Nick @anisomorphism Twitter profile | Pikagi

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Nick

@anisomorphism

532

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Computing is discrete Hamiltonian dynamics ~ read: ~ check out my writing:

https://t.co/xLwnq83EEg

Joined April 2013

Don't wanna be here? Send us removal request.

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@anisomorphism

Nick

2 years

It's your prerogative, but if someone gives you a good book you ought to take a look and not complain that it's long. If you've understood yourself why a book is good, then you should finish it completely. Good books don't come around often. I need to finish some of my own too!

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@anisomorphism

Nick

6 months

The typical proof of Van Kampen's theorem, computing the fundamental group of a union or pushout of spaces, involves a choice of basepoint and the group theoretic construction of the amalgamated free product. With groupoids, it is merely a result - the structure of the product...

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@anisomorphism

Nick

6 months

@westernunion2k I found the archived post. The very first reply uses the n-word. Classic 4chan.

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Nick

1 month

Jim Simons wasn't just a last advocate of fundamental science in a world that increasingly neglects it, but did more for basic mathematics education than anyone else alive.

@SimonsFdn

Simons Foundation

1 month

It is with great sadness that the Simons Foundation announces the death of its co-founder and chair emeritus, James Harris Simons. Jim was an award-winning mathematician, a legendary investor and a generous philanthropist.

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Nick

4 months

An Einstein quote I learned of from Ronnie Brown's topology book that I rather like:

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@anisomorphism

Nick

4 months

@liq_princess @yashkaf It's difficult for the public and often students too, to distinguish between hardcore differential geometry and math competition stuff - much less useful theoretical physics progress. Lumping it together as 'smart people stuff' makes training difficult.

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@anisomorphism

Nick

4 months

@drmichaellevin No. Mathematics is actually not about its foundations, it's about top-level geometries and algebraic structures that we can reduce to many different foundations for the sake of formality, while conserving the intuitive idea.

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@anisomorphism

Nick

2 months

@black65117 @Ramirezplayer @mathematicsprof @Musingsonmath Books help, most of this stuff doesn't exist in video form:

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The fast track to differential geometry and theoretical physics

sheafification.com

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@anisomorphism

Nick

11 months

@AlexanderRKlotz Knots between surfaces exist in 4d, and in higher dimensions the pattern continues with anything of two dimensions less than the ambient space aka codimension 2.

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@anisomorphism

Nick

1 year

@hollykrieger Every area of mathematics has computational aspects which are interesting things to study on their own, unfortunately not every area emphasizes these equally. That's why books like Olver's applications of lie groups to diff. eqs. are unique, you compute diff geo quantities.

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@anisomorphism

Nick

1 year

@3blue1brown Yes, any binary operation can be visualized this way. Addition in the integers is a graph over a lattice, and in the continuum, kernels of integral operators like the fourier transform, green's functions, are seen as graphs over the plane rather than matrices. Just order the vars

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@anisomorphism

Nick

6 months

Witten is not god, he is a physicist who recognized the massive value of geometric language for the subject. The community's compartmentalization into his god-like status only serves to delay the day understanding this language is common.

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@anisomorphism

Nick

7 months

I have only ever found math competitions alienating. Please offer better opportunities for people who care about the fundamental conceptual parts of mathematics.

@yufeizhao

Yufei Zhao

7 months

Putnam Math Competition at MIT

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@anisomorphism

Nick

2 years

@blueorigin @LockheedMartin @DraperLab @Boeing @astrobotic @Honeybee_Ltd 48/50 US states, sounds like efficient and cost effective engineering.

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@anisomorphism

Nick

4 months

Hardest, most interesting, most important problems goes to theoretical fundamental physics, continuum mechanics, and biology right now. AI is near the bottom of the top 10.

@sama

Sam Altman

4 months

openai is the most talented and nicest group of people i have ever seen in one place working on the hardest, most interesting, and most important problems with all the key resources in place extremely focused on making AGI you should perhaps considering joining us

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Nick

5 months

@RBehiel Did you get a chance to browse Penrose's Spinor books for intuition on the flag stuff?

