In 1801 the great German mathematician Carl Friedrich Gauss made the following conjecture [2,3]:
The ring of integers for a quadratic imaginary field
K = Q(√-d) is principal only for a finite number of d,
where d ∈ {1, 2, 3, 7, 11, 19, 43, 67, 163} .
Said another way, Gauss conjectured that the nine numbers in the sequence {1, 2, 3, 7, 11, 19, 43, 67, 163} are the only numbers who's negative square root can be adjoined to the integers to produce a ring with unique factorization [4].
So how did exactly did Gauss come up with the amazing conjecture that there were nine numbers (and just these nine numbers) that could be adjoined to ℤ to produce a unique factorization ring? The answer involves Gauss' work on the determinants of binary quadratic forms. There is quite a bit of commentary on this around the net; see [5] for example.
Gauss was unable to prove this conjecture; that would have to wait until 1952 when amateur mathematician Kurt Heegner proved the conjecture (up to a few minor flaws) [6]. Today these numbers are known as Heegner numbers [7].
I guess instance migration is a good time for an #Introduction post. Hello lovely people, I'm here both as a scientific researcher and as a human being, and you can expect a range of genres of posts and interactions from me.
On the work side, I'm a computational scientist at Lawrence Berkeley National Laboratory in the field of biological X-ray crystallography, specifically at free electron lasers. It's a glorious interdisciplinary mess, and the description I give to non-scientists is that i use my degree in chemistry to write software to do math that models the physics of experiments that we're running to learn about biology.
For fellow structural biologists: I work on crystallography data reduction software for the steps between photons hitting the detector and a merged set of structure factors. I also support XFEL experiments, both on site and remotely, and assist in post-experiment data processing as needed. My PhD focused on using simultaneous XFEL crystallography and XES spectroscopy to probe the water splitting reaction in oxygenic photosynthesis. I did a postdoc in computational methods development for cryoEM, and I'm now back to XFEL crystallography but still in methods development.
For fellow software developers: all of our work is open source and mostly under the cctbx project/repo. It's mostly python with a bunch of C++ under the hood (including some low-level stuff redundant with scipy and numpy because those weren't around yet!), plus a user-facing wxPython GUI. More recently we've done a ton of work with GPU acceleration (using Kokkos, for NVIDIA, Intel and AMD architectures) and scaling up at three different national labs' supercomputing centers in anticipation of next-gen experimental capabilities. I derive too much joy from writing bash-sed-awk monstrosities on the occasions we need them to fix an urgent problem during an experiment, and I guess I'm most proud of the fact that I somewhat understand git.
As far as hobbies, the longest-standing one is probably #coffee, followed closely by #language (s) / #languageLearning and a love of #patterns and #symmetry in various contexts. I have too many different ways of making coffee (they have overrun my coffee cupboard), but my favorite remains the classic latte, and by now I can make a better latte than I can buy. I'm trying to refresh my #Japanese and learn #Dutch and #German simultaneously/comparatively, which of course is terrible for speed of learning, but fascinating. So far I've found #ASL the most challenging but also deeply satisfying -- I only have one semester under my belt but hope to take a lot more. I studied and continue to study all the #math and #science I possibly can. Right now I seem to be pretty engrossed in #electronics, #CAD, #3DPrinting, and just generally #DIY-ing/fixing/repairing things. Other active interests include #sewing, #reading, #cooking, #bike commuting, and #publicTransit. My journeys in #aikido and #pottery are on hold but I definitely want to pick them back up when I'm not already overcommitted. I'm casually interested in #neurophilosophy, #neuropsychology, #neurodivergence and #neuroscience. I've taken one course in neurophilosophy and can read literature in the rest, with effort.
On a personal note, I'm trans and nonbinary and very open about it -- I transitioned back when I had to explain what that meant. I've retired from some forms of community engagement and support but I'm very happy to answer any questions I can about the US legal and medical landscapes, available resources, policy and terminology best practices, or whatever you know you shouldn't ask [person in your life].
Finally, I spend a lot of time with my cat Rory (pictured), who is perfect and the most affectionate creature I have ever met. I promise to share photos of him from time to time.
I was making salsa the other day and got to thinking about the relationship between how many cuts you make and how many pieces you end up with. It's interesting, right? If I make two cuts through a slice of tomato and the cuts are parallel, I get three pieces but if the cuts are perpendicular, I get four. Same number of cuts different outcome. What's going on? It turns out that it has to do with the dimensionality of tomatoes. 1/x #math#mathstodon
This past Thursday, P1GG stunned the Conway's Game of Life world with their discovery of two tiny glider guns of periods 15 and 16.
P1GG's finds are the lowest-period glider guns yet discovered to be true-period. That is, the mechanisms that produce their gliders are actually periodic with periods 15 and 16!
It's a big leap forward for glider gun technology -- previously, the lowest period for which we had a true-period glider gun was 20.
Is there anyone reading this who could give a talk on "Math(s) and Artificial Intelligence"?
It would need to be aimed at a general audience, so while the material itself doesn't need to be deep, the person giving the talk would need to have some first-hand experience of the actual math(s) that's involved.
Anyone?
If you're comfortable doing so, please boost for reach ... Mastodon-the-platform relies on networking effects.
I recently got to ride this fun trike at the math museum in NYC. Reading about it further, I learned that “for just about every shape of wheel there’s an appropriate road to produce a smooth ride, and vice versa,” as one article put it.
For posterity, I extracted that talk from the #GUADEC 2023 recordings, so that it can be easily found instead of being forgotten within a random unnamed 7-hours-long video. Enjoy: https://youtu.be/rRvmS0mABC0
Un mathématicien voit deux personnes entrer dans une maison. Peu de temps après, trois personnes en sortent.
— “Si une personne entrait maintenant, la maison serait alors vide”, dit-il.