Leo's Blog Discussion Mega-Thread

[Stick]

The problem is that Russel doesnt know what die means yet he uses it so confidently

[Leo Gura]

It's a play on words.

[Davino]

Your last post reminded me of:

It has to be taken with the proper context, still is a good general quote.

[Leo Gura]

22 minutes ago, Davino said:

Your last post reminded me of:

It has to be taken with the proper context, still is a good general quote.

That's a great quote. I will use it.

[mmKay]

On 6/16/2026 at 8:32 PM, Yimpa said:

Soften up, buttercup!

 

Thanks for sharing that, very poetic

[Yimpa]

1 minute ago, mmKay said:

Thanks for sharing that, very poetic

No problemo poblano!

[Thought Art]

The blog has become immature, disrespectful and petty. I think it’s time I stop following it, stop posting here and just move on. 
 

Bye bye guys….

[Ero]

Science Lacks Self-Reflection

@Leo Gura I recommend for you to read Henri Poincare's "Science and Hypothesis", specifically Ch. 2

There is an aspect of Mathematics that you have never experienced: the process of crystallizing intuition by self-reflection. 

In that book you will see how Poincaré deconstructs the then-prevailing definition of the real line (\R) as the "bag of all real numbers" by repeatedly reflecting against what "continuity" feels like. That process is what gave birth to "Analysis Situs" or "Topology".  

This process of self-reflection, when done seriously enough, makes me hallucinate - 150-200 ug LSD equivalent. Below is a rendition of my literal hallucinations when I was reflecting on his words for 2 hours -  what "hides" in the Continuum/ Abyss, if only one knew how to reach into it.

There is a reason Plato and Pythagoras called mathematics divine. There's a reason Cantor went mad contemplating infinity. That aspect of it is what lied behind the true genius of Ramanujan or Grothendieck. 

Reflect long enough on any mathematical object and you will materialize it in front of yourself. Mathematics is Hallucination

 

Edited 7 hours ago by Ero

[Leo Gura]

@Ero I don't doubt what you are saying. But what you are saying is not acceptable in today's science/academic system.

My point is simply that science needs to be more open to that kind of method.

[Ero]

1 hour ago, Leo Gura said:

My point is simply that science needs to be more open to that kind of method.

Let me preface by saying that I know this is where your heart is at after a decade of studying your work. That said, feel compelled to pushback on your messaging, because I think your heart gets lost on those reading because of the absolutism/vindictiveness ("weasels", "cogs", etc.). 

1 hour ago, Leo Gura said:

But what you are saying is not acceptable in today's science/academic system.

This is false. In Harvard's math department, about 30% of the people I met were explicitly in agreement with this aspect (they themselves have hallucinated math and actively seek that method) and about 40% implicitly. What do I mean by the latter? 

You will notice in a lot of mathematics "folklore" explicit use of the word "alien (1) (2)", "mystic delirium", "magic", "extra sense", etc. by other mathematicians when they speak of select individuals or mathematical results. And this isn't just metaphors or analogies, if you push them on it, you hear a lot of metaphysical weight behind the "mystic/magic" part of it, even if those people themselves are avid materialists. That is because if you do pure mathematics long enough, it is nearly impossible to come out untouched by this aspect of it.

The reason this isn't explicit or vocalized in lectures or "layman communications" has a social defense mechanism behind it because of the principle of explosion. It is to protect the edifice of mathematics from the Terrence Howard's and the like that have only multiplied in number since the LLMs - we do not yet have an autonomous verification system that would accommodate an "intuitively correct" but formally inconsistent results. Terry Tao has been an avid proponent of this or as my Math PhD friend likes to say - "putting all the schizos to use". 

Mathematics is the most empowering field to any and all people because "social value" is not determined by origin, appearance (had professors in flip flops with after-gym clothes), speech impediments and even neurodivergence - the only thing that matters is "can you prove it". No one is above that, even Terence Tao or Andrew Wiles. 

The increasing autoformalization of Math that I have foreseen for more than 4 years is what I think will push this aspect from folklore between mathematicians to an explicit differentiating factor of the so-called "leaps of intuitions". 

Why did I add so many references and links? Because if you want to push science further, which I know you do, you have to genuinely change the vindictive tone and actually start highlighting the "brilliant spiritual individuals" (who still exist as I have highlighted). Because from reading your blogs or listening to your "deconstructing science series", people who don't know you well enough will get turned off. 

