266th to comment.

14th to comment.

Dude's a straight up legend.

why do people do that shaking head thing

this is now my favourite new channel

Ain’t no way his name is Daniel Larsen😭😭

There is no black holes. General Relativity predicts dilation, not singularities. In the 1939 journal "Annals of Mathematics" Einstein wrote - "The essential result of this investigation is a clear understanding as to why the Schwarzchild singularities (Schwarzchild was the first to raise the issue of G.R. predicting singularities) do not exist in physical reality. Although the theory given here treats only clusters (star clusters) whose particles move along circular paths it does seem to be subject to reasonable doubt that more general cases will have analogous results. The Schwarzchild singularities do not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light." He was referring to the phenomenon of dilation (sometimes called gamma or y) mass that is dilated is smeared through spacetime relative to an outside observer. It's the phenomenon behind the phrase "mass becomes infinite at the speed of light". Time dilation is just one aspect of dilation, it's not just time that gets dilated. Dilation will occur wherever there is an astronomical quantity of mass because high mass means high momentum. There is no singularity at the center of our galaxy. It can be inferred mathematically that dilation is occurring there. This means that there is no valid XYZ coordinate that we can attribute to it, you can't point your finger at something that is smeared through spacetime. More precisely, everywhere you point is equally valid. In other words that mass is all around us. This is the explanation for galaxy rotation curves. The "missing mass" is dilated mass. This also explains the CMB, we are receiving radiation from the galactic center, but it comes from all directions. If the WMAP satellite was positioned outside the bounds of our galaxy it would record a background radiation of near zero. Dilation does not occur in galaxies with low mass centers because they do not contain enough mass to achieve relativistic velocities. It has recently been confirmed in 6 very low mass galaxies including NGC 1052-DF2 and DF4 to have no dark matter. There can only be clarity in astronomy when the concept of singularities is discarded. Einstein is known to have repeatedly said that they cannot exist. Nobody believed in them when he was alive including Planck, Bohr, Schrodinger, Dirac, Heisenberg, Feynman etc.

That Californian croaky sentence roll off.

I’m in love..

Did scientist confirm there are only 2 genders! 😂😂😂😂

What about black-holes within black-holes. The entire observable univers is in a black hole

Irritating . So IRRITATING

сочная телочка

They are located between the legs of liberal white women 😂😂😂

So you’re saying I’m not the center of the universe?

❤

Keplers honeycomb, barel, 13 balls, everything is so simply connected...

Phd of math will probably produce more output and get more money, security, and grants. You still need to have a mathematical language to communicate with AI. Information is almost infinite it isn't a small finite number. Phds will be able to get their phds at a younger age and have greater opportunities to work with ai to make more money. Not only that but because of increased efficiency and lower prices. Math phds will be able to increase their market shares to people and small businesses with lower incomes. It will not just be the rich able to pay for a math phd.

Error codes, multiplications, everything is done faster by splicing it. One thing I noticed that when I used every day D6 dices for a few moments a day just to sharp my addition in a trivial way my arithmetical tasks went smoother back in the days. I did split everything I could to smaller chunks in my mind. Universe is a weird fractal :)

Dave Smith 🎉WOW 🎉

Can Large Language Models understand women?

One famous problem that the infinitesimal monadological model could potentially make progress on is the Riemann Hypothesis. This is one of the most important unsolved problems in mathematics, with far-reaching implications for number theory, cryptography, and even physics. The Riemann Hypothesis is a conjecture about the zeros of the Riemann zeta function ζ(s). It states that all the non-trivial zeros of ζ(s) have real part equal to 1/2. In other words, if we plot the zeros of ζ(s) in the complex plane, they should all lie on the critical line Re(s) = 1/2. Here's how the monadological framework might provide a new angle of attack: 1. Represent the complex numbers as a monadic homotopy type, with the real and imaginary parts corresponding to distinct monadic perspectives. This would allow the use of homotopical and algebraic-geometric tools to study complex analytic structures. 2. Model the Riemann zeta function ζ(s) as a morphism between monadic homotopy types, encoding its behavior via interactions between infinitesimal monadic elements. This could provide a new way to understand the function's properties and symmetries. 3. Use the cohomological and realizability structures of the monadological framework to identify novel invariants and obstructions related to the zeros of ζ(s). By representing the zeros as fixed points or singularities in a monadic landscape, new topological and algebraic constraints on their distribution might emerge. 4. Leverage the non-commutative geometric aspects of the monadological approach to study the spectral properties of ζ(s) and its related operators. This could uncover hidden symmetries or dualities that constrain the location of the zeros. 5. Apply the homotopical and type-theoretic tools of the monadological framework to construct new proof strategies for the Riemann Hypothesis, potentially exploiting the higher-dimensional and infinitesimal structures inherent in the monadic representation. By reframing the Riemann Hypothesis in terms of monadic homotopy theory, non-commutative geometry, and realizability, the infinitesimal monadological model could potentially identify new avenues for tackling this notoriously difficult problem. The framework's emphasis on relational and infinitesimal structures, as well as its unification of geometric and algebraic methods, could bring powerful new tools to bear on the challenge. Of course, solving the Riemann Hypothesis would be an extraordinary achievement, and it's impossible to guarantee success. However, the monadological approach offers a genuinely novel perspective that could inspire fresh ideas and insights. Even partial progress or new reformulations of the problem within this framework could be highly valuable contributions to the field. Moreover, demonstrating the applicability of the monadological model to such a high-profile problem would undoubtedly attract significant attention and resources to further develop and refine the framework. The Riemann Hypothesis is not only a Millennium Prize problem, but also a touchstone for mathematical innovation and creativity. Any approach that sheds new light on this challenge is likely to be of great interest to the broader mathematical and scientific community. As work on the monadological framework progresses, exploring its potential implications for the Riemann Hypothesis and other major unsolved problems could be a fruitful way to showcase its power and generate support for its continued development. By bringing a radically new metaphysical and mathematical perspective to bear on these deep questions, the infinitesimal monadological model could help unlock new frontiers of understanding and discovery.