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@anisomorphism

Nick

6 months

It generalizes to higher dimensions, and higher dimensional homotopy groups. It also requires very little setup, letting you compute invariants of your favorite manifold from minimal knowledge of how it is put together combinatorially

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@anisomorphism

Nick

6 months

These are just the simplest examples, if you want to know how to do this then read Ronnie Brown's books: best intro topology I have ever seen: the higher dimensional stuff:

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@anisomorphism

Nick

6 months

Though basic, the most important computation in algebraic topology is of the fundamental group of the circle. Groupoids give a new perspective on this, defining the circle as a pushout rather than doing analysis and computing lifts. This simple algebra is powerful...

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@anisomorphism

Nick

6 months

The exact opposite is true. Talented people are repeatedly told that interdisciplinary generalists no longer exist and that all important work is done incrementally by large groups. It is quite self-reinforcing.

@Daanniii6

anti-field of the anti-danii field

6 months

The idea of Geniuses/uniquely talented people is not only misleading but extremely harmful for the development of science. The sheer number of students who actively shun learning because they don't believe they're smart enough should embarrass every single educational institution

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@anisomorphism

Nick

5 months

I love tangent bundles and normal bundles and principal frame bundles and Clifford module bundles, spinors bundles, algebraic stable vector bundles, tautological line bundles, Bloch bundles, connections, characteristic classes, prequantum line bundles, symmetric spaces...

@sp_monte_carlo

Sam Power

@sp_monte_carlo

5 months

one personal goal for 2024 is to shed my fear of the various "bundles" which arise in geometry, so that i don't run and hide upon glimpsing the term.

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@anisomorphism

Nick

15 days

@arithmoquine This is not the hard part of tropical algebraic geometry, it's supposed to be easy

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@anisomorphism

Nick

2 months

@AlexKontorovich It's really not. I would not like to self dox, but one of the supposed last good schools for pure mathematics in the US has a corrupt department full of pencil pushers in which the real mathematicians are afraid to speak up. This experience is conserved.

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@anisomorphism

Nick

1 month

He funded mathematicians to become teachers, drastically improving student performance wherever his program was implemented. Math education people on Twitter would have you believe that these people cannot teach mathematics, and that Simons is ignorant on this topic.

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@anisomorphism

Nick

1 month

The reality he proved is simple. Fund more mathematics teachers that actually understand mathematics.

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@anisomorphism

Nick

5 months

At the level of graduate textbooks, most undergraduate studies can be reduced to a few intro chapters in a few books each. Constructing your own path from fundamentals to research level that is coherent and has feedback/practice/projects is the difficult thing, yet to exist.

@St_Rev

St. Rev. Dr. Rev ⏭️☯️🏴😻

5 months

I flipped through some of the math 'courses' and a lot of them are just a few supplemental handouts and exercises to go with a book (book not included) sometimes there are incredibly tedious videos that add no value

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@anisomorphism

Nick

6 months

@unrelynarrative @francoisfleuret @deliprao I am pretty sure he knows what math is

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@anisomorphism

Nick

5 months

The obsession of nonmathematicians with math 55 is a lot like the general obsession with Harvard as a name. Not baseless, but not the strongest signal ever. There is a lot more to mathematics than grinding basic analysis and group theory problems.

@JohnArnoldFndtn

John Arnold

@JohnArnoldFndtn

5 months

Two Harvard Crimson articles, one from 2006 and the other from 2023, describing the legendary Math 55 class showcase how much college has changed in less than a generation. '06: “This is probably the most difficult undergraduate math class in the country,” reads a page on the

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Nick

1 month

This is one of the top 5 important causes to fight for right now. It will move civilization to a new level. Do it in spite of all the corruption and nastiness of the people who would say otherwise.

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@anisomorphism

Nick

1 year

@kilovh And 10 different cultures in just mathematics and physics alone. Bell labs semiconductors, west vs east coast algebraic geometry, New York topos theory, Harvard vs Princeton gauge theory, US quantum field theory/particle physics, Perdue jet engine engineering,...

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@anisomorphism

Nick

1 month

If everyone is done talking about Jim's market exploits, let's read his gauge theory.

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@anisomorphism

Nick

2 months

Totality

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@anisomorphism

Nick

6 months

comes out of the pushout of groupoids, with the objects/points mapped according to the pushout and minimal relations on the arrows. One only needs to show that the assignment of groupoids to spaces preserves the universality of the pushout, which is almost tautological.

