A Universe of Sorts
ยง Siddharth Bhat
 Laziness for C programmers
 Exact sequence of pointed sets
 What is a syzygy?
 Under the spell of Leibniz's dream
 Normal operators: Decomposition into Hermitian operators
 Readable pointers
 The grassmanian, handwavily
 Lie bracket as linearization of conjugation
 Computational Origami
 Katex in duktape
 Kebab case
 Localization: Introducing epsilons
 NaN punning
 Offline Documentation
 Using Gurobi
 osqp: convex optimizer in 6000 LoC
 stars and bars by generating functions
 This is not a place of honor
 Topological proof of infinitude of primes
 Burnside as space average equals time average
 The Ise Grand shrine
 Edward Kmett's list of useful math
 Cokernel is not sheafy
 Von neumann: foundations of QM
 Discrete schild's ladder
 Derivative of step is dirac delta
 Extended euclidian algorithm
 In a PID, all prime ideals are maximal, geometrically
 Prime numbers as maximal among principal ideals
 Axiom of Choice and Zorn's Lemma
 Local ring in terms of invertibility
 Nullstellensatz for schemes
 Perspectives on Yoneda
 Germs, Stalks, Sheaves of differentiable functions
 Connectedness in terms of continuity
 Intuition for limits in category theory
 Finite topologies and DFS numbering
 Categorical definition of products in painful detail
 Why is the spectrum of a ring called so?
 Ergo proxy
 Satisfied and frustrated equations
 Combinatorial intuition for Fermat's little theorem
 An incorrect derivation of special relativity in 1D
 The geometry and dynamics of magnetic monopoles
 Sanskrit and Sumerian
 Writing Cuneiform
 The code of hammurabi
 The implicit and inverse function theorem
 Whalesong hyperbolic space in detail
 Motivating Djikstra's
 Intuitions for hyperbolic space
 Product of compact spaces in compact
 Hyperbolic groups have solvable word problem
 Elementary uses of Sheaves in complex analysis
 Snake lemma
 Kernel, cokernel, image
 The commutator subgroup
 Simplicity of A5 using PSL(2, 5)
 A5 is not solvable
 Complex orthogonality in terms of projective geometry
 Arithmetic sequences, number of integers in a closed interval
 The arg function, continuity, orientation
 Odd partitions, unique partitions
 Continued fractions, mobius transformations
 Permutationsandlyndonfactorization
 Graphs are preorders
 Crash course on domain theory
 Parallelisable version of maximum sum subarray
 Thoughts on implicit heaps
 Discriminant and Resultant
 Polynomial root finding using QR decomposition
 A hacker's guide to numerical analysis
 Mobius inversion on Incidence Algebras
 Finite differences and Umbral calculus
 Permutahedron
 Lyndon + Christoffel = Convex Hull
 Geometric proof of
e^x >= 1+x
, e^(x) >= 1x
 Ranking and Sorting
 Proof of minkowski convex body theorem
 Burrows Wheeler
 Intuitionstic logic as a Heytig algebra
 Edit distance
 Evolution of bee colonies
 Best practices for array indexing
 Algebraic structure for vector clocks
 Networks are now faster than disks
 Einsteinde Haas effect
 Rankselect as adjunction
 Bounding chains: uniformly sample colorings
 Coupling from the past
 Word problems in Russia and America
 Encoding mathematical hieararchies
 Learning code by hearing it
 Your arm can be a spinor
 Self modifying code for function calls: Look ma, I don't need a stack!
 Adjunctions as advice
 Reversible computation as groups on programs
 Blazing fast math rendering on the web
 VC dimension
 Symplectic version of classical mechanics
 Theorems for free
 How to reason with halfopen intervals
 How does one build a fusion bomb?
 Christoffel symbols, geometrically
 A natural vector space without an explicit basis
 Cache oblivious B trees
 KrohnRhodes decomposition
 Proving block matmul using program analysis
 Why I like algebra over analysis

