[dxbydt]

> best LLMs are able to accelerate you

https://www2.math.upenn.edu/~ghrist/preprints/LAEF.pdf - this math textbook was written in just 55 days!

Paraphrasing the acknowledgements -

...Begun November 4, 2024, published December 28, 2024.

...assisted by Claude 3.5 sonnet, trained on my previous books...

...puzzles co-created by the author and Claude

...GPT-4o and -o1 were useful in latex configurations...doing proof-reading.

...Gemini Experimental 1206 was an especially good proof-reader

...Exercises were generated with the help of Claude and may have errors.

...project was impossible without the creative labors of Claude

The obvious comparison is to the classic Strang https://math.mit.edu/~gs/everyone/ which took several *years* to conceptualize, write, peer review, revise and publish.

Ok maybe Strang isn't your cup of tea, :%s/Strang/Halmos/g , :%s/Strang/Lipschutz/g, :%s/Strang/Hefferon/g, :%s/Strang/Larson/g ...

Working through the exercises in this new LLMbook, I'm thinking...maybe this isn't going to stand the test of time. Maybe acceleration is not so hot after all.

[pton_xd]

"The story of linear algebra begins with systems of equations, each line describing a constraint or boundary traced upon abstract space. These simplest mathematical models of limitation — each equation binding variables in measured proportion — conjoin to shape the realm of possible solutions. When several such constraints act in concert, their collaboration yields three possible fates: no solution survives their collective force; exactly one point satisfies all bounds; or infinite possibilities trace curves and planes through the space of satisfaction. This trichotomy — of emptiness, uniqueness, and infinity — echoes through all of linear algebra, appearing in increasingly sophisticated forms as our understanding deepens."

Maybe I'm not the target audience, but... that really doesn't make me interested in continuing to read.

[jcranmer]

That is such supremely bad writing that it can only come from AI being told to spice up the original opening paragraph, and short of the original author being barely literate (and possibly even then), the original text would have been better writing.

The overuse of the $15 synonyms is almost always a bad idea--you want to use them sparingly, where dropping them in for their subtly different meanings enhances the text. But what is extremely sloppy here is that the possibilities of "no solutions, one solution, infinite solutions" is now being described with a different metaphor for solution here. And by the end of the paragraph, I'm not actually sure what point I'm supposed to take away from this text. (As bad as this paragraph is, the next paragraph is actually far worse.)

Mathematics already has a problem for the general audience with a heavy focus on abstraction that can be difficult to intuit on more concrete objects. Adding florid metaphors to spice up your writing makes that problem worse.

[jpc0]

Even putting it here is annoying to me... Those are a lot of words saying nothing that I just spend time reading.

I'm agreeing with you.

[wrs]

It's rather purple prose, but it's entirely meaningful. Maybe it doesn't seem to mean anything until after you know some linear algebra, though...

[dxbydt]

its been a long time, but when i was taught this material, i was told there are only 3 cases -

x+y=1, x+y=2 clearly has no solution since two numbers can’t simultaneously add to both one and two.

x+y=1,2x+2y=2 clearly has infinitely many solutions. There’s only one equation here after canceling the 2, so you can plug in x’s and y’s all day long, no end to it.

x+y=1, 2x+y=1 clearly has exactly one solution (0,1) after elimination.

This example stuck with me so I use it even now. The author/Claude/Gemini/whatever could have just used this simple example instead of “trichotomy of curves through space conjoin through the realm of …” math, not Shakespeare.

[BlueTemplar]

Also, isn't this a great example of "when you have a hammer, everything looks like a nail" ?

To explain this I would first and foremost use a picture, where the 3 cases : parallel, identical, intersection can be intuitively seen (using our visual system, rather than our language system), with merely a glance.

[wrs]

Sure, but saying something in an ornate way is not the same as “saying nothing”.

[sureglymop]

I agree. Not what I would expect from a math book or script.

[datadrivenangel]

Going faster isn't good if the quality drops enough that overall productivity decreases... Infinite slop is only a good thing for pigs.

[cruffle_duffle]

Just use ChatGPT to summarize its own output. It’s like running your JPEG back through the JPEG compressor again!

[kianN]

^ This perfectly encapsulates the story I see every time someone digs into the details of any llm generated or assisted content that has any level of complexity.

Great on the surface but lacks any depth, cohesive, or substance

[mooreds]

I started a book about CIAM (customer identity and access management) using Claude to help outline a chapter. I'd edit and refine the outline to make sure it covered everything.

Then I'd have Claude create text. I'd then edit/refine each chapter's text.

Wow, was it unpleasant. It was kinda cool to see all the words put together, but editing the output was a slog.

It's bad enough editing your own writing, but for some reason this was even worse.

[dxbydt]

just to clarify - I have nothing to do with this book. I was just forwarded a copy and I thought its relevant to the topic at hand. from the wild swings in karma, looks like people are annoyed with the message and shooting down the messenger.