#Tag · Bonfire Dinteg Labs

The corruption of the Roberts court expands and expands. There's no longer even a tiny pretense -- what Donald Trump and his Republican apparatchiks and lackeys want is what the court will approve.

https://talkingpointsmemo.com/news/supreme-court-just-okayed-one-neat-trick-to-illegally-gerrymander-your-state

TPM – Talking Points Memo

Supreme Court Just Okayed One Neat Trick to Illegally Gerrymander Your State

The Supreme Court was simply hamstrung, Justice Samuel Alito wrote, unable to...

Preston MacDougall

@ChemicalEyeGuy@mstdn.science replied · 11 hours ago

@dangillmor
#SCOTUS + #Trump = #SCROTUS

#Resist #USpol #MATH

Kerry Mitchell 🍁

@KerryMitchell@mastodon.social · 3 days ago

A 24-year-old Stanford dropout has wooed top Meta AI researchers to her nascent startup, which is building an AI mathematician. https://www.businessinsider.com/axiom-math-stanford-dropout-meta-ai-researchers-startup-2025-12 #artificialintelligence #math

Business Insider

A 24-year-old Stanford Ph.D. dropout shares how she lured Meta's top AI researchers and raised $64 million for her math startup

24-year-old Axiom Math founder Carina Hong wooed top Meta researchers in a competitive AI talent market.

GhostOnTheHalfShell boosted

Daniel Lakeland

@dlakelan@mastodon.sdf.org · 5 days ago

Any #mathematics professors want to take a shot at explaining to someone with say a typical math major undergrad background what the deal is with the recent introduction of exacting and ultraexacting cardinals?

#math #maths #settheory #zfc

https://arxiv.org/abs/2411.11568

arXiv.org

Large cardinals, structural reflection, and the HOD Conjecture

We introduce exacting cardinals and a strengthening of these, ultraexacting cardinals. These are natural large cardinals defined equivalently as weak forms of rank-Berkeley cardinals, strong forms of Jónsson cardinals, or in terms of principles of structural reflection. However, they challenge commonly held intuition on strong axioms of infinity. We prove that ultraexacting cardinals are consistent with Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC) relative to the existence of an I0 embedding. However, the existence of an ultraexacting cardinal below a measurable cardinal implies the consistency of ZFC with a proper class of I0 embeddings, thus challenging the linear--incremental picture of the large cardinal hierarchy. We show that the existence of an exacting cardinal implies that V is not equal to HOD (Gödel's universe of Hereditarily Ordinal Definable sets), showing that these cardinals surpass the current hierarchy of large cardinals consistent with ZFC. Moreover, we prove that the existence of an exacting cardinal above an extendible cardinal implies the "V is far from HOD" alternative of Woodin's HOD Dichotomy. In particular, it follows that the consistency of ZFC with an exacting cardinal above an extendible cardinal would refute Woodin's HOD Conjecture and Ultimate-L Conjecture. Finally, we show that the consistency of ZF with certain large cardinals beyond choice implies the consistency of ZFC with the existence of an exacting cardinal above an extendible cardinal.

Daniel Lakeland

@dlakelan@mastodon.sdf.org · 5 days ago

#math #maths #settheory #zfc

https://arxiv.org/abs/2411.11568

arXiv.org

Large cardinals, structural reflection, and the HOD Conjecture

James Hawley and 1 other boosted

puleo

@puleo@mathstodon.xyz · 2 weeks ago

Hi folks -- I'm still kind of figuring out this whole Mastodon thing, so please pardon any clumsiness in my posting. I'm a former academic mathematician in graph theory, and while I'm no longer working in academia and publishing papers, it turns out I still have a strong drive to keep doing mathematics in some form or another.

Lately, the form that has taken has been creating small mathematically-inflected games in the #godotengine. Often my process is to work out a little theorem for myself and then to try and create a path through those ideas that might allow someone to arrive at the same theorem for themselves from first principles -- maybe encountering some of the same false-starts and little breakthroughs that make the research process so engaging.

When I hear professional game designers talking about game design I often hear them opining about how they are pleasantly surprised to lay down the basic rules of a game and then hear those rules "talking back" to them and leading to consequences they had not initially foreseen. What mathematician can hear that and not immediately recognize it as the thrill of mathematical discovery?

#introduction #math