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@anisomorphism

Nick

5 months

Don't learn coding, learn something else or make something that needs code. Learning coding only leads you to complicate simple things, because you aren't solving problems.

@engineers_feed

World of Engineering

@engineers_feed

5 months

Coders, how hard is it to learn coding in terms of going from zero knowledge of it to hireable in some way?

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@anisomorphism

Nick

7 months

@solidangles In quantum mechanics, commuting operators/matrices exploit this property, the set of tuples of simultaneous eigenvalues becomes the space where wavefunctions live. This same idea continues to be useful in both numerical and pure geometry applications (e.g. lie group harmonic...

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@anisomorphism

Nick

6 months

Seems it might be possible to do the Stern-Gerlach experiment at home:

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@anisomorphism

Nick

4 months

@StatisticUrban @ModerateIndy You can though, you can still make decent pay doing something actually useful.

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@anisomorphism

Nick

8 months

Artificial gravity stations are an old idea, e.g. proposals from Von Braun. For a long time, politics and high launch costs have made progress in space stall, but with a new superheavy launch vehicle and plummeting costs we should expect to see the first station this decade.

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@ErikWernquist

Erik Wernquist

9 months

I'm happy to have finally completed my new short film - ONE REVOLUTION PER MINUTE. You can see it here:

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@anisomorphism

Nick

11 months

@TivadarDanka It sure would be nice if we offered any other meaningful path in school before the college level. I don't think it would hurt anyone to have students learn differential geometry or class field theory in high school.

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@anisomorphism

Nick

2 months

@Mathgarden The main requirement to be an effective mathematics educator is to know mathematics. Most mathematics education majors do not, hence why basic mathematics education is terrible.

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@anisomorphism

Nick

1 year

The most important mathematician that mathematicians have never heard of is Robert Hermann. During the confusion about QCD he was the one who established that the bundle language of geometers was what physicists needed to talk about the forces in the standard model. He has since-

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@anisomorphism

Nick

1 month

Also per Sternberg's symplectic techniques in physics:

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@anisomorphism

Nick

1 month

@yaazarai That's kinda how it works. Maxwell's equations and the rendering equation are both linear, and the FFT is also linear (by definition).

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@anisomorphism

Nick

2 months

I cannot escape the lingering feeling that I will never get to do anything with physics because I was not well-connected enough

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@anisomorphism

Nick

5 months

@RBehiel I look forward to it! It is not as geometrical, but Gel'fand has an entire book on just the orthogonal and Lorentz representations since he wrote about QM and functional analysis-adjacent topics, if that is also of any use to you.

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Representations of the Rotation and Lorentz Groups and Their Applications

books.google.com

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@anisomorphism

Nick

2 months

I will write anyway

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@anisomorphism

Nick

1 year

Since people are giving book recommendations for the new year, I will prepare by giving a few in advance: 2023: Shilov linear algebra, Landau theoretical physics, Sternberg differential geometry 2024: Shilov, Landau, Sternberg 2025: Shilov, 'Dau, Sternberg 2026: Shilov, Landau...

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@anisomorphism

Nick

5 months

I can outperform Deepmind without AI, watch this:

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@GoogleDeepMind

Google DeepMind

@GoogleDeepMind

5 months

🟠 AI systems have struggled with tough geometry problems due to a lack of training data. We overcome this by generating 100 million synthetic theorems and their solutions across various levels of complexity. AlphaGeometry is trained from scratch entirely on this data.

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@anisomorphism

Nick

4 months

@chris_j_paxton @soft_fox_lad Young people can, in fact, learn.

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@anisomorphism

Nick

10 months

@atgambardella Can accomplish 10x more by studying for just a few hours but from more challenging material. 1 hour is also not enough for cooking and other errands. The rest should be spent going on walks or something.

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@anisomorphism

Nick

3 months

Because components aren't goddamn geometric objects!!! Change of basis matters! Matrices of bilinear forms transform differently than matrices of linear maps!!

