dxbydt
Joined 15 years ago
Joined 15 years ago
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.
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.
Its quite wild that the AM GM convergence is almost immediate - in just 2 steps, whereas to get a decent convergence for the Gauss's constant via HM, you need like 15 steps.You can dispense with expensive operators like square root but you end up paying for it with numerous iterations.
All of that has gone out the door. What you have with javascript is something that looks like X. So I can use a html canvas element and get its drawing context and do an arc with the right parameters and fill and hide the scrollbar with some css and pretend that what you now see is like the X. But its not! To actually get rid of the browser window and only have the white dot, you would need a full blown electron install or worse. And it still wouldn’t get you to the X. We already had X. Now we have something that barely approaches X after a great deal of effort.This is supposed to be progress ?!!
Rigetti $RGTI is up 400% this month. 135% this week alone. He’s right.