using
for cleaner function type typedefs  A walkway of lanterns
 Natural transformations
 The hilarious commentary by dinosaure in OCaml git
 How to link against MLIR with CMake
 Energy as triangulaizing state space
 The cutest way to write semidirect products
 My Favourite APLisms
 Proof of chinese remainder theorem on rings
 monic and epic arrows
 The geometry of Lagrange multipliers
 Efficient tree transformations on GPUs
 Things I wish I knew when I was learning APL
 Every ideal that is maximal wrt. being disjoint from a multiplicative subset is prime
 Getting started with APL
 SpaceChem was the best compiler I ever used
 Mnemonic for Kruskal and Prim
 Legendre transform
 Cartesian Trees
 DFS numbers as a monotone map
 Self attention? not really
 Coarse structures
 Matroids for greedy algorithms
 Grokking Zariski
 My preferred version of quicksort
 Geometric proof of Cauchy Schwarz inequality
 Dataflow analysis using Grobner basis
 Fenwick trees and orbits
 Dirichlet inversion
 Incunabulum for the 21st century: Making the J interpreter compile in 2020
 An example of a sequence whose successive terms get closer together but isn't Cauchy (does not converge)
 Krylov subspace method
 Good reference to the Rete pattern matching algorithm
 Leapfrog Integration
 Comparison of forward and reverse mode AD
 An invitation to homology and cohomology, Part 1  Homology
 An invitation to homology and cohomology, Part 2  Cohomology
 Stuff I learnt in 2019
 A motivation for padic analysis
 Line of investigation to build physical intuition for semidirect products
 Topology is really about computation  part 2
 Topology is really about computation  part 1
 PSLQ algorithm: finding integer relations between reals
 Geometric characterization of normal subgroups
 Handy characterization of adding an element into an ideal, proof that maximal ideal is prime
 Radical ideals, nilpotents, and reduced rings
 My disenchantment with abstract interpretation
 Computing equivalent gate sets using grobner bases
 The janus programming language  Time reversible computation

A = B
 A book about proofs of combinatorial closed forms  Generating
k
bitsets of a given length n
:  Bondi kcalculus
 Topology as an object telling us what zerolocus is closed:
 Vivado toolchain craziness
 What the hell is a Grobner basis? Ideals as rewrite systems
 Lie bracket versus torsion
 Blog post: Weekend paper replication of STOKE, the stochastic superoptimizer
 Collapsing
BlockId
, Label
, Unique
:  Spatial partitioning data structures in molecular dynamics
 Vector: Arthur Whitney and text editors
 Representing CPS in LLVM using the
@coro.*
intrinsics  Bug in the LLVM code generator: Lowering of
MO_Add2
and MO_AddWordC
 Discrete random distributions with conditioning in 20 lines of haskell
 Everything you know about word2vec is wrong
 Hamiltonian monte carlo, leapfrog integrators, and sympletic geometry
 Small Haskell MCMC implementation
 The smallest implementation of reverse mode AD (autograd) ever:
 Timings of passes in GHC, and low hanging fruit in the backend:
 Varargs in GHC:
T7160.hs
 Debugging debug info in GHC
 GHC LLVM code generator: Switch to unreachable
 Concurrency in Haskell
 Handy list of differential geometry definitions
 Lazy programs have space leaks, Strict programs have time leaks
 Presburger arithmetic can represent the Collatz Conjecture
 Using compactness to argue about covers
 Japanese Financial Counting system
 Stephen wolfram's live stream

Cleave
as a word has some of the most irregular inflections  McCune's single axiom for group theory

Word2Vec
C code implements gradient descent really weirdly  Arthur Whitney: dense code
 How does one work with arrays in a linear language?
 Linear optimisation is the same as linear feasibility checking
 Quantum computation without complex numbers
 Linguistic fun fact: Comparative Illusion
 Longform posts:
 Big list of emacs gripes
 Big list of Coq
 Big list of writing
 Big list of Latex
 Big list of Architecture
 Big list of Recipes
 Big list of history
 Big list of words
 Big list of Music
 Big list of Social Science