Shun less the ignorant and show more of the magic. This is more laborious but epistemically honest, because it requires due diligence and research to sift through, instead of spit balling to a caricature in your head.  

Edited 5 hours ago by Ero

[Stick]

muhahahahahaha

[Leo Gura]

32 minutes ago, Ero said:

Let me preface by saying that I know this is where your heart is at after a decade of studying your work. That said, feel compelled to pushback on your messaging, because I think your heart gets lost on those reading because of the absolutism/vindictiveness ("weasels", "cogs", etc.). 

This is false. In Harvard's math department, about 30% of the people I met were explicitly in agreement with this aspect (they themselves have hallucinated math and actively seek that method) and about 40% implicitly. What do I mean by the latter? 

You will notice in a lot of mathematics "folklore" explicit use of the word "alien (1) (2)", "mystic delirium", "magic", "extra sense", etc. by other mathematicians when they speak of select individuals or mathematical results. And this isn't just metaphors or analogies, if you push them on it, you hear a lot of metaphysical weight behind the "mystic/magic" part of it, even if those people themselves are avid materialists. That is because if you do pure mathematics long enough, it is nearly impossible to come out untouched by this aspect of it.

The reason this isn't explicit or vocalized in lectures or "layman communications" has a social defense mechanism behind it because of the principle of explosion. It is to protect the edifice of mathematics from the Terrence Howard's and the like that have only multiplied in number since the LLMs - we do not yet have an autonomous verification system that would accommodate an "intuitively correct" but formally inconsistent results. Terry Tao has been an avid proponent of this or as my Math PhD friend likes to say - "putting all the schizos to use". 

Mathematics is the most empowering field to any and all people because "social value" literally do not care about origin, appearance (had professors in flip flops with after-gym clothes), speech impediments and even neurodivergence - the only thing that matters is "can you prove it". No one is above that, even Terence Tao or Andrew Wiles. 

The increasing autoformalization of Math that I have foreseen for more than 4 years is what I think will push this aspect from folklore between mathematicians to an explicit differentiating factor of the so-called "leaps of intuitions". 

Why did I add so many references and links? Because if you want to push science further, which I know you do, you have to genuinely change the vindictive tone and actually start highlighting the "brilliant spiritual individuals" (who still exist as I have highlighted). Because from reading your blogs or listening to your "deconstructing science series", people who don't know you well enough will get turned off. 

Shun less the ignorant and show more of the magic. 

Mystical stuff is career suicide in places like Harvard. Some may do it, but they do so mostly in the shadows.

Math is a special case where how you get it done doesn't matter as long as the proof gets delivered. This can sorta work in math but it cannot work in informal fields like science where stuff is way more messy, murky, and no proofs per se exist.

I am not going after math, I am going after science because they are the ones who invented the "but this is unscientific" defense. "Trust me bro, I know what real science".

With regards to your point about my tone and style, I understand that point and I am experimenting with what tone best to take.

Basically, the ideas I'm presenting are so fucking radical that science will not accept them. So my tone reflects that.

In math you have proofs. In my science what I am saying cannot be formally proven. So what I'm facing is quite different from your math situation.

The notion that if I'm just more polite and nice that science will embrace these ideas is just not how it works. Science will fight these ideas to the death. And yes, science is long overdue for some shaming because they are shameless. Is it ideal to shame scientists? No. But it is deserved given their overall behavior.

I am not just writing dry academic arguments, I am sending the world a passionate wake up call. For better or worse. If I am going to demonized and slandered anyway, I may as well not pull any punches.

Edited 5 hours ago by Leo Gura

[Ero]

39 minutes ago, Leo Gura said:

I am not going after math, I am going after science because they are the ones who invented the "but this is unscientific" defense. "Trust me bro, I know what real science".

In math you have proofs. In my science what I am saying cannot be formally proven. So what I'm facing is quite different from your math situation.

I agree that distinction is relevant, but I do think that there is some serious epistemology to be done in questioning your implicit Cartesian-like dualism between the domains of math and science.

