Making enterprise data and APIs agent-ready: the reliable, governable foundation that AI agents act on, after two decades in financial-services data and platforms.https://vamshij.com/en-GBhttps://vamshij.com/writing/an-answer-that-runs/https://vamshij.com/writing/an-answer-that-runs/A generated query that runs is not one you can trust, and the gap widens as the data outgrows what a human can check by eye. What an agent harness for interactive data discovery has to do, told through a quant at a hedge fund: keep the analyst able to trust a result they can no longer inspect.Fri, 12 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/the-cushions/https://vamshij.com/writing/the-cushions/An agent that works beautifully on your laptop is standing on cushions you stopped noticing: a human watching, a single user, your own credentials, a visible trace, your own judgment, and an undo key. Production removes them one by one. Engineering them back is what reliability actually means, and most of it is not a modeling problem.Wed, 03 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/coase-vibe-coding/https://vamshij.com/writing/coase-vibe-coding/Vibe coding has not only moved the make-or-buy boundary; it has turned building into a cheap option that reprices the whole decision, even for the core systems the cloud era taught everyone to rent. What should decide it is no longer the falling cost of code but the costs that do not fall with it, amortisation, accountability, data, and optionality.Sat, 30 May 2026 00:00:00 GMTstrategywritinghttps://vamshij.com/mathematics/faulty_traffic_signal/https://vamshij.com/mathematics/faulty_traffic_signal/A 15-second pedestrian signal whose red/green split is itself uniformly random. Closed forms for the probability of red, the expected wait, and the expected total time to cross, each from a one-line integral, with a sample-space picture, an account of length-biasing, and a Monte Carlo check of every result.Fri, 29 May 2026 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/staring_sheep/https://vamshij.com/mathematics/staring_sheep/A Fiddler puzzle on mutual visibility: sheep at random points in a square, facing random directions, each with a 180-degree field of view. Two sheep see each other with probability 1/4 whatever the pen; for three, the probability reduces to an average of (pi - alpha)(pi - beta)(pi - gamma) over the triangle's angles and comes to about 0.0272, with a Monte Carlo check.Fri, 29 May 2026 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/charlottes_web/https://vamshij.com/mathematics/charlottes_web/A circular billiard puzzle by Xavier Durawa: Charlotte's strands reflect inside a circular frame; how many earlier strands does the n-th strand cross on average? A self-contained walk through the geometry, the modular-arithmetic reformulation, the piecewise integration, the antipode trick, and the telescoping sum that lands the exact closed form.Sat, 09 May 2026 00:00:00 GMTmathematicshttps://vamshij.com/writing/agent-ready-financial-data/https://vamshij.com/writing/agent-ready-financial-data/An architectural view of how a financial data provider can make its data ready for autonomous and semi-autonomous agents. Workflow archetypes, the three human-in-the-loop bands, the surfaces (REST, SDK, MCP, agents.md, skills, code-as-action), and why the semantic layer is the product.Sat, 02 May 2026 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/beautiful-problems/https://vamshij.com/mathematics/beautiful-problems/On the hunt for beautiful olympiad problems, the indignity of badly typeset mathematics on the web, and a small side project to surface AI training datasets back to the human readers the problems were originally written for.Sun, 26 Apr 2026 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/fiddler_2025_oct17/https://vamshij.com/mathematics/fiddler_2025_oct17/Two puzzles from Fiddler on the Proof: starting at the centre of a unit square, move in a uniformly random direction until you hit the boundary — what is the expected distance travelled? Same question in a unit cube.Sun, 19 Oct 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/cozy_circles/https://vamshij.com/mathematics/cozy_circles/A puzzle by Xavier Durawa: in a regular polygon, place a circle at the midpoint of each side, tangent to the side and as large as possible without overlap. What fraction of the polygon's area is covered by the n circles?Mon, 21 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/notes/2025-04-cozy-circles/https://vamshij.com/notes/2025-04-cozy-circles/Closed form for the ratio