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• Post #2158810

  I have a lot lined for this summer: 1) An internship on Non-Interactive Tensor Evaluation. 2) Preparing for my undergrad thesis on Type and Category Theory. 3) Studying advanced Analytic Number Theory, Abstract Algebra (especially Galois Theory) 4) My self-supervised work on Cryptanalysis of Legendre-PRF 5) Differential Geometry for General Relativity course next sem. 6) Revising Quantum Mechanics for String theory course next sem. writing all of this down for a little clarity...

• Post #2158808

  I think that if 100-200 years down the line, if some other intelligence is able to develop all the beautiful and elegant mathematical intuitions and instincts like we are, and maybe even "better", though I doubt we can truly objectify this. But yeah, that wont be a deafeat at all. At the end, being awed by all the different ways to perceive numbers is all that matters. I really like Klowden and @tao 's Copernican reframing. Earth is one of seemingly infite planets, and...

• Post #2158807

  ok so the fact that only one identity arrow exists for an object, proves similar fact for all these different instances... trippy but getting there

• Post #2158805

  These typos in this Ramsey Theory text are really messing up with my brain and playing with me ...

• Post #2158802

  If I colour all the edges of a complete graph with n vertices red, then in a way, I "forced" this "Ramsey-situation": \(K(N, p; 2)\)

• Post #2158796

  I just read somethings from Tegmark's book "Life 3.0", and I feel it's quite black and white. Nature does not operate in extremes of only black or only white. In the second version of life, often called “Life 2.0,” we never lost our biological roots. We still sleep, eat, savor food, and follow our urges. So if Life 3.0 is technological, claiming that it will exist purely as silicon is more science fiction than reality. AI models are trained on data generated e...

• Post #2158792

  A follow-up to my previous post on Life 3.0: I want to be clear, I am not predicting where AI will or won't go, how much will be invested in it, or how deeply it will reshape society. That is genuinely uncertain. What I am doing is something narrower: discarding a black-and-white vision. The argument I made works almost like a proof by contradiction. Suppose we grant the most optimistic assumptions, that silicon, hardware, and training data can fully internalize embodied experience, qua...

• Post #2158789

  Ok so the list of integers corresponding to the colors available while coloring $r$-subsets of \(\{1, \cdots, N\}\) also tune the value of \( N \), other words, tune the Ramsey Number.

• Post #2158787

  Completely re-designed my blogging website: https://da1729.github.io/ Never posted about my blogs here, so y'all have never seen the old design. It was very overdone and misaligned. I mostly write about the stuff I study and work on. So math, cryptography and physics. There are some internal references to other blogs that no longer exist. I deleted them because many were half-assed, produced during a short phase when I tried studying just to write blogs, which I quickly realized was a...

• Post #2158784

  I had been ignoring AI security, assuming it was just a modernized version of traditional systems security. Interesting, sure, but not really suited to my patient, math-oriented mindset. But honestly, the security issues in AI don’t revolve around systems and software as much as I expected. There’s an added layer of “psychology,” which is actually quite intriguing. With increasing complexity of agentic AI, at some point a person with better social understanding will be a better AI security exp...

• Post #2158779

  Added a new "theorems" section on my blogging site: https://da1729.github.io/theorems.html for writing proofs of some theorems/lemmas I find interesting. Claude also added this really elite looking dark mode.

• Post #2158777

  RE: https://mathstodon.xyz/@MartinEscardo/116466453766199677 Makes sense.. going to be thinking more about it

• Post #2158774

  RE: https://mathstodon.xyz/@tao/116477356329813670 Intersting... this analogy implies proof writing might become more of a hobby or perhaps a recreational ritual similar to gardening, garden farming and hunting. I have this whole theory of humans always finding out new ways to condense and compress their knowledge gathered. Like how we invented writing and books, which was followed by computers and high density storage devices. Now that we have advanced just enough, and all the proof writing...

• Post #2158773

  I just encountered this really interesting hypothesis. Over the course of evolution, our digestive system initially increased in size but later shrank. It is theorized that humans began offloading some of the digestive workload to external processes, such as using fire to cook food and break down starches. Similarly, while human brains increased in size over much of our evolutionary history, there is evidence they may now be shrinking. My theory is that we have begun outsourcing some cognitiv...