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λ · μ = lk(∂λ, ∂μ) + ∑ handles intersections Watching Lisa Piccirillo own the blackboard like this; intersection forms on homology modules, handle cancellations in 4-manifolds; hits different. The precision, the chalk dust, the way she just sees the topology. This is pure 4D magic: where smooth vs...

275,063 görüntüleme • 4 ay önce •via X (Twitter)

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Axiom Math's Carina Hong on why verification isn't about catching mistakes, it's how you drive the cost of a proof to zero: "Formal verification is going to make your life slightly better if you're facing a proof with one million lines. Remember the Erdős unit distance problem, the chain of thought being generated? There are actual mathematicians trying to follow it step by step and scrutinize it. That seems very difficult if you're not in that very niche domain of discrete geometry intersecting with algebraic number theory." "But if you have a Lean proof accompanying it, you can just run it. And running the Lean proof gives you that provable guarantee that this proof is sound." "I have a hot take. People think Lean is this library built on the existing Mathlib. I think it's going to grow significantly. A lot of the hurdles where Lean is difficult is that the basic definitions of some mathematical fields are just not in the library." "My hot take is the scaling law, if you go down the formal mathematics path, is going to be a lot steeper than informal mathematics. So it's not just for verification, for trust, it's also for performance, it's also for optimal generation." "Verification is not like insurance. It's not something where, oh, we want to make sure there's no flaw. That's great, but it also helps you generate mathematics, both proofs and conjectures and theories, a lot better." "So imagine the cost of proof goes to zero. Then you can massage the problem statements, and even if it's an open problem, a lot more easily, flexibly, and adaptively." Carina Hong Axiom

MTS

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Some Respectful Questions for Candace Owens Where are the photos? Why were no photos taken at all—not even a casual selfie—of her meeting with Erika Kirk? In an age where nearly every public or semi-public encounter leaves some digital trace, the complete absence of photographic evidence is difficult to understand. A multi-million dollar CEO of a $100,000,000 enterprise, a few days before the big Amfest conference, flies from AZ to TN to sit down with Candace? Where was the blood? Photos of the backseat of the black SUV reportedly connected to the incident show zero visible blood, and far as I can tell. Given the seriousness of what was implied, how is this absence explained? The time problem and the clarity problem (together): On her livestream, she said the meeting lasted four and a half hours, yet her one hour+ summary left many listeners more confused than before. Why did so much time produce so little clarity? What essential facts were established that listeners should clearly understand—but currently don’t? Egyptian planes: What exactly do Egyptian military or private aircraft, allegedly flying around the country and perhaps following Erica Kirk, have to do with this story? What’s the material connection? To many listeners, this detail feels like a shiny metal object tossed into an already complicated narrative, adding intrigue but not illumination. Proof that Charlie Kirk is dead: I did a short video after Candace announced that Charlie got a Catholic Mass and funeral, and burial in a Catholic cemetery. Since Charlie and Erika were attending St. Bernadette’s parish in Scottsdale, and she lives there, I contacted all the relevant agencies just to make sure I “had the receipts” – and all of them refused to confirm or deny anything. Does Candace know there is no extant proof that her friend Charlie is dead?