of inscribed-circle area to polygon area when circles tangent to each side at its midpoint are maximal.Mon, 21 Apr 2025 00:00:00 GMTnotehttps://vamshij.com/mathematics/apollonian_gasket/https://vamshij.com/mathematics/apollonian_gasket/Constructing the Apollonian gasket fractal from Descartes' Circle Theorem and its complex extension. Includes an elementary algebraic proof, the Lagarias-Mallows-Wilks complex form, and a queue-based Python implementation.Sat, 12 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/cherry_blossom_puzzle/https://vamshij.com/mathematics/cherry_blossom_puzzle/A geometric-probability puzzle by Xavier Durawa: a random chord across a circle intersects a diameter; given that intersection, what is the expected ratio of the shorter segment of the diameter to the longer?Fri, 04 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/posidoku/https://vamshij.com/mathematics/posidoku/A Sudoku variant by Alf Smith with no number clues, only positional gold cells whose values must equal their row, column, or box position. Solved with Google's CP-SAT.Mon, 10 Feb 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/monkey_puzzle/https://vamshij.com/mathematics/monkey_puzzle/For which n can the integers 1..n^2 be placed in an n x n grid so that the multiset of row products matches the multiset of column products? Includes a prime-counting impossibility bound and an integer-programming formulation.Mon, 20 Jan 2025 00:00:00 GMTmathematicshttps://vamshij.com/writing/taste-in-api-design/https://vamshij.com/writing/taste-in-api-design/APIs aren't just functional contracts, they're user interfaces for developers. Great API design requires the same aesthetic judgment and taste that defines excellent product design.Mon, 30 Dec 2024 00:00:00 GMTapiwritinghttps://vamshij.com/writing/llm-api-designer-critic/https://vamshij.com/writing/llm-api-designer-critic/When AI builds the API, then evaluates its own work, a dialogue exploring how LLMs design, critique, and consume geospatial APIs.Sun, 15 Dec 2024 00:00:00 GMTaiwritinghttps://vamshij.com/writing/ironies-ai-automation/https://vamshij.com/writing/ironies-ai-automation/A practitioner's guide to Bainbridge's framework, understanding why more AI automation often means we need more human expertise, not less.Tue, 10 Dec 2024 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/figurine_figuring/https://vamshij.com/mathematics/figurine_figuring/A Jane Street holiday puzzle: 78 figurines (12 drummers, 11 pipers, 10 lords, … 1 partridge) are shuffled and drawn without replacement until the partridge emerges. What is the expected value of the maximum count of any one figurine type drawn?Sun, 01 Dec 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/jumping_julia/https://vamshij.com/mathematics/jumping_julia/A puzzle from the Julia Robinson Mathematics Festival: navigate from the top-left corner of a grid to the goal cell at the bottom-right, where each cell's number specifies the exact distance you may jump horizontally or vertically to the next cell.Sun, 01 Dec 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/linkedin_tango/https://vamshij.com/mathematics/linkedin_tango/A Z3 solver for LinkedIn's daily Tango puzzle: fill an n×n grid with suns and moons such that no three adjacent cells in any row or column share a symbol; row and column counts are balanced; and pairs of cells linked by = or × constraints match or oppose.Tue, 26 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/beside_the_point/https://vamshij.com/mathematics/beside_the_point/A Jane Street geometric-probability puzzle: two random points (red and blue) are drawn uniformly from a unit square. What is the probability that there is a point on the blue-nearest side of the square equidistant from both?Sun, 17 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/number_hooks/https://vamshij.com/mathematics/number_hooks/A 9x9 grid puzzle: in each L-shaped hook of size k, place exactly k copies of digit k, with row and column sums fixed. Solved with Z3.Fri, 15 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/projectile_trajectory/https://vamshij.com/mathematics/projectile_trajectory/At what angle should a projectile be launched, under uniform gravity and no air resistance, so that the arc length of its trajectory is maximised? A standard integral and one implicit equation give the answer.Fri, 01 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/some_off_square/https://vamshij.com/mathematics/some_off_square/A geometric-probability puzzle: two random points in a unit square define a circle's