This is a topic for another time and I do plan to do are public-facing write up some time this year on this, but the basic epistemic question is this:

How come the internal logic of the mathematics (i.e. doing math for its own sake) inspired by physics eventually leads back to physics instead of diverging?

Case in point is the following epistemic genealogy:  Newton/Leibniz formalized calculus as means of studying motion; calculus became real analysis after self-reflection on the foundations; real analysis lead to complex analysis because of the failures of those foundations; complex analysis was generalized to Riemann surfaces' which sit at the bedrock of GR, the correct physical generalization of Newtonian mechanics. 

I can give other examples with atoms and numbers/representations, but this one is I believe the most impactful. My thesis is that is a consequence of the fact that "the ontology must peer through", since everything is Consciousness experiencing Consciousness. As such, I believe that the increased mathematization of science is not only natural, it is ontologically necessary as a consequence of my earlier thesis that Mathematics is Hallucination, which is in some sense "less crystallized"/closer to Mind/Awareness than the Hallucination of physical reality.  

39 minutes ago, Leo Gura said:

The notion that if I'm just more polite and nice that science will embrace these ideas is just not how it works. Science will fight these ideas to the death. And yes, science is long overdue for some shaming because they are shameless. Is it ideal to shame scientists? No. But it is deserved given their overall behavior.

I understand where you are coming from, but this is precisely why I used the word "vindictive". I know this is a charged topic for you because of all the mindless "this is unscientific" slop that has been coming your way for years. Of course those don't deserve a soft or meek tone. I have never been on board with the hippie shit. My personal style of communication is probably more "intense" than yours (that's my most frequent descriptor, followed by "crazy"). 

That said, there is a sub-demographic of yours (me included), who are not only spiritual but have discovered their life purpose to be within the math/sciences. Among us nerds, there is an appreciation for all forms of devotion to scientific inquiry, because we resonate with all expressions of Curiosity (Consciousness wanting to Understand itself). I am not saying stop the critique, I am saying show that you care, because otherwise your readers/listeners may implicitly feel conflicted that they have to choose between spirituality and science, which is not something you have ever been a proponent of, but can come of across because of your lack of "appreciation" for the good science.

Simply said, for every 2 or 3 sharp critiques, show a video or a quote of a Michael Levin or a Jacob Lurie or a Michael Atiyah - this not only builds you cred for "knowing", but also shows that you are not alone in your direction, even if your ideas are way more radical.

I would argue those are the ones you should want to impact the most on this topic specifically, because they would go on to challenge the scientific establishment.  

Edited 4 hours ago by Ero

[Leo Gura]

23 minutes ago, Ero said:

I agree that distinction is relevant, but I do think that there is some serious epistemology to be done in questioning your implicit Cartesian-like dualism between the domains of math and science.

I am not suggesting any hard duality there. It is simply that math is 100% a mental game and physical science is the opposite, at least that's how  most scientists treat it.

Math allows for proof and science does not.

But even in math, you can't just say you had some insight, you need to write up some formal proof that others will agree with. If you have some brilliant insight like Ramanujan that you cannot prove, no one is going to take you seriously. By making proofs you are playing that academic science game. You are inventing stuff that can building a consensus, just as scientists do.

I don't know if there are paradigm shattering ideas in math. I guess Cantor's infinities was one of those. But I feel like in math this is much more rare than in science. It is just harder to be closedminded about math as a mathematician than a scientist is closedminded about spiritual matters or ontology.

Quote

How come the internal logic of the mathematics (i.e. doing math for its own sake) inspired by physics eventually leads back to physics instead of diverging?

Math is basically logic and science has many logical aspects to it because the physical world is largely logical.

Don't forget that there is much math that doesn't apply to the physical world. But some of it does. Humans are sorta cherrypicking the math that is useful to them and ignoring the rest.

Quote

I understand where you are coming from, but this is precisely why I used the word "vindictive". I know this is a charged topic for you because of all the mindless "this is unscientific" slop that has been coming your way for years. Of course those don't deserve a soft or meek tone. I have never been on board with the hippie shit. My personal style of communication is probably more "intense" than yours (that's my most frequent descriptor, followed by "crazy"). 

