Ciro Santilli @cirosantilli 37

This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.

One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.

Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.

Google's quantum hardware/software effort.

The "AI" part is just prerequisite buzzword of the AI boom era for any project and completely bullshit.

According to job postings such as: archive.ph/wip/Fdgsv their center is in Goleta, California, near Santa Barbara. Though Google tends to promote it more as Santa Barbara, see e.g. Daniel's t-shirt at Video "Building a quantum computer with superconducting qubits by Daniel Sank (2019)".

List of handbooks open as of 2022 at: www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/handbooks-synopses Kudos, e.g. unlike the physics course of the University of Oxford which paywalled them. 2022 one: www.maths.ox.ac.uk/system/files/attachments/UG%20Handbook%202022.pdf

The Oxford mathematics Moodle has detailed course listings, and most PDFs are not paywalled.

E.g. the 2024 course:

By Ciro Santilli: Section "How to teach".

Others:

Some views:

Published on the session reports of the Royal Prussian Academy of Sciences at Berlin 1918 page 464.

Is about Maxwell's equations in curved spacetime, and notably introduces gauge theory.

Viewable for free at: archive.org/details/mobot31753002089727/page/464/mode/2up.

This one is a little confusing: the upper case looks exactly like a letter P, but as the name suggests, it actually corresponds to the letter R. The letter P corresponds to pi instead.

Invertible matrices. Or if you think a bit more generally, an invertible linear map.

When the field $F$ is not given, it defaults to the real numbers.

Non-invertible are excluded "because" otherwise it would not form a group (every element must have an inverse). This is therefore the largest possible group under matrix multiplication, other matrix multiplication groups being subgroups of it.

Besides the understandable Wikipedia definition, Video "Simple Groups - Abstract Algebra by Socratica (2018)" gives an understandable one:

We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:

In particular, this is hard because you can't just take the direct product of groups to retrieve the original group: Section "Relationship between the quotient group and direct products".

Combination of electromagnetism and general relativity. Unlike combining quantum mechanics and general relativity, this combination was easier.

TODO any experiments of interest at all?