MathGears @MathGears

The shortest-known paper in a math journal. Just two sentences.

Why does a simple integer rule produce such a beautiful structure?

I'm not that well informed, yet when a post reads "<something> that nobody is talking about" I have already talked about it. Am I a nobody?

Incredibly detailed composite image of Mars

Some important known galaxies

Until March 2025, Saturn had 146 moons, then astronomers discovered another 128, bringing the total number of moons around this gas giant to 274—far more than any other planet in our solar system. 🪐 This is the choreography of their dance. ☄️ BLACK HOLE. Subscribe.

Parker Solar Probe is one of the most extreme spacecraft ever built. It is currently flying through the Sun’s outer atmosphere, the corona, at about 430,000 miles per hour, or roughly 690,000 km/h, making it the fastest human-made object ever recorded. At that speed, it could cross the continental United States in around 20 seconds. But the most remarkable part is not only how fast it moves. It is that it can survive while repeatedly passing just 3.8 million miles, about 6.2 million kilometres, above the Sun’s visible surface, closer than any spacecraft before it. NASA confirmed that Parker matched this record distance and speed again during its 27th close approach on March 11, 2026. The spacecraft survives because of a very precise piece of engineering: its Thermal Protection System, usually called the heat shield. This shield is only 4.5 inches thick, about 11.5 centimetres, and is made from a lightweight carbon foam core placed between carbon-carbon composite panels. Its Sun-facing side is coated in a specially designed white material that reflects as much solar energy as possible. The shield does not make the whole spacecraft immune to the Sun. Instead, it creates a protected shadow. The instruments and spacecraft body stay hidden behind it, while the shield takes the direct solar radiation. This is why Parker Solar Probe can move through a region where the corona can reach temperatures of millions of degrees. That sounds impossible at first, but temperature and heat are not the same thing. Temperature measures the average energy of particles; heat is the amount of energy actually transferred to an object. The corona is extremely hot, but it is also extremely tenuous, almost a vacuum compared with air on Earth. There are not enough particles there to transfer heat in the same way a dense gas or liquid would. The greater threat comes from intense sunlight and radiation, which is why the shield’s orientation is critical. If sensitive parts of the spacecraft moved out of the shield’s shadow during closest approach, they could be damaged very quickly. Parker did not simply launch straight toward the Sun. That would actually require an enormous amount of energy because Earth is already moving around the Sun very fast. To fall inward efficiently, the spacecraft used repeated gravity assists from Venus, gradually reducing its orbital energy and lowering its closest approach to the Sun. After its final Venus flyby in November 2024, Parker entered the orbit that allows these record-setting solar passes. Its extreme speed is mainly the result of falling deep into the Sun’s gravitational well: as it approaches the Sun, gravity accelerates it dramatically, and as it moves away, it slows down again. Scientifically, Parker Solar Probe is important because it is measuring the Sun from inside the region where many key solar processes begin. It studies the solar wind, magnetic fields, energetic particles, plasma turbulence, coronal mass ejections, and the Alfvén surface, the boundary where solar material stops being magnetically tied to the Sun and escapes outward as solar wind. These measurements matter because solar activity affects the whole Solar System, including Earth. Strong solar storms can disturb satellites, GPS, radio communications, aviation routes, astronaut safety, and even power grids. The mission is also helping us investigate one of solar physics’ long-standing puzzles: why the Sun’s corona is far hotter than the visible surface below it. The photosphere is around 5,500 degrees Celsius, while the corona can reach millions of degrees. Parker’s close measurements allow us to test how magnetic reconnection, plasma waves, turbulence, and energetic particles may contribute to that heating and to the acceleration of the solar wind. The deeper achievement of Parker Solar Probe is not just its speed, but its control. It has to stay correctly oriented, manage its temperature, collect data, survive communication blackouts, and operate autonomously during the most dangerous parts of each orbit. It is not “touching” the Sun in a solid sense, because the Sun has no hard surface, but it is directly sampling the outer solar atmosphere in a way no previous spacecraft could. In practical terms, Parker is showing that a spacecraft can survive at the edge of a star’s atmosphere with a shield thinner than many books, as long as the physics, materials, geometry, and autonomy are engineered with extraordinary precision.

US President Bill Clinton, thanks to the opposition Congress, signed the Balanced Budget Act of 1997. On this day in 1999, Clinton ceremoniously presented the US budget deficit as $0, but then he changed it to $1 (because 0!=1).

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@sulekhat95 MIT OpenCourseWare from 2018. How to Speak Professor Patrick Winston IAP 2018 youtube.com/watch?v=Unzc73… An hour well spent.

Neural Network Visualization

@earthtojake @fdotinc @REK Humanoid robot G1_Humanoid Robot Functions_Humanoid Robot Price | Unitree Robotics unitree.com/g1

@earthtojake @fdotinc @REK Where can I get one of those?

Being a senior developer must be tough 😪

Disheartening. thatprivacyguy.com/blog/anthropic…

Our new Stanford class "CME 296: Diffusion & Large Vision Models" is now available on YouTube!

Scientific American: See NASA’s Artemis II mission around the moon in 12 stunning photos scientificamerican.com/article/see-na…

Mathematics is very meditative—it heals a man by involving him (in his entirety) in a purposeful objective. If pursued relentlessly, it empowers you to dissociate yourself from life’s difficulties & direct your energy to constructivism; in doing so, you understand yourself better

Breakthrough @brkthroughprize

3 months ago

Ewin Tang, 2025 Maryam Mirzakhani New Frontiers Prize laureate, speaks about mathematics as an artistic practice that can be challenging and, at times, unrewarding. She reflects on the collaborative nature of the work, describing moments of intense idea-sharing and how, in those

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We are also releasing self-contained lecture notes that explain flow matching and diffusion models from scratch. This goes from "zero" to the state-of-the-art in modern Generative AI. 📖 Read the notes here: arxiv.org/abs/2506.02070 Joint work with @EErives40101.

Peter Holderrieth @peholderrieth

3 months ago

🚀MIT Flow Matching and Diffusion Lecture 2026 Released (diffusion.csail.mit.edu)! We just released our new MIT 2026 course on flow matching and diffusion models! We teach the full stack of modern AI image, video, protein generators - theory and practice. We include: 📺 Videos:

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There is geometry in the humming of the strings, there is music in the spacing of the spheres. - Pythagoras (c. 569–490 BCE)

Even Pythagoras couldn’t stay calm.