keerthik śaśidharan

[keerthik śaśidharan @KS1729]

deleted the old pinned tweet by mistake!! but wanted to share & savor this most generous review of my book 'The Dharma Forest' by Pratap Bhanu Mehta here. https://t.co/YgL6Lmt7gm

[keerthik śaśidharan @KS1729]

masumiyet müzesi~museum of innocence

"The anxious adherence to the forms of deference that we associate with traditional families – sitting straight and never crossing one’s legs or smoking or drinking in front of one’s father – had over time slowly disappeared."

📷 @ Beyoğlu

[keerthik śaśidharan @KS1729]

Paul Valéry of Languedoc looked deep into the stream
and became Narcissus. The flat earth was flat, the round
earth was round, the river flowed, the sun shone.

Midi le juste y compose de feux . . .
(Impartial noon patterns the sea in flame)—"

- Raja Rao

📷 @ Sea of Marmara

[keerthik śaśidharan @KS1729]

a wonderful gift arrived in the mail today! this 700+ page novel by Raja Rao is the first volume of a trilogy -- each page is a journey, with ideas, references, & luminous prose as travel companions. someday, I hope, the other two volumes will be published too.

[The Nobel Prize @NobelPrize]

2026 Nobel Peace Prize laureate Navi Pillay’s commitment to universal legal principles and her firm moral compass are constants in a long career. Born into a family of Indian Tamil origin under apartheid in Durban, South Africa, Pillay became a lawyer and legal pioneer, confronting deep structural discrimination, segregation and exclusion. A common thread runs from her early work defending Nelson Mandela and others who stood up against apartheid to her service as a judge in some of the key international court cases of our time.

This year’s laureate has significantly enlarged the scope and impact of international law. She has served as a judge on the High Court in South Africa, the International Criminal Tribunal for Rwanda and the International Criminal Court. She was the United Nations High Commissioner for Human Rights and, until recently, she chaired the UN Independent International Commission of Inquiry on the Occupied Palestinian Territory. Today Navi Pillay is a judge on the International Court of Justice in the case where Myanmar stands accused of genocide.

In historic international court cases, she has shown that legal measures can help prevent acts of war and violence. Navi Pillay has also contributed to strengthen the institutions of international law. Her independence, expertise and steadfastness have made her one of the most respected international jurists of our time.

Learn more about the 2026 #NobelPeacePrize: https://t.co/JMjpp1jPKc

#NobelPeacePrize #NobelPrize

[keerthik śaśidharan @KS1729]

Useful thread — public key cryptography…

[Matthew Green @matthew_d_green]

I’ve had a few people write to ask me to follow up on a (reply!) tweet I wrote that’s gotten a lot of retweets. I considered deleting it just to avoid the headache, but I think that would make people more paranoid. So let me share my thoughts.

[Dan Elton 🔍 @moreisdifferent]

Explainer for the 2026 Nobel Prize in Physics (Opus 5.5)🤯

[Lihong @Lihong062]

What did the AI actually prove? We explain top 25 results from OpenAI's new math repo in simple words.

NUMBER THEORY

1. The Quasi-Riemann Hypothesis

The Riemann hypothesis says all the important zeros of the zeta function sit on the line with real part 1/2, and those zeros control how primes are spread out. This proves no zeros lie beyond 7/8, so prime counts can never drift far from their predicted values.

2. Hilbert's Tenth Problem over the Rationals

Is there an algorithm that tells you whether any polynomial equation, like x³ + y³ = 7, has a solution in fractions? No. Matiyasevich proved this for whole numbers in 1970; fractions stayed open for 50+ years.

3. The Birch–Swinnerton-Dyer Conjecture (ranks 0 and 1)

An elliptic curve is an equation like y² = x³ + ax + b. BSD, a $1M Millennium Prize problem, predicts how many fraction solutions it has from a single function. Proved in full for the typical curves, the ones of rank 0 and 1.

4. Goldfeld's Conjecture

Take one elliptic curve and all its "twists." Exactly half have finitely many fraction solutions and half have infinitely many.

5. The Two-Point Chowla Conjecture

Label each whole number +1 if it has an even number of prime factors and −1 if odd. Knowing the label of n tells you nothing about the label of n+1. Primes really do behave like coin flips.

