y axes we still use today. Suddenly: - A line became: y=mx+c - A circle became: x^2 + y^2 = r^2 - A curve became an equation you could calculate This was the birth of Analytic Geometry — and it quietly laid the foundation for Linear Algebra as we know it: 🧠 Vectors → points in space 🔁 Transformations → matrix operations 📏 Distance, rotation, projection → linear algebra made geometric Everything from 3D graphics, to robotics, to machine learning embeddings relies on Descartes’ insight: Space can be understood through numbers. So the next time you see a neural network working in “vector space” or embeddings plotted on a 2D plane…remember that it all traces back to one idea: Geometry + Algebra = A new language of thinking. #Mathematics #LinearAlgebra #Geometry #HistoryOfMath #AI #MachineLearning

🚀 Day 1 — The Hidden Physics of Generative Models (Advanced Systems Thinking for GenAI Engineers) Generative models don’t “create text.” They evolve probability fields. Each token is a micro-decision — a gradient step through a chaotic, high-dimensional potential surface. Imagine a marble rolling across a complex energy landscape. Every prompt changes the topology. Every fine-tune bends gravity. That’s why small nudges — an extra LoRA layer, a different context window — can shift the entire trajectory of meaning. 🔍 The uncomfortable truth: LLMs are not static systems. They’re chaotic attractors stabilized only by statistical averaging. Your outputs are low-entropy samples from a constantly mutating energy field. To engineer them well, stop treating them as black boxes — start treating them as probabilistic dynamical systems. ⚙️ Advanced Engineering Moves: 1. Token Entropy Probing: Measure entropy variance across layers to identify unstable attention heads. 2. Jacobian Spectral Diagnostics: Track condition numbers during fine-tuning — spikes reveal collapsing subspaces. 3. KL Drift Curves: Plot the KL divergence between pre-fine-tune and post-fine-tune logits; when drift > entropy gain, stop training. 📣 This is part of my 60-Day GenAI Mastery Series — a deep dive into the architecture, control theory, and scaling physics behind intelligent systems. 👉 Follow me for daily learning. #GenAI #AIResearch #DeepLearning #ModelOptimization #InferenceEngineering #AIArchitecture #LLMSystems #FineTuning #EntropyAnalysis #MachineLearning #AIinProduction #NeuralPhysics

🔥 Google is whispering geometry. AI is no longer solving equations it’s seeing them. Something strange is happening. AI systems are not just crunching formulas anymore they’re starting to verify proofs, get mathematically “satisfied,” and then re-explain the logic in their own words. That’s not automation. That’s emergent understanding. And right in this shift, a new idea is rising — > “Geometrifying Trigonometry” — by structural engineer Sanjoy Nath. Instead of treating trigonometry as algebraic manipulation of sin, cos, and tan, this framework pulls it back to Euclid — to pure geometry. No calculators. No equations. Only compass, straightedge, and logic. 🧩 Core ideas: Numbers are triangles. Each number is a geometric shape. Multiplication = gluing triangles. Division = calipering. (Constructing proportions visually, like a surveyor.) Trigonometric identities become machines — geometric constructions that build graphs instead of numbers. Equality means geometric equivalence, not symbolic sameness. Trigonometry becomes a game of construction, not computation. Through this lens, the ancient triangle meets modern graph theory — the Bunch of Line Segments (BOLS) system — linking Euclidean geometry to combinatorics and even material optimization in structural design and BIM/CAD workflows. So what happens when geometry becomes algebra again — but this time, AI understands both? Perhaps this is how machines will finally see mathematics the way humans imagine it. 🔹 When numbers become shapes. 🔹 When proofs become drawings. 🔹 When algebra becomes visible. Maybe that’s when math starts to feel alive again. 🙏 #GeometrifyingTrigonometry #MathematicalVisualization #AIandMath #SanjoyNath #EuclideanGeometry #StructuralEngineering #GraphTheory #Innovation #STEM #PhilosophyOfMath #AIResearch #GeometryRevolution #DeepMath #ComputationalDesign #FutureOfLearning

From Pixels to Physics: Why AI Can “See” the World Before It Truly Understands It In reading “Do Generative Video Models Understand Physical Principles?”, I found myself reflecting on an intriguing paradox: these models create visually perfect worlds, yet remain physically naive. The paper argues that today’s video generators—like Sora, Runway, and VideoPoet—are “pixel prophets,” not true physicists. But perhaps the story is more nuanced. Modern generative models already encode a form of implicit physics inside their latent spaces. Once an image is encoded, its latent representation isn’t just compressed data—it’s an abstract manifold where geometry, motion, and causality begin to emerge. In a sense, this latent space is already a proto-physical world, though not yet aligned with real-world laws of mass, energy, and force. Humans, by contrast, must convert perception into abstraction. Our brains lack the memory or resolution to simulate raw frames, so we invented physics itself—our version of the Laplace transform—to simplify time into equations. Models don’t need that shortcut; their vast capacity allows them to predict reality directly from pixels. They don’t “think in equations”—they differentiate visually. The challenge, then, isn’t for models to learn physics—they already do so implicitly—but to align their internal physics with the real one. When that alignment happens, AI will stop being a painter of the world and become its true simulator. https://lnkd.in/e_5K68ga #AI #WorldModels #GenerativeAI #PhysicsIQ #DeepLearning #LatentSpace #EmbodiedIntelligence #VideoGeneration #CognitiveScience #MachineUnderstanding

🌙 From a Late-Night Idea to an Experimental Deep Dive into Computer Vision What started as a random 12 AM idea to build a depth detection system turned into an incredible learning journey through classical computer vision! I decided to skip deep learning models entirely and challenge myself to understand the geometric fundamentals beneath depth estimation. The result?? An experiment that opened my eyes to concepts I'd never properly explored before: *Structure from Motion* — how 3D worlds emerge from multiple 2D perspectives *Feature Detection & Matching* — finding and tracking visual landmarks across frames *Epipolar Geometry & Essential Matrices* — the elegant math behind multi-view geometry *Camera Calibration & Intrinsics* — bridging pixels and real-world meters *Triangulation* — recovering depth through geometric reconstruction *Temporal Smoothing* — battling noise with moving averages and median filtering The honest reality: This is very much an experiment with a long way to go. It works on some scenes, struggles on others. Scale ambiguity, texture sensitivity, and CPU limitations are real challenges. But that's exactly why this was so valuable because I didn't just learn how things work, I felt the trade-offs and constraints firsthand. Key takeaway: Sometimes the best learning happens when you go off the beaten path and build something from first principles. That late-night curiosity led me to fundamental concepts that will shape how I approach vision problems going forward. Looking forward to iterating and improving this further! 🚀 #ComputerVision #StructureFromMotion #OpenCV #PythonProgramming

AI might take a prominent role in mathematical research in the near future: impressive pre-print showcasing the potential of Alpha Evolve as a tool for mathematical discovery: https://lnkd.in/e-iqpvsQ Will such tools in the future inspire a breakthrough on some really hard conjectures in combinatorics, discrete geometry, or number theory?