Patrick Coffin

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American Surgeon shows the actual letter from UnitedHealthcare DENYING a patient in emergency condition from receiving care “This is a woman who was in the emergency room with pulmonary embolisms” “I think we all knew this would happen. I had another patient come in and share with me that UnitedHealthcare denied her inpatient's day. So this is a patient who had shortness of breath and some chest pain, and she just knew that something wasn't right in her body. She had a family history of blood clots and she'd had a deep flap surgery a couple of weeks ago. She went to the hospital and they saw her and they found that she had a life threatening condition known as pulmonary embolisms. So she was admitted to the hospital and taken care of really well by the doctors there. And they ordered all the right things. After a couple of days, she was discharged. She got a letter from UnitedHealthcare explaining that they didn't agree with the level of her care and that they would not cover it. So I'm gonna share some of the language of that letter with you, and I want you to know that my patient that we talked about previously who had her surgery denied had almost exactly the same letter shared. So there's some troubling things in this letter. I think this term is really interesting. United is saying they reviewed the request for inpatient admission. So let's all just pause and consider that. This is a woman who was in the emergency room with pulmonary embolisms, and the doctor wasn't really requesting anything. They were saying this patient needs to be in the hospital. But an insurance company sees this as a request, and that's part of this prior auth environment that we're living in. So I think it's important as patients and as physicians to just acknowledge that this is our reality now. Someone can think that there's a good medical decision for you and can write orders and wanna do the right thing for you, but your insurance company is seeing that as a request and deciding whether or not they wanna do it. One of the criteria that this insurance company used to decide whether or not to accept or deny this request was whether it's medically necessary. And it's so interesting that we're letting insurance companies and the doctors who work for insurance companies determine what's medically necessary and not just the doctor in front of the patient in the emergency room. So this is a really bold statement from UnitedHealthcare for my patient. They say you did not have to be admitted as an inpatient to the hospital for this care. I think we all need to just reflect on that. An insurance company is telling a patient and her doctor that they disagree with the plan of care to keep that patient safe. I know that this is boiling down to whether it's an inpatient admission or an observation admission, and that's really about money. But what I wanna point out to you is they're making medical decisions. This insurance company is actually weighing in and disagreeing with a doctor who made a medical decision to admit this patient for her safety. So this specific sentence, when a doctor or facility treats a patient above the recommended level of care, we cannot cover it. What the heck? That's what we do. We go above and beyond as physicians. It's clear that insurance companies don't, and they're actually saying it here.”

Wall Street Apes

115,712 görüntüleme • 1 yıl önce

One guy built this app in a month and now it makes him more than $1,000,000 a year. No team. No investors. No marketing department. One developer. One month. One clever idea. The app is a camera for events. In its first month it got 100,000 downloads and he did not spend a single dollar on ads. Here is how he did it because the most interesting part is the growth itself. He did not bolt marketing onto the product. He made using the product the marketing itself. After that things kick in that almost nobody figures out. 1. You cannot use the app alone. For it to work the host has to pull every guest into it. Each install drags in dozens more right away. 2. One wedding is not one user but a whole crowd at once. 200 people scan one code in an evening and install the app. No ad brings that many for the same money and here the money is zero. 3. The guest becomes the host. He liked it at someone else's wedding and a month later he throws his own event and brings his own people. The loop spins itself and for free. 4. It does not look like an ad. To the guest it is a gift not some app forced on him. So they install it gladly and all of them do. 5. It all runs on emotion. A wedding. Memories. Shared shots. People film it and show their own people and a new wave comes in. Now let us count the money plain and honest. The subscription runs from 2 to 50 dollars. Say only every 20th person pays. That is 5,000 people out of 100,000. The average check a modest 20 dollars. 5,000 times 20 is 100,000 dollars a month. More than 3,000 a day. More than $1,000,000 a year. And all of this is one guy in a month without a single dollar on ads. He did not win on budget and not on a team. He won by sewing distribution into the very use of the product. You can lift almost any product this way. Could you build something like this on your own or is it just luck?

Blaze

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KIDS: This may be one of the most scathing clips I've ever done, but it's a great teaching point from a coaches perspective that I think is important for all young players to hear. This shift started with a faceoff at 12:08 on the clock. When Hall gets this puck midshift and chips it in, it's at 11:32 - 36 seconds later. Being on the ice for 36 seconds already - two or three of the Chicago players should change. But no. They are clearly tired yet decide to go and forecheck in the ozone anyway. And the effort on the forecheck and track here are absolutely abysmal. When a player extends their shift when the puck is going up the ice offensively in a situation when they're tired and should change, it's one of coaches' biggest pet peeves. All in all - it's selfish. And in this case, it ends up in the back of their net. Just look at the effort on the forecheck and the backcheck...yikes. I looked up the three players and how they're doing this year. All immensely talented players but between Hall, Bertuzzi, and Kurashev... They have a combined 18 games played and 4 points. On a team where Kurashev is fighting for a top 6 role and Hall/Bertuzzi were brought in to provide veteran leadership. This is one of those plays that gets highlighted in team video the next day. It can't happen. It's putting yourself above the team and not focusing on the little things that don't show up on the scoreboard that championship teams do. This is a culture teaching clip.

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Featherless AI

39,769 görüntüleme • 11 gün önce