Hacker News: kurlberg

New comment by kurlberg in "Mathematicians still don't know the fastest way to multiply numbers"

kurlberg — Sun, 19 Jul 2026 09:48:01 +0000

It's complicated. :-)

There is a nice picture of the "best" choice for different ranges of sizes of numbers to be multiplied at http://gmplib.org/devel/log.i7.1024.png

More context and explanation can be found at: http://gmplib.org/devel/

New comment by kurlberg in "I'm skeptical about efforts to revolutionize schooling"

kurlberg — Fri, 05 Jun 2026 10:59:02 +0000

"Learning styles" might be a myth. Eg, see

Learning Styles: VAK Doesn't Exist (Here's What Research Actually Shows)

https://www.structural-learning.com/post/learning-styles-myt...

Belief in Learning Styles Myth May Be Detrimental (by American Psychological Association)

https://www.apa.org/news/press/releases/2019/05/learning-sty...

New comment by kurlberg in "Sum-product, unit distances, and number fields"

kurlberg — Thu, 04 Jun 2026 22:10:01 +0000

Even Terry Tao struggled at times: "When I was a graduate student in Princeton, Tom Wolff came and gave a course on recent progress on the restriction and Kakeya conjectures, starting from the breakthrough work of Jean Bourgain in a now famous 1991 paper in Geom. Func. Anal.. I struggled with that paper for many months; it was by far the most difficult paper I had to read as a graduate student, as Jean would focus on the most essential components of an argument, treating more secondary details (such as rigorously formalising the uncertainty principle) in very brief sentences."

More details at

https://terrytao.wordpress.com/2018/12/29/jean-bourgain/

(In particular, see the "???" in the Tao's annotated copy of Bourgain's paper.)

New comment by kurlberg in "Sum-product, unit distances, and number fields"

kurlberg — Thu, 04 Jun 2026 22:01:22 +0000

There is a joke saying "a mathematician says X, writes Y on the board and means Z". The really amusing(?) thing is that other mathematicians still (sort of) perfectly understands Z. Once you have enough experience you fill in the blanks automatically.

Math exposition is tricky: too few details and you're just floating in the sky, too many details and the audience loses sight of the forest for all the trees. You can go (more or less) all formal, but it's a pain for the writer and a pain for the experienced reader.

If it's any consolation, the punchline to the joke is that it often is small/big lie: the other mathematicians reads "Y" and goes WTF!? And then 1 minute, 1 hour, 1 day, or one week later says "aaah, that's what he/she meant! I guess it was 'obvious' all along". :-)

New comment by kurlberg in "Only 17% of all 64-bit Integers are products of two 32-bit integers"

kurlberg — Wed, 03 Jun 2026 22:20:06 +0000

Where?

New comment by kurlberg in "Only 17% of all 64-bit Integers are products of two 32-bit integers"

kurlberg — Mon, 01 Jun 2026 17:18:01 +0000

There is a cute argument (I think it is due to Erdos) that, asymptotically, 0% of the integers in [0,n^2] appears in the "n by n multiplication table":

By Erdos-Kac, almost all integers of size about n^2 have about log(log(n^2)) ~ log(log(n)) prime factors. However, almost all integers in the multiplication table have about 2*log(log(n)) prime factors.

Kevin Ford gets much more precise asymptotic estimates.

New comment by kurlberg in "Canonical/Ubuntu have been under DDoS"

kurlberg — Fri, 01 May 2026 15:12:06 +0000

I had the same impulse (or at least copy.fail inducing many to upgrade at the same time.) However, it might be a "pro-Iran hacktivist group" according to

https://www.theregister.com/2026/05/01/canonical_confirms_ub...

"Canonical says its web infrastructure is under attack after a pro-Iran hacktivist group instructed its members to target the open source giant."

Perhaps more to do with extortion rather than activism. (I have no idea how accurate theregister is on this story.)

New comment by kurlberg in "The math that explains why bell curves are everywhere"

kurlberg — Thu, 19 Mar 2026 14:21:19 +0000

Convolution alone does not smooth. Eg consider a random variable supported on the pts 0 and 1 (delta masses at 2 pts.) No matter how many convolutions you do, you still have support on integers - not smooth at all. You need appropriate rescaling for a gaussian.

Also, convolving a distribution with itself is NOT a linear operation, hence cannot be described by a matrix multiplication with a fixed matrix.

New comment by kurlberg in "Ask HN: Books to learn 6502 ASM and the Apple II"

kurlberg — Tue, 27 Jan 2026 14:31:40 +0000

Read it as a young teenager, can recommend.