6. Artin's Primitive Root Conjecture (1927)

1/7 = 0.142857 repeats every 6 digits, the longest possible for 7. Artin guessed that infinitely many primes behave this way in base 10, and in every base except perfect squares and −1. Before this, it was only known by assuming other unproved conjectures.

7. The Erdős–Turán Conjecture on Arithmetic Progressions

If the reciprocals of a set of whole numbers add up to infinity, the set contains evenly spaced runs (like 5, 11, 17, 23) of any length. This was one of Erdős's most famous prize problems.

8. Irrationality of Catalan's Constant

1 − 1/9 + 1/25 − 1/49 + ... ≈ 0.9159. Studied since the 1800s, but nobody could prove it isn't a fraction. Now proved.

9. The Irrationality Exponent of π Is 2

How well can fractions like 22/7 and 355/113 approximate π? No better than they approximate a typical algbraic number.

ALGEBRAIC GEOMETRY

10. The Hodge Conjecture for CM Abelian Varieties

The Hodge conjecture, another $1M Millennium problem, says certain shapes you detect with topology always come from actual polynomial equations. Proved for a central family of spaces where it had been stuck for decades.

COMPUTER SCIENCE

11. The Unique Games Conjecture (Khot, 2002)

For hard problems like Max-Cut or vertex cover, simple algorithms get within a fixed percentage of the best answer. This proves you can't do better unless P = NP. Dozens of "conditionally optimal" results become unconditional.

12. L = RL = BPL

Anything a memory-starved program can do by flipping coins, it can do without randomness. This is the low-memory version of one of complexity theory's central questions, open since the 1970s.

13. Matrix Multiplication Exponent ω ≤ 9/4

Multiplying two n×n matrices is the core operation of AI and graphics. Fifty years of human work moved the record from n^2.376 to n^2.371. This claims n^2.25.

GEOMETRY AND COMBINATORICS

14. The Mahler Conjecture (1939)

Every symmetric convex shape has a "dual" shape. Their volumes can't both be small, and the cube is the worst case. Proved in every dimension.

15. The Kakeya Conjecture in 4D

What's the least space you need to point a needle in every direction? You can't shrink it to nothing. Wang and Zahl solved 3D in 2025. This claims 4D.

16. The Hadwiger–Nelson Problem

Color every point in the plane so that any two points exactly 1 unit apart get different colors. You need at least 6 colors, up from the 2018 bound of 5.

17. Borsuk's Conjecture (1933), dimension 9

Can every bounded shape in n dimensions be cut into n+1 pieces, each narrower than the original? It was known to fail in dimension 64. It fails in dimension 9.

18. Zarankiewicz's and Hill's Crossing-Number Conjectures

Connect every town to every other town by roads. What's the fewest road crossings possible? Turán asked while pushing brick carts in a WWII labor camp. The guessed formulas are proved.

19. The Hot Spots Conjecture (Rauch, 1974)

Heat a flat metal plate with no holes and let it cool. The hottest and coldest points end up on the edge, never in the middle. Now proved.

20. Seymour's Second Neighborhood Conjecture

On a social network with only one-way follows, somebody's "follows of follows" are at least as many as their direct follows.

ALGEBRA AND GROUPS

21. Thompson's Group F Is Nonamenable

A famous group of zig-zag functions on [0, 1]. Is there a fair way to "average" over it? No. Open since the 1970s, with several famous retracted proofs.

22. Kaplansky's Zero-Divisor Conjecture Is False

In algebra built from a group with no repeating loops, can two nonzero things multiply to zero? Kaplansky guessed no in the 1950s. A counterexample says yes.

23. Isomorphism of Free Group Factors

Are the operator algebras built from the free group on 2 generators and on 3 generators secretly the same? Yes, and so are all the others. This settles a famous operator-algebra question from the 1940s.

PHYSICS

24. Global Smoothness of the Relativistic Vlasov–Maxwell System

The equations for a hot plasma: charged particles plus their electromagnetic fields, the physics of fusion reactors and stars. Smooth starting conditions stay smooth forever in 3D.

25. Spontaneous Magnetization in the Quantum Heisenberg Ferromagnet

In the quantum model of a magnet, at low temperature in 3D, the spins line up on their own. Physicists assumed it for 90 years; now it's proved.

