CoreformGreg

Knowing the answer to Fermat’s Last Theorem wasn’t valuable. But the pursuit of it led to many developments in other fields of mathematics that were valuable (where value is measured in terms of $).

Technically they explicitly said “how do I get the”

We use it - specifically we use its Scribble package to define self-documented file formats that autogenerate C++ & Python sources.

The other reply is really good. To add to that, the intersection of two bi-cubic Bezier patches (each being but one part of a cubic B-spline surface) is an implicit equation of degree 18^2=324. This simply cannot be implemented exactly in a geometry kernel and thus must be approximated. How do you want to approximate this? If you choose trimming (the industry standard) now you have to handle gaps in your geometry. If you choose remapping into an unstructured watertight spline, you need to solve a constraint system that is NP-hard. If you choose reparameterizing… well, see nVariate’s watertight Boolean technique (disclaimer: I once sponsored a project with nVariate).

Now, generally speaking, in a CAD model most surfaces will be “analytic” (plane, torus, conical, arc, line, etc). But whenever some complex surface that joins these surfaces is required, (NUR)B-splines are the principal technique for “covering” the gap.

They’re (possibly) referring to “Scalable Geometric Modeler” (SGM)

https://github.com/sandialabs/sgm

Originally open-source, but since taken back in-house. As I understand, which should not be construed as an accurate accounting, Sandia wants to flesh out the basics further before (potentially) open-sourcing it again.

I wouldn’t, solely because it’s still in version 0.X - for any long-term, important project (e.g., PhD dissertation) I’d recommend LaTeX due to A) it’s mature and B) many universities provide LaTeX templates.

A team of four PhDs + seven other academics manage to unfold a single protein in an egg white using a "vortex fluid device" to produce a Couette flow, heat treatment, dilution in phosphate-buffered saline, dissolution in ureal, use of recombinant proteins, etc., etc.,

Meanwhile, my four-year old niece can boil a dozen eggs in the time it took me to read their paper.

I think it's still accurate to say unboiling an egg is "difficult"!

If you're not aware, you may be interested in checking out https://www.osti.gov and https://www.osti.gov/search-tools