New comment by kurlberg in "DIY NAS: 2026 Edition"

kurlberg — Thu, 27 Nov 2025 09:15:59 +0000

This has been discussed on HN some times before. User xornot looked at the zfs source code and debunked "faulty ram corrupts more and more on scrub", for more details see https://news.ycombinator.com/item?id=14207520

New comment by kurlberg in "The Microsoft SoftCard for the Apple II: Getting two processors to share memory"

kurlberg — Wed, 05 Nov 2025 12:33:56 +0000

I don't think this is entirely due to Wozniak. Early "home" computer systems were based on connecting cards to a bus (eg the S-100 bus), eg. with one card supporting the CPU, another RAM, a third for disk drive, video card etc, etc. The cards where then memory mapped, presumably you controlled the memory mapping by setting jumpers. (I guess you're saying that Apple II managed this automatically?) Of course the full story might be a bit more complicated: 6502 and 6800 used memory mapped I/O, whereas 8080 (and Z80?) had certain I/O pins coming out of the CPU.

New comment by kurlberg in "The Unknotting Number Is Not Additive"

kurlberg — Thu, 09 Oct 2025 09:18:02 +0000

Fun historical fact: knot theory got a big boost when lord Kelvin (yeah, that one) proposed understanding atoms by thinking of them as "knotted vortices in the ether".

New comment by kurlberg in "Busy beaver hunters reach numbers that overwhelm ordinary math"

kurlberg — Mon, 25 Aug 2025 06:29:03 +0000

If you have a child who likes math I highly recommend "Really Big Numbers" by Richard Schwarz. Tons of nice illustrations on how to "take bigger and bigger steps".

"Infinity is farther away than you thought."

New comment by kurlberg in "FreeBSD for hi-fi audio: real-time processing, equalizer, MPD and FFmpeg"

kurlberg — Thu, 06 Feb 2025 14:26:00 +0000

I recently got into making some sort of budget hifi setup, and found audiosciencereview.com quite helpful - a good amount of reviewed gadgets with focus on measurements. Ended up with kali lp-6v2 speakers and a SMSL SU-1 dac. Please don't tell me I screwed up. :-)

New comment by kurlberg in "OpenWrt 24.10.0 – First Stable Release"

kurlberg — Thu, 06 Feb 2025 09:57:13 +0000

I have used merlin for quite a while, mostly happy (except for some security holes...) However, once asus drops support for older devices (e.g. rt-ac68u and rt-ac86u), merlin might also drop it. For now rt-ac68u is dropped by merlin, but ac86u is fine for now (at least until the end of the year.)

Upshot: if you care about very long term support, openwrt is nice.

New comment by kurlberg in "OpenWrt 24.10.0 – First Stable Release"

kurlberg — Thu, 06 Feb 2025 09:52:44 +0000

Based on reddit [1] and other some other recommendations I got an asus ax4200 and put openwrt on it. I'm fairly happy, but some people have run into connection dropping (possibly due to ISP power saving resulting in link dropping down to 10 mbs, and something then goes wrong.) With forum help [2] I found a workaround: either turn off auto negotiation (works) or using a lan port as a wan port (have not tried).

https://www.reddit.com/r/openwrt/comments/1cr1lvp/is_the_asu...

https://github.com/openwrt/openwrt/issues/14192#issuecomment...

New comment by kurlberg in "Convolutions, Fast Fourier Transform and polynomials (2022)"

kurlberg — Mon, 01 Jul 2024 14:55:54 +0000

PS: if you're interested in multiplying "ludicrously large numbers", Harvey and van der Hoeven had a nice breakthrough and got multiplication down to "FFT speed" (n*log(n)), see

https://hal.science/hal-02070778v2/document

A pop-sci description can be found at

https://theconversation.com/weve-found-a-quicker-way-to-mult...

New comment by kurlberg in "Convolutions, Fast Fourier Transform and polynomials (2022)"

kurlberg — Mon, 01 Jul 2024 14:46:16 +0000

There is a nice picture of the "best" for different ranges of sizes of numbers to be multiplied at

http://gmplib.org/devel/log.i7.1024.png

More context and explanation can be found at: http://gmplib.org/devel/

BTW, I like Bernstein's survey of different multiplication algorithms at

https://cr.yp.to/papers/m3.pdf

(there is a unifying theme about using ring isomorphisms to explain many of the "standard" routines.)

New comment by kurlberg in "Making AI better at math tutoring"

kurlberg — Thu, 27 Jun 2024 16:19:03 +0000

Check out "Diamond Age" by Neal Stephenson.

New comment by kurlberg in "How to generate uniformly random points on n-spheres and in n-balls"

kurlberg — Wed, 06 Mar 2024 07:16:31 +0000

It's very inefficient, both on terms of runtime and in terms wasted entropy.