Deniz Kural

@psychiel I am genuinely so glad you posted this, as it helps me feel less insane. I remain similarly baffled.

It's still baffling to me that you can make a length 2 zig-zag look arbitrarily close to a length sqrt(2) line without changing its own length at all I know we can say "arc length isn't continuous wrt pointwise convergence", but that only renames the fact, it doesn't debaffle it

I propose a life ban from arXiv when there is an argmin/min/argmax/max/expectation operator without saying over **what**, or when the "over what" variable doesn't appear in the operand expression.

@Jeffliu6068Liu @josiezayner What parts of the video are fake? It does not actually work that way?

@josiezayner Hi I'm the cofounder ceo of FinalDose, if you're interested in how it actually works, reach out Jeff.liu@finaldose.ai

Wut?

Some concrete examples here: 👉 modern cardiovascular drug development has been largely shaped by targets, where variation in their genes has been linked to disease risk (PCSK9, APOC3, ANGPTL3, FXI, LPA, IL6 etc.) 👉 specifically, human genetic evidence has been translated to approved drugs for hypercholesterolemia (PCSK9, approved), boosted the clinical development of new categories of drugs (e.g. LPA, IL6, in phase 3), or informed new translational pathways and indications for others (e.g. FXI, awaiting approval for non-cardioembolic ischemic stroke) 👉 GWAS hits in Alzheimer's disease (e.g. TREM2, CLU, BIN1) have pointed to neuroinflammation and microglial biology, influencing drug development, even if clinical translation is still ongoing (TREM2) 👉 similar story for ALS, where beyond pointing to Mendelian cases, for which targeted therapies are being developed, drugs emerging from GWAS hits are about to start being tested in clinical trials (UNC13A) 👉 many similar examples from autoimmune diseases, e.g. IL23/IL23R approved for psoriasis and inflammatory bowel disease, TYK2 inhibition approved for psoriasis now expanding to other indications, PTPN22/LYP emerging as a promising target in clinical development 👉 first approved drugs for dry age-related macular degeneration (C3 and C5 inhibitors) targeting the complement, were largely influenced by discovery of hits in several complement genes in GWAS 👉 the whole booming field of RNA therapeutics (especially liver-targeting) depends on sequencing the targets and so is directly linked to the human genome project

This paper exists because teams of people started an unglamorous data collection project many years ago. The Interventions Testing Program (ITP) is a long-running project by the NIH-NIA with the goal to identify interventions that extend lifespan in mice. The ITP was not built around the analysis this paper eventually performed. Instead, the paper’s method emerged because a group of scientists had access to a sufficiently large dataset generated by the ITP and realized there were better questions to ask of it. Computational power is scaling rapidly. What isn't scaling is the generation of biological data that requires organisms to age, populations to evolve, or longitudinal measurements to accumulate across years. If someone starts a 10-year dataset now, by the time it matures the analytical tools available to interrogate it will be dramatically more powerful than anything we have today. But if nobody starts the dataset, those tools have nothing to work with. For those thinking about the overall progress of longevity, it’s now obvious that AI will be bottlenecked by the lack of high quality biological datasets. nature.com/articles/s4158…

Many countries finance pension gaps via the general budget, which in turn is increasingly financed via government borrowing - thus avoiding current difficult choices (i.e. increased taxes / lower spending), to be paid back by (diminished) future generations.

In other words, it's a vicious cycle. As the dependency ratio gets worse, in a voting democracy, the retiree cohort will have even more electoral power, making it even harder to change government spending priorities.

As the retiree-to-working.age ratio gets worse across various countries, progressively more of the GDP is being spent on retirement benefits; further starving investment in infrastructure that would actually help reverse population decline, making the dependency ratio even worse.

There's a common misconception that Brutalist buildings were unpainted, but thanks to microscopic analysis of the exteriors we can now recreate what they looked like in their prime.