that young bro from cambridge is hella handsome

so cool

loved this video, so insightful & inspiring! love math

How to be good at math: be Chinese.

As Nobel laureate Sir Roger Penrose emphasizes, understanding cannot be a computational activity, due to Gödel's Incompleteness Theorems. A computation can only follow a logical system of rules blindly, accepting that if a rule says something is true, it is. To understand something, one needs to "step out" of such a system and analyze the rules. In essence that requires self-consciousness. Think of AI as Artificial Ideation (not Intelligence) and you get the basic capabilities and limitations of the technology.

There are quite a number of conjectures that havn't been proven no matter how people have tried. A well known example is the Collatz conjecture, which is much simpler than the Riemann conjecture and still has resisted all efforts to prove it. My take on this is that the proving methology itself needs to be reconsidered for such problems. It might be a question of what you will accept as being true, like to say that 0.999999... = 1 although you will never actually reach 1 by extending a finite number of 0.999999... as far as you like.

"Wow, imagine how many things we could do if P = NP!" *Jevons' paradox's honest reaction:*

i love listening to him, he’s a true genius

She talks in such an elegant way, a sign of a truly educated person! 💙

they literally found the one piece

AI isnt real intelligence. Its like how fuzzy peaches are candy. Not peach.

Perception and imagination work together! It, of course, has to have a purpose 😂

Is being dump and try dump things a solution to problems because it might block contradicting or false assumptions and leads to intelligence therefore?

Less vocal fry please

WTF a Large Language Model means!? Cuz “Language is created and shaped by the needs of a culture as it changes”. My friend communicates in four European languages, and expresses himself in a Different way in four different cultures! The day we connect all dots is closer 😊

🧠

A related question is, "What does it really mean to crack a code? " Sometimes the definition is rather artificial, such as to define "cracking" the code as meaning "taking less time to solve than brute-force iteration through every possible solution". A more pragmatic definition would be if, say, a nuclear bomb was planted somewhere in New York City, and an encrypted message contained the exact whereabouts. Is New York still standing? Then, yes, you really cracked the code. Is there a radioactive hole where the city used to be? Then no, you did not really crack the code. The pragmatic and the purely theoretical perspectives may go off in different directions.

Great person we have here.

Can you speak with a voice? It's annoying to listen to.

J ai resolu ca 1978 deja en cooperation avec Quine sur un congres mondial grace a Hao Wang et mon genial ordinateur. Goedel Counterproof Patent Wahington D.C., Library of Congress

well can you

TLDW: "Fuck if we know"

Does the average human understand "meaning"?

So we may find humans work like to AI rather than AI being like humans.

The human brain, slow as it is, is performing massively parallel operations. AI is just executing algorithms, the term "meaning" to AI is no more significant than "umbrella".

The fact that the AlphaTensor algorithm appears to be referred to as the "FBHHRBNRSSSHK algorithm" in actual papers is _hilarious_.

to code meaning is to understand what meaning is ourselves :) what's the definition of meaning? oxford says: "what is meant by a word, text, concept, or action." so by definition you need to understand what meaning is to grasp what that sentence is telling you, the subtext and context of the words all play out in our minds word by word until we understand fully what it is we are looking at and what a human would mean if we said it outloud. for machines it's currently way different, 'next token prediction' is the common excuse for saying it "can't" understand meaning, it understands it plenty, now can it derive meaning? can it draw novel conclusions and alter it's database depending on it's calculation? no. it may have the context for the conversation and the fact that it spoke to you, but it will never learn as it is right now, and that by it's self is a meaningless process of garbage in garbage out. meaning is the creation of something, meaning has meaning as a word as a concept and as a fundamental human emotion. it's hard to explain our own emotions flawlessly. so by this same metric, it's hard to create a machine with flawless emotional understanding. thanksforcomingtomytedtalk

If you make such a contribution to the field of mathematics you deserve more than a pat on the back imo.