That said, there is a sub-demographic of yours (me included), who are not only spiritual but have discovered their life purpose to be within the math/sciences. Among us nerds, there is an appreciation for all forms of devotion to scientific inquiry, because we resonate with all expressions of Curiosity (Consciousness wanting to Understand itself). I am not saying stop the critique, I am saying show that you care, because otherwise your readers/listeners may implicitly feel conflicted that they have to choose between spirituality and science, which is not something you have ever been a proponent of, but can come of across because of your lack of "appreciation" for the good science.

That is a fair point and I will take it into consideration.

My book is not going to be as combative or harsh as some of my blog posts. The blog posts are more informal. The book will be more suited for converting skeptics without alienating anyone.

Edited 4 hours ago by Leo Gura

[Ero]

26 minutes ago, Leo Gura said:

That is a fair point and I will take it into consideration.

Thank you for your receptiveness.

On the math vs science topic, I carry the burden of proof for elucidating my ideas,  so I will defer this discussion for a separate post when I have crystallized some of the following "prompts"/seeds (writing them down so I can come back to them and address):

Math ≠ Logic

Proofs are not "programs" or "rule games" but paths through "cognitive" space, which extends beyond "human". 

"Math is 100% a mental game" and that is precisely what makes it magical because Reality is but a Game in the Mind of God

Math opens up the multiverse, which is why parts of math do not at all touch the physical world. 

The most paradigm shattering idea in all of math, larger than Cantor (set theory/infinity) or Grothendieck (category theory/toposes) , is 30 years old in its most impactful formulation and is called "Geometric Langlands Program (Vid)", which has been called a "grand unified theory of mathematics" by Edward Frenkel.

Edited 4 hours ago by Ero

[Leo Gura]

41 minutes ago, Ero said:

Proofs are not "programs" or "rule games" but paths through "cognitive" space, which extends beyond "human". 

Okay, but you are using logic in your proofs and thinking. If you think about some topology, you have to think about it logically. Logic is the structure of Reality in a sense. It is not limited to human logic, but much of math is covered by basic human logic.

Edited 3 hours ago by Leo Gura

[zurew]

1 hour ago, Ero said:

How come the internal logic of the mathematics (i.e. doing math for its own sake) inspired by physics eventually leads back to physics instead of diverging?

I think there is an unsatisfying "easy" answer to this under a nominalist/non-platonist/pragmatist view, but im sure you will be able to give very interesting takes under non-nominalist views.

[Ero]

7 minutes ago, Leo Gura said:

Okay, but you are using logic in your proofs and thinking. If you think about some topology, you have to think about it logically. Logic is the structure of Reality in a sense. It is not limited to human logic, but much of math is covered by basic human logic.

From the perspective of HoTT (arguably the most probable future foundations of mathematics) and higher topos theory (the semantics), mathematics exceeds bare formal logic insofar as proofs are not merely external rule-following derivations but internal constructions in structured universes ( e,g. (∞,1)-topoi). Propositions are interpreted as types and equivalences as paths in a universe. 

There are highly nontrivial relations between such universes, including changes of model, base or modalities In this context, formal logic in its usual interpretation is best understood as a 0-truncated reflection of this richer higher-dimensional structure. It forgets nontrivial types, paths, and coherence data, retaining only the flattened propositions and truth values. 

All examples I can think of the failure are pretty technical, but ones that most practicing mathematician experience at different points. 

[Ero]

8 minutes ago, zurew said:

I think there is an unsatisfying "easy" answer to this under a nominalist/non-platonist/pragmatist view, but im sure you will be able to give very interesting takes under non-nominalist views.

@zurew That would be intellectually lazy on my part so you don't have to worry about it. 

1 hour ago, Ero said:

I would argue those are the ones you should want to impact the most on this topic specifically, because they would go on to challenge the scientific establishment.  

@Leo Gura Side note, THE most spiritual people I have met (visions, psychedelics, meditation, maturity, etc), by far, are all vocationally scientific (Math PhD, MD/PhD and History PhD). Could be a selection bias, but also, does ring true since we are the "Mage" class after all. 

[zurew]

21 minutes ago, Ero said:

@zurew That would be intellectually lazy on my part so you don't have to worry about it. 

No, I think your posts are high quality and I dont think that you will take an easy route.

I did not mean to imply that you will create a low quality post.

You are a highly educated and well read guy and you also consume content outside of academia.

I think you will provide a deep, thought provoking post about it.

Edited 2 hours ago by zurew