Just posted a paper (with Aaron Smith) that solves the mixing time of Kac's walk on the rotation group; this walk was introduced by Hastings in his seminal paper in 1970 that started the MCMC revolution and is used in statistics, statistical physics, and cryptography, to name a few. Its mixing time has been open for decades. Even just a few months ago, I thought this problem was impossible! This problem has been studied by many people over the last 30 years. The main difficulty was that, as a community, we don't have the tools to study mixing time in continuous state spaces. AI influence was key (GPT 5.4 pro) in our solution: it acted as a Rosetta Stone, translating ideas from another part of probability (Malliavin calculus) to Markov chains, and also pointed out a specific lemma from the literature that makes this translation work! Of course, the hard work was in verification. This also gives a genuinely new tool to study the mixing times of such constrained systems. Very satisfying and grateful to be able to prove this result and be a part of this journey. I am more optimistic than ever about what's possible as the tools continue to get better. arxiv.org/abs/2604.23828

This tape contains Paul Dirac’s lecture (yes, that Paul Dirac, one of the founders of quantum mechanics) at the University of South Carolina. This tape is also legendary; it has been missing for the past 32 years! And guess what: Prof. Frank Avignone found it today!

What a cool calculus test

Now do living tissue! This is among many problems life forms solve in myriad ways.

@DeivonDrago @davidbessis Topology can be a lot of fun. Abstraction by itself doesnt turn me off. Its just that Munkres is very slow going in the first few chapters building up general topology. Zero pedagogy.

@denizkural @davidbessis If you found Munkres problematic, you’d find category theory is much worse.

General topology is like software engineering where everything is dynamically typed and there is no permission control.

@davidbessis I feel like I have PTSD from Munkres as my college intro text. What existing undergrad/grad book would you recommend for algebrwic topology to learn from? (Given that our ideal book looking at AT from a cat viewpoint doesnt yet exist).

By the way, this is why Algebraic Topology books are so tedious and dysfunctional—they are in a constant fight to silence the permissiveness that is seeping through the lower layers. We should kill Algebraic Topology and replaced it by something like Categorical Homotopy Theory.

The worst cancers with respect to lethality get the least federal funding support jamanetwork.com/journals/jaman…

In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets. This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it. [Primitive sets are a vast generalization of the prime numbers: A set S is called primitive if no number in S divides another.] Now Erdős#1196 is an asymptotic version of Erdős' conjecture, for primitive sets of "large" numbers. It was posed in 1966 by the Hungarian legends Paul Erdős, András Sárközy, and Endre Szemerédi. I'd been working on it for many years, and consulted/badgered many experts about it, including my mentors Carl Pomerance and James Maynard. The the proof produced by GPT5.4 Pro was quite surprising, since it rejected the "gambit" that was implicit in all works on the subject since Erdős' original 1935 paper. The idea to pass from analysis to probability was so natural & tempting from a human-conceptual point of view, that it obscured a technical possibility to retain (efficient, yet counter-intuitve) analytic terminology throughout, by use of the von Mangoldt function \Lambda(n). The closest analogy I would give would be that the main openings in chess were well-studied, but AI discovers a new opening line that had been overlooked based on human aesthetics and convention. In fact, the von Mangoldt function itself is celebrated for it's connection to primes and the Riemann zeta function--but its piecewise definition appears to be odd and unmotivated to students seeing it for the first time. By the same token, in Erdős#1196, the von Mangoldt weights seem odd and unmotivated but turn out to cleverly encode a fundamental identity \sum_{q|n}\Lambda(q) = \log n, which is equivalent to unique factorization of n into primes. This is the exact trick that breaks the analytic issues arising in the "usual opening". Moreover, Terry Tao has long suspected that the applications of probability to number theory are unnecessarily complicated and this "trick" might actually clarify the general theory, which would have a broader impact than solving a single conjecture.

Lang's definition of the exponential function is a function 𝑓 such that 𝑓'=𝑓 and 𝑓(0)=1, from this he proves its uniqueness and derives its properties, including the definition of the number 𝑒. His treatment of the sine and cosine is similar.