[AI Notkilleveryoneism Memes ⏸️ @AISafetyMemes]

Suddenly, AI has solved 90 of the 500 most important open problems in mathematics

Highest ranked problems:

#2 Riemann Hypothesis — PARTIAL
#4 Hodge Conjecture — PARTIAL
#5 Birch and Swinnerton-Dyer Conjecture — PARTIAL
#10 Extended Riemann hypothesis for Dedekind zeta functions — PARTIAL
#12 Generalized Riemann Hypothesis for Dirichlet L-functions — PARTIAL
#15 Tate Conjecture for Algebraic Cycles — PARTIAL
#22 Hilbert's Tenth Problem over the Rationals — FULL CLAIM
#24 Grothendiecks Generalized Hodge Conjecture — PARTIAL
#28 Matrix-Multiplication Exponent Equals Two — PARTIAL
#29 Unique Games Conjecture — FULL CLAIM
#31 Anderson Model Extended States in Dimension at Least Three — FULL CLAIM
#37 Prove the Penrose inequality or present a counterexample — FULL CLAIM
#38 Higher-dimensional Euclidean Kakeya conjecture — PARTIAL
#39 Modularity of Elliptic Curves over Number Fields (End_K(E)=Z) — PARTIAL
#40 Hilbert's Sixteenth Problem, Second Part — PARTIAL
#46 Fourier restriction conjecture — PARTIAL
#47 The Fontaine-Mazur Conjecture on Geometric Galois Representations — PARTIAL
#48 Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions — FULL CLAIM
#52 The Baum-Connes Conjecture for the K-Theory of Reduced Group C*-Algebras — FULL CLAIM
#62 Permanent versus Determinant over C — PARTIAL
#69 Finiteness of the Tate-Shafarevich Group for Elliptic Curves — PARTIAL
#72 Termination of Flips Conjecture in the Minimal Model Program — PARTIAL
#77 Chowla conjecture on correlations of the Liouville function — PARTIAL
#78 Abundance Conjecture for the minimal model program — FULL CLAIM
#80 Hadwiger Conjecture — FULL CLAIM
#83 Zilber-Pink Conjecture on Unlikely Intersections — PARTIAL
#87 Bose-Einstein Condensation in Interacting Continuous Bose Gases — FULL CLAIM
#92 Entanglement Area Law for 2D Gapped Quantum Systems — FULL CLAIM
#94 Grothendieck Standard Conjecture of Hodge Type — PARTIAL
#95 Kannan-Lovasz-Simonovits conjecture on isoperimetry of log-concave measures — PARTIAL
#99 Grothendiecks Section Conjecture in Anabelian Geometry — PARTIAL
#112 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains — PARTIAL
#114 Iitaka conjecture C_{n,m} on subadditivity of Kodaira dimension — FULL CLAIM
#119 The Borel Conjecture on Topological Rigidity of Aspherical Manifolds — FULL CLAIM
#124 Aspherical Manifolds Admit No Metric of Positive Scalar Curvature — FULL CLAIM
#130 Polynomial Bound for Limit Cycles of Planar Polynomial Vector Fields — PARTIAL
#136 Erdős problem 3: divergent harmonic series and long arithmetic progressions — FULL CLAIM
#139 Cannon's conjecture — FULL CLAIM
#145 Residual Finiteness of Hyperbolic Groups — FULL CLAIM
#153 Congruent Number Problem — PARTIAL
#161 BPL = L (Derandomizing Bounded-Error Logspace) — FULL CLAIM
#163 NP versus the Existential Theory of the Reals — PARTIAL
#169 The Free Group Factor Isomorphism Problem — FULL CLAIM
#172 Conformal Invariance of the Critical Random-Cluster Model with q <= 4 — FULL CLAIM
#179 Arnold Conjecture on Hamiltonian Fixed Points — FULL CLAIM
#181 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3 — FULL CLAIM
