Comments URL: https://news.ycombinator.com/item?id=45385325

Points: 2

# Comments: 0

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.

https://imgur.com/a/UkxkPzW

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.

Comments URL: https://news.ycombinator.com/item?id=42413220

Points: 1

# Comments: 0

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.

8th,9th,10th,11th & 12th graders = 20 million.

So 20 million students are eligible for AMC10/AMC12

Of them, only 300K took the AMC10/AMC12

Of them, only 10K were invited to take the AIME

Of them, only 500 were invited to take the USAMO

Of them, only 50 went to the MOPs

Of them, only 6 went to the IMO & won.

The article is about 4th & 8th graders, of which we have 8 million.

Now, suppose those 4th graders get to 8th grade, then the 8th graders would be in 12. That makes both cohorts eligible for AMC10/12. At that point, they become 8 million out of the 20 million. So 120K of them take the AMCs, 4K take the AIME, 200 get into USAMO, 20 get invited into the MOPs, and best case 2 kids make it into the IMO.

So from this grand experiment, 2 kids will emerge the victor, and we are supposed to back-extrapolate that 8 million kids do ok. Aaalright then.../s

(display (foldl + 0 (map (lambda (x) (/ x (+ x 1))) (range 0 1000))))

The solution matched and I was happy. Then I thought wouldn't it be neat to do this in a dozen languages and benchmark...but got nowhere with that idea. None of the languages supported fraction addition without jumping through whole bunch of hoops. I wonder if its still the same situation. If someone wants to give this a shot, the answer if you do this for the first ten is 17819/2520.

there is a youtube video ( pls don’t watch ) that gave me nightmares for days on end. i had completely forgotten about those pelicans and now you had to bring it up again in the comments. the little pelican had a broken leg. It was limping, so mom and brother together pushed it out of the nest. Very cruel.

This is strictly false. A consistent warming trend reduces the occurrence of extreme cold events. This will narrow the range of temperature fluctuations, which directly reduces the time derivative of temperature variance.

Also, oceans redistribute heat more efficiently due to climate change. This causes the temperature gradients between regions to weaken. Once again the time derivative of temperature variance is reduced. Empirically, one can observe this decrease in temperature variance in the tropics.

I wrote a lot of QBASIC. 1986-90ish, old Bangalore. I was 12. There was no Mac or Unix or Windows in India those days. Only MSDOS. I had a 386 box. I would insert a 5.25" floppy, boot into command.com, then CD to GWBASIC.EXE and enter GWBASIC. Wrote a lot of GWBASIC to annoy friends and family by emitting high pitched sounds. You could do SOUND 2000+i, j, where i is the frequency & j was duration. You could even control volume from BASIC. I would put that in a WHILE WEND loop and make it go crazy. People didn't know how to turn it off once it got going. Then suddenly one day DOS went away and we had something called MS WINDOWS 3.1 and you had to insert a white round ball into a mouse and click on icons, no more command line, and even GWBASIC was gone, they put QBASIC and it came with snake program. Then I got into the graphics craze. We had a CGA & so I did SCREEN 2, then used LINE and CIRCLE to my heart's content. Few colors only. Then we upgraded to VGA monitor then SCREEN 12 was a full 640x480, I wrote QBASIC to make annoying sounds while drawing. It was an amazing childhood, thanks to this miracle language. BASIC led to something called CLIPPER, then I did some FOXPRO, got paid actual rupees to write an inventory control system in FOXPRO, then MFC, Borland C++...all the way upto today.

But it all started with BASIC. Amazing language. Thank you, Dr. Kurtz.

So why does the richest country on the planet have "very scarce resources" only when it comes to educating its kids ? Of course, that very same public school has a stadium that is easily several times larger than facilities provided for Olympic level athletes in a poor country like India. That same school has a music program with a huge ballroom, recording studio, fancy musical instruments...bass sax, harps, bassoons and contrabassoons, double bass, violas...like literally, even a top of the line Bollywood studio doesn't have half of this. USA has chosen to prioritize just about everything other than basic classroom stem education. Then when you ask the math teacher why the kids don't know their logarithms and trig tables, he is like...well we have calculators and chromebooks. I have spent multiple years trying to engage with school board officials in public schools here in the mid-west. The most reasonable, unemotional, takeaway after all this engagement is that Americans are simply not interested in classroom education. They don't have teacher, don't have the time to teach, don't care for books or chalkboards...its simply not their thing. That's fine. I do hope all of this hyper-investment in music and sports produces some world class track and field athlete who can run a mile under three minutes while playing the bassoon.