I can’t recall all of it, but most of my calculus courses all the way to multi variate calc and my signals processing all required understanding and using memorized and abstract trig functions which can all be solved using algebra to solve polynomials. One of the big leaps that enables us to go from trig functions to doing limits to calc happen when we used language to understand that summation can tell us what the “area” under the curve is. Geometric functions, odd/even etc is all algebra and trig. If this model can use language to solve those challenges those abstractions can be made more useful to future linguistic models. That’s so much more to teach and embedded in these “statistical” models and NNs. (Edited, because I forgot to check how bad my autocorrect is)

The thing is, in general computing it was humans who figured out how to build the support for complex abstractions up from support for the simplest concepts, whilst this would have to not just support the simple concepts but actually figure out and build support for complex abstractions by itself to be GAI.

Absolutely

“breaktrough” here is that they got an LLM - which is a very specific kind of NN, for language - to do it)

To some degree this is how humans are able to go about creating abstractions. Intelligence isn’t 1:1 with language but it’s part of the puzzle. Communication of your mathematical concepts and abstractions in a way that can be replicated and confirmed using a rigorous proofing/scientific method requires the use of communication through language.

Speech and writing are touch at a distance. Speech moves the air to eventually touch nerve endings in ear and brain. Similarly, yet very differen, writing stores ideas (symbols, emotions, images, words, etc) as an abstraction on/in some type of storage media (ink on paper, stone etching stone, laser cutting words into metal, a stick in the mud…) to reflect just the right wavelengths of light into sensors in your retina focused by your lenses “touching” you from a distance as well.

Having two+ “language” models be capable of using an abstraction to solve mathematical ideas is absolutely the big deal…

Many of the building blocks of computing come from complex abstractions built on top of less complex abstractions built on top of even simpler concepts in algebra and arithmetic. If Q* can pass middle school math, then building more abstractions can be a big leap.

Huge computing resources only seem ridiculous, unsustainable, and abstract until they aren’t anymore. Like typing messages a bending glass screens for other people to read…

Kudos to having wide-ranging interests. We need both types of people (and many many in between) to survive and progress in this world together :)