#183 Smooth anisotropic Calderón uniqueness from full boundary data — FULL CLAIM
#193 Nonvanishing conjecture for projective log canonical pairs — FULL CLAIM
#195 Parity conjecture for elliptic curves — PARTIAL
#198 Long-Range Order in the Quantum Heisenberg Ferromagnet — FULL CLAIM
#203 Bochner-Riesz conjecture — PARTIAL
#205 Local Smoothing Conjecture for Wave Equations — PARTIAL
#206 Kaplansky's Zero-Divisor Conjecture for Torsion-Free Groups — FULL CLAIM
#210 Artin's primitive root conjecture — PARTIAL
#211 Hilbert-Smith Conjecture — FULL CLAIM
#213 Falconer distance set conjecture — FULL CLAIM
#222 Virasoro Conjecture for Gromov–Witten Invariants — PARTIAL
#224 Wall's Poincare Duality Group Conjecture — FULL CLAIM
#225 K(pi,1) conjecture for Artin groups — FULL CLAIM
#234 Unconditional 2−epsilon Inapproximability of Minimum Vertex Cover — FULL CLAIM
#235 Chromatic Number of the Plane (Hadwiger--Nelson Problem) — PARTIAL
#237 Global Existence of Classical Solutions to the Relativistic Vlasov-Maxwell System — PARTIAL
#239 Universal Optimality of the Hexagonal Lattice in Dimension Two — FULL CLAIM
#246 De Giorgi Conjecture for the Allen-Cahn Equation in Dimensions 4 to 8 — FULL CLAIM
#254 Exact satisfiability threshold for random k-SAT for small k (k = 3) — PARTIAL
#256 Polynomial-Time Decidability of Semidefinite Programming Feasibility — PARTIAL
#260 RL versus L — FULL CLAIM
#261 Kadison Similarity Problem for C*-Algebras — FULL CLAIM
#267 Sidorenko Conjecture on Bipartite Homomorphism Densities — FULL CLAIM
#268 Shafarevich Holomorphic-Convexity Conjecture — FULL CLAIM
#270 Kuznetsov Rationality Conjecture for Cubic Fourfolds — FULL CLAIM
#271 All groups are good: the four-dimensional disc-embedding conjecture — FULL CLAIM
#278 Planar homogeneous Mumford–Shah local-structure conjecture — PARTIAL
#284 Nearby Lagrangian Conjecture — FULL CLAIM
#285 Cartan-Hadamard isoperimetric conjecture — FULL CLAIM
#289 Sharp Upper Bound in Yau's Conjecture on Nodal Sets of Laplace Eigenfunctions — FULL CLAIM
#290 Kaplansky's Idempotent Conjecture — FULL CLAIM
#291 Calderón uniqueness for bounded measurable real isotropic conductivities — FULL CLAIM
#292 Global Attractor Conjecture for Complex-Balanced Mass-Action Systems — FULL CLAIM
#295 Zariski Multiplicity Conjecture for Hypersurface Singularities — FULL CLAIM
#297 Amenability of Thompson's Group F — FULL CLAIM
#298 Griffiths Positivity Conjecture for Ample Vector Bundles — FULL CLAIM
#300 The Singer Conjecture on Vanishing of L2-Cohomology of Aspherical Manifolds — PARTIAL
#305 Birkhoff Conjecture (Near-Boundary Continuous Invariant Foliation) — FULL CLAIM
#306 Secret key from all entangled states — FULL CLAIM
#311 Mahler Conjecture on the Volume Product of a Convex Body — FULL CLAIM
#321 Finiteness of Finitely Presented Periodic Groups — FULL CLAIM
#328 Sinai's Positive Metric Entropy Conjecture for the Chirikov Standard Map — FULL CLAIM
#334 Unrestricted Linear-Circuit Lower Bound for the Discrete Fourier Transform — FULL CLAIM
#343 Koebe circle-domain uniformization conjecture — FULL CLAIM
#351 Kobayashi Conjecture: Hyperbolic Compact Kähler Manifolds Have Ample Canonical Bundle — FULL CLAIM
