Kalman filtering is a recursive algorithm used to estimate the hidden state of dynamic systems from noisy observations. In statistics, it’s applied for state-space modeling and time-series smoothing. In machine learning, it underlies online learning, Bayesian filtering, and sequential data prediction. Real-life uses include navigation systems, GPS tracking, financial forecasting, sensor fusion in robotics, and object tracking in autonomous vehicles, where it balances noise and uncertainty efficiently. Image: share.google/LUV6O4ho41m9Fxx…

A new open-source physics engine just dropped… and it could change how robots learn. Newton, built by @nvidia with support from @GoogleDeepMind and Disney Research, is now part of The Linux Foundation. It’s designed to bring precise, GPU-powered physics to robotics and simulation research. Why it stands out: ✅ Runs entirely on the GPU for faster, richer simulations ✅ Open and modular, so you can plug in your own solvers or use it for differentiable physics ✅ Works with OpenUSD, Isaac Lab, and MuJoCo Warp ✅ Fully open-source under the Linux Foundation Another simulator? It’s a shared foundation for faster iteration and more realistic training before deploying in the real world. 🔗 Docs: newton-physics.github.io/new… 🔗 NVIDIA announcement: developer.nvidia.com/blog/an… —- Weekly robotics and AI insights. Subscribe free: scalingdeep.tech

In 1872 the German mathematician Karl Weierstrass introduced a surprising function: continuous at every point but differentiable at none. It broke the common belief that continuous curves should be smooth at most points, changing how mathematicians think about functions in analysis.

The Doppler effect, which describes the change in frequency of a wave due to the relative motion between the source and the observer.

You can prove that π< 22/7, simply by solving an integral.

The great advances in mathematics have not been made by logic but by creative imagination. The title of mathematician can scarcely be denied to Ramanujan who hardly gave any proofs of the many theorems which he enumerated. - George Frederick James Temple

When geometry speaks, words become unnecessary.

Dandelin Spheres in the Cylinder Visualization |Animation | Interactive applet @geogebra geogebra.org/u/daniel+mentra… #geogebra #math #science #iteachmath #mtbos #visualization #elearning @bancoche #physics

Trigonometry is fun, but non-euclidean fun is better! Just remember: the angles of a triangle on a sphere add up to more than 180 degrees and its sides divided by the radius are just angles. #MathType #math #mathematics #mathematician #mathproblems #mathfacts

What is the common way to read this mathematical expression aloud? A. The logarithm of x to the base of a B. The logarithm, base a, of x C. log, base a, of x #sharingisthenewlearning

For the light cone of future civilizations

In machine learning, we use the dot product every day. However, its definition is far from revealing. For instance, what does it have to do with similarity? There is a beautiful geometric explanation behind:

Mathematics. Circles. Epicycles. Roller Coaster of the Gods. By Juan Carlos, @jcponcemath, dynamicmath.xyz/, Used with permission.

🌅

Mario Bollini explains the decision behind Atlas’s superhuman design, with continuously rotating joints that let it pivot without stepping.

🚨BREAKING: @amazon launches a new multi-arm robot! The company just introduced Blue Jay, a new system that combines three robotic arms on a track to pick, sort, and consolidate items in a single workstation. Up to 10 robots can operate simultaneously on the tracks. Each robot supports a payload of up to 5.5 kg. The system features a hybrid gripping mechanism with both suction and fingers. Currently testing in South Carolina, Blue Jay is designed to expand Amazon’s “Sub-Same Day” offering, where packages arrive in hours, not days. The system can handle about 75% of shippable items in a fulfillment center. Unlike previous systems (Cardinal, Sparrow, Robin), Blue Jay was developed in just over a year, thanks to heavy use of digital twin simulations. Super impressive to see the machine live! Keep rocking Amazon Robotics team!

Data without math is blind. Math without data is silent.

One of the coolest ideas in mathematics is the estimation of a shape's area by throwing random points at it. Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.) Here is what's behind the magic:

what??? $1,403😳 Beijing NOETIX Robotics is releasing an affordable humanoid robot called Bumi. I don't know what people will do with it. But the price of a computer might attract people to try it.

Euler Method Approximation for First Order Differential Equation Visualization |Animation | Interactive applet @geogebra geogebra.org/u/daniel+mentra… #geogebra #math #science #iteachmath #mtbos #visualization #elearning @bancoche #physics