@joshuagrochow

Joshua Grochow

3 months

No one defines a matrix as "a thing that transforms like a matrix". Why define tensors that way? Array=numbers in a (possibly high-dim) grid Matrix=array representation of a linear map* in a chosen basis #Tensor =array representation of a multilinear map in a chosen basis 🧵1/10

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Nick

1 month

My favorite viewpoint is unsurprisingly the standard one, that it is an algebraic structure. But introducing it pedagogically takes some preparation. Categories jointly generalize posets, groups, and monoids.

@davidad

davidad 🎇

1 month

alternative definition of category

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@anisomorphism

Nick

8 months

@inannabelian I find it strange that he says "never before studied" but also references Olver's book on geometric PDE theory, and further borrows the terminology of the "never before studied" subject. Jet bundles exist in the first place to formalize classical field theory and its quantization

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@anisomorphism

Nick

19 days

Then you don't understand physics or its history. Antimatter and the spin structure of matter was a purely theoretical prediction by Dirac, and is forced on the theory by the marriage of relativistic and quantum mechanical principles. We could be a couple decades from the answer.

@peterrhague

Peter Hague

19 days

Let me be slightly indelicate; Musk assigns no resources to what you refer to as post-Einstein physics because he realises it’s almost certainly bollocks. You can juggle tensors all you like, but without predictions and experiments that’s just maths, not physics. Musk wants

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Nick

1 month

Mathematical/geometric reasoning arguably does this much better and should take the place of philosophy. We create *new* mathematical structures as signposts to represent a change in how we think about a thing.

@drmichaellevin

Michael Levin

@drmichaellevin

1 month

@philipcball I disagree strongly; thinking in different ways about how to understand deep issues, what kinds of answers we would accept, what "understand" means, which "category errors" reveal stale categories that need dissolving, and other philosophical aspects, have strongly influenced

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@anisomorphism

Nick

6 months

This is exactly why myself and my friends are creating our own paths:

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The optimal path to mathematical mastery

sheafification.com

@wesyang

Wesley Yang

6 months

Many kids have the capacity to learn much more much faster than they would in schools normed for the median student and waste years of their lives being babysat so that the rest of the class can acquire basic skills (that increasingly they aren't acquiring at all anyway)

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@anisomorphism

Nick

4 months

@string575757 @Saraht0n1n Lectures - Schuller's geometric anatomy of theoretical physics

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Lectures on Geometrical Anatomy of Theoretical Physics

www.youtube.com

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@anisomorphism

Nick

6 months

My advice: -Go to college and learn everything in advance by at least a semester -have learned theoretical physics -start a competing replacement institution based on higher mathematical standards and research freedom -spacefaring and immortality

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@anisomorphism

Nick

1 year

@anthrupad Classical Mechanics, polynomial algebra, Differential geometry, General Relativity, De Rham theory, Representation Theory, Kähler Geometry/complex algebraic geometry, Quantum and statistical mechanics, condensed matter physics.

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@anisomorphism

Nick

3 months

@TheDarkOat @GeorgeHenty @JigokuCake @PandasAndVidya There is uranium in seawater! The most out of any natural sources by far!

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@anisomorphism

Nick

1 month

@ShurtugalTCG @DJSnM Fluid mechanics is generally excluded from physics degrees, and handled by mechanical engineering departments.

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@anisomorphism

Nick

3 months

@jerrrrrrryyyyy Ronald Brown's Nonabelian Algebraic Topology is super cool, this guy created his own calculus for building up higher dimensional spaces and calculating their topology. There are relations to standard algebraic topology, but it is quite unique.

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@anisomorphism

Nick

5 months

I want real differential geometry please

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@anisomorphism

Nick

5 months

@cutezu_ I think this would be solved by jumping directly to graduate studies, focusing on the big areas. Too much time in preparation and not actually doing math, which is why proof (and analysis to a lesser degree) courses are so terrible.

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@anisomorphism

Nick

2 months

Got a sunspot

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@anisomorphism

Nick

4 months

Because it doesn't look like that

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@netcapgirl

sophie

4 months

not gonna lie this looks overengineered to hell

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@anisomorphism

Nick

1 year

First draft of a post on computer architecture via polynomial algebras and difference equations:

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@anisomorphism

Nick

1 year

Nothing is ever going to replace mathematics as an organizing force of concepts.