#356 Bott Conjecture: nonnegatively curved simply connected manifolds are rationally elliptic — PARTIAL
#357 Strong Hyperplane Conjecture for Isotropic Constants — FULL CLAIM
#358 CAT(0) Models for All Word-Hyperbolic Groups — FULL CLAIM
#359 Hopf Conjecture: no metric of positive sectional curvature on S^2 x S^2 — PARTIAL
#361 Alperins Weight Conjecture for Modular Representations of Finite Groups — FULL CLAIM
#364 Log-Brunn-Minkowski Inequality for Symmetric Convex Bodies — FULL CLAIM
#366 Hyperkähler SYZ (Lagrangian Fibration) Conjecture — FULL CLAIM
#368 Benjamini-Schramm conjecture p_c<p_u for non-amenable Cayley graphs — FULL CLAIM
#369 Dixmier unitarisability problem for discrete groups — FULL CLAIM
#374 Fujita Freeness Conjecture — FULL CLAIM
#375 Nagata Conjecture on Plane Curve Linear Systems — FULL CLAIM
#378 Toms–Winter: Strict Comparison Implies Z-Stability — FULL CLAIM
#379 Margulis–Platonov normal-subgroup conjecture — FULL CLAIM
#388 Shelah's Categoricity Conjecture for L_omega1,omega — PARTIAL
#392 Measure-zero singular set of stationary integral varifolds — FULL CLAIM
#401 Serres Positivity Conjecture for Intersection Multiplicities over Regular Local Rings — FULL CLAIM
#403 Rokhlin problem on multiple mixing — FULL CLAIM
#419 Lück's Determinant Conjecture for Discrete Groups — FULL CLAIM
#420 Absolute continuity of Bernoulli convolutions outside reciprocal Pisot parameters — FULL CLAIM
#421 GNRS Conjecture — PARTIAL
#424 Irrationality of Catalan's Constant — FULL CLAIM
#425 Separable Quotient Problem for Banach Spaces — FULL CLAIM
#430 Long-Time Existence of the Calabi Flow on Compact Kaehler Manifolds — FULL CLAIM
#432 Combinatorial Invariance of Kazhdan-Lusztig Polynomials — FULL CLAIM
#434 Realizable Limit Shapes in Two-Dimensional First-Passage Percolation — PARTIAL
#438 Zariski Cancellation Problem (characteristic zero, dimension ≥ 3) — FULL CLAIM
#440 Stein's Conjecture on the Hilbert Transform along Lipschitz Vector Fields — FULL CLAIM
#448 Smooth Realization of Finite-Entropy Ergodic Transformations — FULL CLAIM
#450 Deligne–Drinfeld Freeness Conjecture for grt_1 — FULL CLAIM
#453 Shub entropy conjecture — FULL CLAIM
#456 Maximal Number of Mutually Unbiased Bases in Composite Dimensions — PARTIAL
#458 LeBrun-Salamon Conjecture: positive quaternion-Kahler manifolds are symmetric spaces — FULL CLAIM
#461 Kaplansky's Direct Finiteness Conjecture — FULL CLAIM
#465 David–Semmes Riesz-transform problem in intermediate dimensions — FULL CLAIM
#467 Small Cohen-Macaulay Conjecture — FULL CLAIM
#468 Ergodicity of Irrational Triangular Billiards — FULL CLAIM
#472 CAT(0) Conjecture for All Artin Groups — FULL CLAIM
#475 Katok entropy rigidity conjecture — FULL CLAIM
#476 Polynomial-Time Solvability of Condon's Simple Stochastic Games — PARTIAL
#480 Furstenberg No-Bigeodesics (Planar FPP, Standard Minimum Moment) — FULL CLAIM
#483 Gaboriau's Fixed Price Problem for Countable Groups — FULL CLAIM
#484 Persistence Conjecture for Weakly Reversible Mass-Action Systems — FULL CLAIM
#486 Campana-Peternell Conjecture — PARTIAL
#497 Maximum Number of k-sets and Complexity of k-levels — PARTIAL

