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Here you sit, an undergraduate with a calculus book open before you, or a pre-thesis graduate student with one of those books whose first ten pages, at least, you would like to master, or a research mathematician (established or would-be) with an article fresh off the press—what do you do now? How do you study, how do you penetrate the darkness, how do you learn something?

All I can tell you for sure is what I do, but I do suspect that the same sort of thing works for everyone. It's been said before and often, but it cannot be overemphasized: study actively. Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

— Paul Halmos, “I Want to Be a Mathematician”, Study.

Some books simply built around this protocol, some are making it “easier” so they’re more popular and sell more.

They do. You get some in the prose, and then more in the exercises.

Learn ____ the hard way.

That is the poetry. When all parts clicks together.

From the preface

“You cannot read mathematics the way you read a novel.

If you zip through a page in less than an hour, you are probably going too fast.

When you encounter the phrase “as you should verify”, you should indeed do the verification, which will usually require some writing on your part.

When steps are left out, you need to supply the missing pieces.

You should ponder and internalize each definition.

For each theorem, you should seek examples to show why each hypothesis is necessary.”

It is a math studying book, not a let me chew it for you before you take it in type of a book. It requires effort, focus and missing steps are missing on purpose so you will discover them. This is the fun about studying mathematics.

Sorry you fell that way, but the book in my opinion is a masterpiece in math composition.

Chapter 7 of Linear Algebra Done Right by Sheldon Axler reads almost as poetry.

https://linear.axler.net/

For me, Edward Witten (1), Sheldon Axler (2), Patrick Winston (3) and many others do a far better job.

1. https://youtu.be/UW_M7hotSlk

2. https://youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV...

3. https://youtu.be/TjZBTDzGeGg

200,000,000,000÷30÷24÷60÷60÷119

648 queries/second/location.

Obviously not all locations are equal and not all seconds or minutes of the day are.

Indeed an impressive scale.

https://web.archive.org/web/20260621140445/https://www.wsj.c...

A. Disable the Gemini suggestions if you don’t want it (I did so).

B. If one’s using a free mail service for 16 years, and then came to not liking its recent development, in which world shitting on it in public is the right and necessary thing to do?

C. In which world someone switching mail provider is a top front page news item?

D. If the case in B is not free, then this means the OP was heavier user than my teenage daughter. Thus consumed more of it.

The study, which was used by EY consultants in Canada to market their cyber security business, used made-up data, misattributed citations and referenced a McKinsey report that doesn't exist.

All content as markdown repository https://github.com/antoniolupetti/algebrica

Well,

    npm install …

What are the sources for the “facts” presented in this post?

Code: https://github.com/jeffhuber/rubiks-solver

Anthropic’s roadmap is widely underappreciated; it is the company defining AI productivity today.

Seems similar to operation night watch by the Rijksmuseum in Amsterdam

https://www.rijksmuseum.nl/en/stories/operation-night-watch/...

In direct relation to his older post: https://terrytao.wordpress.com/career-advice/theres-more-to-...

Also slides are available at https://terrytao.wordpress.com/wp-content/uploads/2026/03/ta...

Boris Cherny on this

https://x.com/bcherny/status/2040206440556826908?s=20

More details: https://x.com/FabianGloeckle/status/2040082785851904401

One day a kid came home breathing heavily, to his father’s surprise face he tells, daddy daddy, I saved a dollar fifty!

How did you do it? ask the father

Instead of taking the bus, I ran after it all the way home.

If you were smarter, you could have save us $22 by running after a taxi!

This old joke came to mind while reading this post.

A tech company spends hundreds of thousands of dollars per year, “for years”, on a piece of software that could have been replaced by a month of coding top? (prior to LLM and all), you sit and write and save the money.

If I was an investor in this company I would have hire a team to look through their entire stack. See, if this JSON thingy alone is half a million a year, their entire cloud is at least $35MM annually.

Perhaps this is not even a bad business idea. One can offer companies to provide drop-in replacement for their costly “micro services that no one dares to touch” and share the cost savings.

May or may not. You open the UDP ports, you get flooded, they block all incoming traffic, and this way or another your assets are not resolvable.

One must distinguish between application layer attacks HTTP/S and UDP, cloud vendors won’t protect you implicitly for network layer attacks unless you purchased such service from them.

Large scale dns vendors have a multi million dollars worth of network layer traffic filtering equipment pipelined in front of their DNS servers (or in house solutions such as Google).

Just remember, if you run your own DNS, and you do so for a mission critical platform, the platform is exposed to a udp DDoS that will be hard to detect let alone prevent.

Unless of course you will invest 5-6 figures worth of US dollars worth of equipment, which by then you can look back and ask yourself, was I better off with Google Cloud DNS, AWS Route 53 and the likes.

I see.

Nowadays I fly nothing, but I do see them Iranian drones get intercepted from my porch in Abu Dhabi.

The fact I am watching it and not panicking anymore tells about how cooked I am.

8 inches drone cannot carry much of explosive at all. In order to dump 10 kg load of explosives, you need an “agricultural drone” one that can carry 45kg, since the additional mechanisms and their batteries (and the drone’s backup batteries) are heavy.

Those are bigger and noisier.

DJI ARGAS Series are good starting point.

https://ag.dji.com/mobile

hence: "what's falling into the AI category here perhaps is the key question"

YOLO is a good example for something that can work.

https://docs.ultralytics.com/models/yolov8/

"let alone with AI" what's falling into the AI category here perhaps is the key question, since microseconds counts, and LLM are very slow!

Even the fastest "real-time" LLM frameworks currently report sub-second latencies around 120ms. This is fine for high-level mission planning (e.g., "fly to the red house") but too slow to prevent a drone from hitting a tree at 50mph (80 KM/h)[1]

Whilst the Shahed-136 kamikaze drone typically flies at a maximum speed of around 185 km/h (roughly 115 mph or 100 knots).

[1] https://arxiv.org/html/2602.19534v1 [2] https://en.wikipedia.org/wiki/HESA_Shahed_136

There are 2 short segments in the video showing the actual performance and thus far it is a complete [1] failure [2].

The guy has a talent, and he put together a nice prototype based on OpenRocket [3], but with all due respect, this is not a rocket, and you are not going to win any war with this toy, even if all your enemy has are rocks thrown at you from pretty much similar distance.

The remix of computer games / Ukraine / Martin Luther King / Vietnam / David Koresh just adding more to the amateur spirit and confusion.

[1] https://youtu.be/DDO2EvXyncE [2] https://youtu.be/DDO2EvXyncE?t=280 [3] https://openrocket.info/

Given the navigation is done by the cameras (not GPS) you will also need to do some work with the second repository (by the same guy)-

https://github.com/novatic14/Distributed-Camera-Node-Trackin...

Setting aside the DIY and hacking spirit of the project, let's remember that, with the commonly accepted figure of 2,500 kcal/day for an adult male, a whole iceberg lettuce (~600g) provides about ~87 kcal which is roughly 3.5% of what one's need.