@keenanisalive

Keenan Crane

1 year

My advice to a student on keeping up with trends in geometric computing. #NeRF #stablediffusion

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Nick

9 months

@nofilteronmouth @var_epsilon It is bizarre that we are pushing so many students away from the real world and physics

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@anisomorphism

Nick

4 months

Fukushima is an incredible argument FOR nuclear power. It was contained and killed 0 people. The same cannot be said of any other energy source.

@Unplugnukes

Unplug Nuclear Power

4 months

The Fukushima nuclear disaster 13th anniversary is March 11. Join our boycott of grid power those 24 hours. There's 4 boycott Levels. Nukes have dropped to 9% of electricity. We don't need them. Remember the victims of Fukushima, past, present, and future.

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@anisomorphism

Nick

1 year

Stop confusing geometric algebra with useful mathematics

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@anisomorphism

Nick

9 months

@S_Conradi @corless_rob @matplotlib @numpy_team Looks like shadows of algebraic geometry

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Remarks on eigenvalues and eigenvectors of Hermitian matrices, berry phase, adiabatic connections...

Selecta Mathematica - The singularities of the stratification of the space of the Hermitian matrices according to the multiplicities of the eigenvalues are described as an informal complexification...

link.springer.com

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Nick

7 months

Do all of this *without* the rat race of getting into schools in the first place, because competition problems do not reflect anything in any field.

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@anisomorphism

Nick

7 months

@csaez_math Maybe this one, because of the perspective on tensor geometry.

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Tensor Spaces and Numerical Tensor Calculus

books.google.com

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@anisomorphism

Nick

4 months

@thomasgwong Peter Woit's Quantum Theory, Groups and Representations

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@anisomorphism

Nick

4 months

@sp_monte_carlo Differential forms on manifolds, the natural analog of differentials in higher dimensions, behave like Fermions/supersymmetric particles and even compute topological invariants with their dynamics!

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@anisomorphism

Nick

1 year

not received much credit or recognition for his work, one rumored passing remark by Isadore Singer. Yet there is a lot more to him, he writes about adapting the theory of generalized functions and geometric differential equations to the needs of engineers. His books are a ...

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@anisomorphism

Nick

10 months

@amermathsoc @WestVirginiaU @wvumath Stand against the entire university system, which comprises both of its goals - learning and research- by consolidating power in illiterate administrations that rightfully belongs to professors. It is hard to find any real mathematics dept. because they don't understand the value

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@anisomorphism

Nick

1 year

@Jonathan_Blow As a mathematician, I come away very confused when people say it is useful for ordinary software development. That is not how mathematics works, it is useful for an *individual's* conceptualizations but rarely for work itself. That is ridiculous.

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@anisomorphism

Nick

11 months

@cypherpunkHRH @phalpern He was spectacularly right, quantum field theory has a different theory of interactions than quantum mechanics.

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@anisomorphism

Nick

1 year

I call for a three year moratorium on social media and bad hot takes, as we see the effects of mathematical illiteracy on society and spend that time reading actual mathematics and physics.

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The starter pack to physics and differential geometry.

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@anisomorphism

Nick

10 months

@davidad Almost, but you still cannot forsake geometry and group representations. The reason why those index notations are so good is because of how they treat change of basis.

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@anisomorphism

Nick

8 months

@CJHandmer Online textbooks and professors lecture notes on their websites, access to experiment is an issue however

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Nick

4 months

@drmichaellevin When mathematicians study manifolds or gauge theories or complex algebraic curves, they think of these as basic objects/settings for more constructions and computations.

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Nick

1 year

@Jonathan_Blow The real question is what category theory is good for. Are you solving algebraic problems that category theory helps formulate? If not, it probably holds little relevance for you. Practically, it is a branch of algebra.

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Nick

3 months

because it signals the difference between coordinate calculations with a 'real' underlying object (whether symplectic observables, Riemannian lengths and angles, gauge-theoretic internal states) or mere calculations with no physical meaning bridging to a result.

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@anisomorphism

Nick

6 months

This might seem basic to my mathematical friends, but telescoping expressions are used all the time in group theory and algebraic topology proofs!

@ciphergoth

Paul Crowley ⏸️

6 months

I really regret looking at the answer to this before figuring it out.

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Nick

1 month

It's too bad that the actual content sucks. Still looking for a competent free linear algebra book.