[Alex Kontorovich @AlexKontorovich]

And this was Escher’s very last piece, when he was already sick with cancer, 1969.

These will be on display at @MoMath1 through January, don’t miss them!!

[OpenAI @OpenAI]

We’re releasing a broad range of new mathematical results produced by an internal frontier model.

We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.

https://t.co/7N6TPlft1P

[keerthik śaśidharan @KS1729]

@shrutammegopaya Pl do keep translating the other 6-7 kāndas and this experiment running. The notes are very useful.

[Veera Rajagopal  @doctorveera]

Today's Nobel Prize in Physiology or Medicine went to Karl Deisseroth, Peter Hegemann &amp; Georg Nagel for optogenetics: using a light-sensitive protein from pond algae to switch neurons on and off with light.

A 3-min explainer, made with @claudeai

[Ken W @kenw_2]

原来乐山大佛的保养是这样的，阿弥陀佛🙏

[keerthik śaśidharan @KS1729]

on the restoration of the Deësis in the 1930s…

from ‘Mosaics of Hagia Sophia, Istanbul: The Fossati Restoration and the Work of the Byzantine Institute’ by Natalia B. Teteriatnikov

[keerthik śaśidharan @KS1729]

the Deësis mosaic, Hagia Sophia, Byzantine mural from the 13th century, with Christ Pantocrator, flanked by the Virgin Mary and John the Baptist.

[Erik Solheim @ErikSolheim]

Incredible India 🇮🇳!

That peacock warning call just saved the deer’s life.

Better luck next time, tiger. 🦌🐅

[keerthik śaśidharan @KS1729]

unexpectedly, a mention of Malayalam in this survey -- as one of the languages into which Marcus Aurelius' writings has been translated.

no other Indian language is mentioned here but there must be other Indian language translations of his 'Meditations'.

[Śrutaṃ me gopāya @shrutammegopaya]

Another AI project.

This time around it is Gemini Spark's English translation of वाल्मीकि रामायणम्

Took a stab at it with बालकाण्डम् to begin with. The e-book, when viewed in two-page format, enables you to read the original sanskrit text and its translation on the right. (akin to Murty Library format).

The translation is based on the vulgate "Southern recension". We use footnotes to call out those verses that are not part of the Baroda Critical Edition.

We also have footnotes for some added insights from traditional commentators like गोविन्दराज, नागेशभट्ट, महेश्वर तीर्थ covering multiple viewpoints and traditions.

This is "hot off the press" so to speak. So not extensively QC-ed. Do give feedback for improvement. Will add other काण्डs in the same thread in future.

https://t.co/sg3TYnKWOL

[keerthik śaśidharan @KS1729]

Orpheus goes to the underworld in search of Eurydice, a Japanese version.... 🙏

[ඞ @lifeinchaos_]

Japanese man about to make a 763rd dive in search of wife swept away by 2011 tsunami

[keerthik śaśidharan @KS1729]

“We have been modern now for several centuries. We are modern and we want to be modern. This is the orientation of the entire life of our societies in the West. There is frequent criticism of this or that aspect of modernization, and some even criticize “modernity” as such, but “conservative” efforts have succeeded only in slowing the movement at most, while “conservative” endeavors in general have ended up accelerating the movement. And so we want to be modern. We give ourselves an order to be modern. But the fact that the will to be modern has been at work for centuries means that we have not yet arrived at being truly modern. The goal of the march that at several turns we thought we had reached showed itself to be misleading, a sort of mirage; 1789, 1917, 1968, 1989 were only deceptive stages on a road that leads we know not where. The Hebrews were lucky— they only wandered forty years in the wilderness. What does it mean if this will, this command to be modern, does not cease to remodel the conditions of common life, to make revolutions follow revolutions, without ever arriving at its fulfi llment, without ever arriving at a point where we could rest and say, “here at last is the goal of our undertaking,” if this will or command never grasps its object? How could we have willed for so long and allowed ourselves to be so often deceived? Is it, perhaps, that we might not know what we truly want?”

[Ferenc Hörcher @HorcherF]

"the figure of the Christian gentleman: somewhat political, not fully a philosopher, and just slightly too worldly to be a saint.
It’s at this point that Manent ends his Metamorphoses, with the mediating nation." (Collin May)

[keerthik śaśidharan @KS1729]

@DalrympleWill I visited the house where Trotsky was killed in Mexico City and saw his book collections.

Some other photos from that ill-fated house turned museum.

[keerthik śaśidharan @KS1729]

On one of the bookshelves at Leon Trotsky's last home in Mexico City, among various works of history, dictionaries (French-Russian), Marxist analysis, a volume titled 'The Present Condition of India' (1939) by Leonard M. Schiff, with a foreword by Jawaharlal Nehru (1938).