Home on Ladan Golshanara

AI Solved Navier--Stokes? Here's What It Actually Solved

Thu, 17 Sep 2026 23:26:28 +0000

Early this month, there was a lot of hype around the claim that OpenAI had solved the Navier–Stokes Millennium Prize Problem. If you only read the headlines, it was easy to come away thinking that AI had finally figured out how water flows down a river, air moves around an airplane wing, or turbulence works.

That is not what happened.

The result is primarily a mathematical breakthrough: an AI system constructed a counterexample showing that, under the conditions allowed by the Clay Mathematics Institute’s official problem, a smooth three-dimensional Navier–Stokes flow is not guaranteed to remain smooth forever.

I Taught an AI to Lie (It Was Terrible at It)

Sun, 14 Dec 2025 04:46:48 -0500

Being on mat leave has given me a lot of time to think and very fragmented time to learn.

There’s a specific kind of FOMO that comes from realizing your entire industry has picked a direction and started moving fast. Agents are suddenly everywhere. Everyone seems to be integrating them into their workflows, becoming 10× more productive, automating the boring parts, shipping faster, thinking bigger.

Meanwhile, I’m searching for things like: is green poop normal?

Entering the Era of Personal Droids with ChatGPT

Sat, 18 Mar 2023 01:02:56 +0000

As a tech enthusiast I feel incredibly fortunate to have access to cutting-edge technology like ChatGPT by OpenAI. I use ChatGPT to make my everyday tasks more efficient, enjoyable, and, for any writing I do, linguistically polished. In fact, ChatGPT is my co-author in this blog post. For me, this is reminiscent of C-3PO. It’s like my very own personal droid from the Star Wars universe. We can talk to it, ask it questions, ask it to do things for us, ask it to translate things for us, etc.

JUCE 2D Graphics 2: Affine Transformations on Paths

Sat, 23 Apr 2022 01:42:40 +0000

Drawing a Pretty Circle

In the last post, we used Path objects and clipping tricks to shade the intersection of two overlapping cricles.

In this post, I’ll take it a step further and introduce transformation operations that can be applied to Paths to efficiently draw things like the pleasant looking circle at the top of this post.

Drawing the Circle

First we create the circle, which is just a Path that can be created using the method Path::addElipse(). We then draw it like any other Path.

JUCE 2D Graphics: Paths and Basic Geometry

Thu, 07 Apr 2022 22:34:59 +0000

Experiments with the JUCE 2D graphics API

A while ago I had to learn a bit of JUCE 2D graphics programming for some experiments we were doing at TONZ. I thought it was super interesting at the time and kind of fun, so I’ve spent a little bit more outside of work playing with the graphics subsystem to learn to do more things.

I’ll walk through how to make a Venn Diagram using JUCE GUI geometry and graphics primitives.