One book cited several times in the preprint of OP is the volume 2 of the famous book series of Knuth, The Art of Computer Programming, notably its section 4.6.4. For readers interested in this kind of results, it is a really interesting gathering of classical theorems and useful tricks to evaluate quickly polynomials.
> I found that it was an overflow in the glue code (now fixed) that converts the exact rationals coordinates of the output mesh, for which we prove the specification, to floats
Preserving the topology of mesh intersections while rounding the coordinates is a hard problem. In particular, it is only in 2020 that an algorithm was found that handles all the cases [1]. In practice, an efficient algorithm for that was published last year [2].
An interesting approach is the dual GPL and commercial license. This is used for example by the CGAL geometry library [1]. In this case, a user of the library has the choice of either paying for the library, or open sourcing the code of their software.
Some libraries let you borrow Playstation video games. I wonder if those libraries will have access to a system that allows people to borrow digital video games.
Beyond the technical aspects, this new technology also leads to fundamental social changes.
In particular, until now, mathematics were one of the rare sciences were great scientists could emerge from any country with a good education system.
With the raise of strong AI tools, only scientists in rich countries with access to those tools might be able to advance faster on the most difficult problems like the millennium problems.
Mathematics might become like experimental sciences were you need to build expensive machines to make further progress, such as nuclear fusion.
Actually, even now, the strongest models in mathematics are only available to a few engineers and a few mathematicians selected by Openai and Google.
> mathematics were one of the rare sciences were great scientists could emerge from any country with a good education system.
But would they be able to realize their potential without further (mostly monetary and institutional) support from their country? In that way, things now are not so different from before. However, the story will probably change in a few years' time.
Computational intelligence obviates the role of the human in making capital reproduce and multiply. Mathematics as its own field of study might become pointless other than as a hobby - an endeavour reserved for those entitled to the machine's output. What the machine develops in the place of mathematics may not be recognizable enough to even share the same label - that is, if it even uses mathematical principles rather than just finding correlations that are 'good enough' for its use.
> IDK how the custom hardware exploits this; would love to hear any ideas!
You might like this article [1], titled "FPGA-based CNN Acceleration using
Pattern-Aware Pruning". More context and details can be found in the PhD thesis of Léo Pradels [2].
Actually, in Europe, Gemini is officially not available for kids even at home [1]. In some countries like Germany, the restriction applies until 16 [2]. I find unsettling that even for supervised account, parents are forbidden to let their kids learn how to use Gemini, even between 14 and 16 yo.
Note that this restriction does not seem to appear from other AI company. So from outside, it looks like unsolicited interference from Google in the parental education choices.
> unsolicited interference from Google in the parental education choices.
They are a company offering a product and they decided not to offer it to kids.
It's not like they are telling you as a parent what you need to do.
Why don't you get a similar product from a different company for your kids?
This reminds me an interview of the author Patrick Modiano, just after he won the literature Nobel price. The presenter asked him if the money would help. His answer was something like: "well, I don't see how the money will help the next time I will be in front of a white page".
> How do we handle AI doing creative work? How do we treat AI creative work? How much creative work do we feel comfortable handing over to AI?
Just as a good for thought, looking back into history, during the late 1920s, mass production had a critical impact on Art Deco [1]. Artists were divided on the question if mass-produced art (using new industrial methods) could have a quality similar to hand-crafted art. It is clear that different people will have different opinion on the subject.
The technology is not there yet, but one example of mass production from AI would be book adaptation into movies. I'm sure that there are many other examples hard to predict that might: empower people, degrade art quality, improve art quality, divide people or maybe gather people.
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