diameter. What is the probability that part of the circle lies outside the square?Tue, 15 Oct 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/subsets_consecutive_pair/https://vamshij.com/mathematics/subsets_consecutive_pair/A generating-function argument in which the count is the convolution of Fibonacci numbers; partial fractions over the golden-ratio roots give a closed form involving Fibonacci and Lucas numbers, with f(10) = 235.Tue, 01 Oct 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/die_puzzle/https://vamshij.com/mathematics/die_puzzle/Roll a fair six-sided die until the running total first exceeds 12. What is the most likely final total?Wed, 07 Feb 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/block_party/https://vamshij.com/mathematics/block_party/A Jane Street puzzle: fill each region of a 9×9 irregularly-partitioned grid with the numbers 1 through N (where N is the region size), such that for every cell containing K, the nearest matching K (taxicab distance) is exactly K cells away.Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/block_party4/https://vamshij.com/mathematics/block_party4/A Jane Street variant of Block Party on a 10×10 grid: fill each region with 1 through N, but with a cleaner taxicab constraint expressed as two implication clauses per cell.Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/dancer_pairs/https://vamshij.com/mathematics/dancer_pairs/A Jane Street puzzle: fifteen dancers stand in an equilateral-triangle formation, each unit-distant from their nearest neighbours. Each dancer pairs up with one neighbour; all but one are part of a pair. How many distinct sets of seven pairs are possible?Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/linkedin_queens/https://vamshij.com/mathematics/linkedin_queens/LinkedIn's Queens puzzle: place one queen per row, column, and colour region of an n×n board, with the additional constraint that no two queens touch, not even diagonally.Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/well_well_well/https://vamshij.com/mathematics/well_well_well/A Jane Street puzzle: a 7×7 well with per-cell depths 1 through 49 is filled at 1 cubic foot per minute from the cell marked 1; water disperses evenly among adjacent lower-depth regions. After how many minutes does the water level in cell 43 start to rise?Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/writing/catalog-as-query-interface/https://vamshij.com/writing/catalog-as-query-interface/An essay from 2023 arguing that natural-language queries would replace SQL as the primary interface to enterprise data, with the data catalog as the substrate that makes those queries trustworthy. Republished with a 2026 note.Fri, 15 Sep 2023 00:00:00 GMTdatawritinghttps://vamshij.com/writing/llm-apis-the-new-customer/https://vamshij.com/writing/llm-apis-the-new-customer/An essay from 2023 arguing that LLMs would become primary consumers of APIs, that API documentation would become in-demand training data, and that API product managers would soon be designing for a non-human customer. Republished with a 2026 note.Fri, 01 Sep 2023 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/geometric_expectation_polygon/https://vamshij.com/mathematics/geometric_expectation_polygon/Closed form for the expected distance from the centre of a regular n-gon of unit circumradius, via a Jacobian substitution on one fundamental triangle; three triangle-sampling methods for computational verification.Fri, 18 Dec 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/knights-on-a-chessboard/https://vamshij.com/mathematics/knights-on-a-chessboard/A white knight and a black knight on diagonally opposite corners of a 3×3 square. What is the expected number of moves until the black knight captures the white one? A clean Markov-chain problem with a closed form.Thu, 19 Nov 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/inversion/https://vamshij.com/mathematics/inversion/Inversion in a circle transforms two hard problems about tangent circles into routine ones: a Pappus chain (prove that the height of the n-th circle equals 2n times its radius) and the distance between the circumscribed and inscribed circles of three mutually tangent circles of radii 1, 2, 3.Mon, 08 Jun 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/islamic_geometric_patterns/https://vamshij.com/mathematics/islamic_geometric_patterns/A computational construction of star patterns from the Islamic tradition: translational units, motifs, rosettes, and the rosette dual, implemented in Python with NumPy.Tue, 28 Jan 2020 00:00:00 GMTmathematics