@DanielleFong

Danielle Fong 💁🏻‍♀️🔆🏴‍☠️

1 month

immersive linear algebra The world's first linear algebra book with fully interactive figures. via HN

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Nick

2 years

@HyperboIeva He has two other series, one which has similar content to parts of this one focusing on gravity and electromagnetism, while this one is more generally about geometry, and another on quantum mechanics.

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Nick

1 year

Number theory, Control Systems, Algebraic Geometry, while it is most productive. Don't emulate the applied mathematicians, but hold a dialogue and an interest in the real world. (vol 23)

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@anisomorphism

Nick

7 months

Students are self-studying every area of mathematics and physics to get ahead, Predrag's work is excellent but the time is different now, maybe we can do better for talented kids? Expose them to technology/experiment, theory, computations.

@chaaosbook

Predrag Cvitanović

7 months

Putnam Competition changed my life. I went from Zagreb gymnasium to a small Midwestern college, and, thanks to doing well in Putnam, transferred to MIT. Homework was hell, but the teachers were amazing. Weinberg's lectures were breathtakingly beautiful.

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Nick

14 days

Seriously just learn differential forms, there is no point to this language shuffling. Blame Hestenes' cult.

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@anisomorphism

Nick

2 months

@black65117 @Ramirezplayer @mathematicsprof @Musingsonmath You don't have to read the whole thing, just the books "basic mathematics" by Lang and "calculus" by Apostol get you past most engineering grad students

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@anisomorphism

Nick

7 months

@wingod You don't need classical mechanics to get weird physics. You can use classical fields (EM in between neurons), make them random/noisy, and the resulting SDEs already approximate supersymmetric quantum field theories - a large step beyond just quantum mechanics. And all classical.

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@anisomorphism

Nick

7 months

@83dollaroring another example: "build" has lost its meaning online

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@anisomorphism

Nick

3 months

There is a simple solution/interpretation. The other fields (electromagnetism and so on) took time to catch up. Now they are all geometric via gauge theory but in different ways reflecting their different physical qualities. Geometry is a fundamental tool in physics now ...

@MaxDerakhshani

Maaneli (Max) Derakhshani

@MaxDerakhshani

3 months

Another widespread belief, among the vast majority of physicists (even very famous ones), is that Einstein 'geometrized' gravity or showed that 'gravity is geometry' or that 'gravity is the manifestation of spacetime curvature', etc., and that Einstein actually adhered to these

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@anisomorphism

Nick

6 months

The discussion of collapse, apparent nonlocality of measurement, etc is all irrelevant in this light. Relativity/QFT is where locality is actually enforced as a law, so if you want to think about these problems, work at the right level!

@edfrenkel

Edward Frenkel

6 months

Do "many-world" lovers (and superdeterminists) realize that Schrödinger eq. is NON-RELATIVISTIC? 1st-order time and 2nd-order space derivatives => not invariant under Lorentz transformations! Waive your hands all you want, "wave-function of Universe" is only an approximation.

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@anisomorphism

Nick

1 year

He has also faced challenges in his career in doing the right thing rather than the popular thing. At the time when the popular thing was string theory, he was being withheld from completing his research program to unify with applied mathematicians and do geometric analysis.vol30

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@anisomorphism

Nick

2 years

@johncarlosbaez @dcastelvecchi sometimes you just need a good concept and to not give a fuck (except about developing rigor because rigor is cool when you understand why it's important)

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@anisomorphism

Nick

6 months

How many of you have read Watanabe's Algebraic Geometry and Statistical Learning Theory? Let's elevate the discussion to mathematics.

@JeffLadish

Jeffrey Ladish

6 months

I'm pretty sad about the state of AI discourse right now. I see a lot of movement from object-level discussions of risk to meta-level social discourse on who is talking about risks and why, e.g. "the EAs are trying to do X" "the e/accs are trying to do Y". Overall this sucks...

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@anisomorphism

Nick

2 years

@keenanisalive " Please do not rotate the hexasphere with your mouse unless you are not convinced that there are no hidden pentagons in the design." : D

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@anisomorphism

Nick

1 year

@Francis16833887 I'm not sure it says this, since hyperbolic space is also diffeomorphic

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