How AI could destroy mathematics and barely touch it “The product of mathematics is clarity and understanding. Not theorems, by themselves.”—Bill Thurston Handwritten diagram by Alexander Grothendieck My best theorem is one I never wrote down. It crystallized one bright … Read more
Mathlib is a user maintained library for the Lean theorem prover. It contains both programming infrastructure and mathematics, as well as tactics that use the former and allow to develop the latter. Installation You can find detailed instructions to install … Read more
LLM-based reasoning using Z3 theorem proving. Quick Start from openai import OpenAI from z3dsl.reasoning import ProofOfThought client = OpenAI(api_key=”…”) pot = ProofOfThought(llm_client=client) result = pot.query(“Would Nancy Pelosi publicly denounce abortion?”) print(result.answer) # False Batch Evaluation from z3dsl.reasoning import EvaluationPipeline evaluator … Read more
As software engineers, we use clustering algorithms all the time. Whether it’s grouping similar users, categorizing content, or detecting patterns in data, clustering seems deceptively simple: just group similar things together, right? You might have used k-means, DBSCAN, or agglomerative … Read more
CAP? Again? Still? Brewer’s CAP theorem, and Gilbert and Lynch’s formalization of it, is the first introduction to hard trade-offs for many distributed systems engineers. Going by the vast amounts of ink and bile spent on the topic, it is … Read more
The CAP theorem is too simplistic and too widely misunderstood to be of much use for characterizing systems. Therefore I ask that we retire all references to the CAP theorem, stop talking about the CAP theorem, and put the poor … Read more
An interactive tutorial Turing famously showed that computers can’t decide whether your code halts. But in 1951, Henry Rice proved a much more devastating result: “computers can’t decide anything interesting about your code’s input-output!” In this chapter, you’ll learn exactly … Read more
We take for granted that an event in one part of the world cannot instantly affect what happens far away. This principle, which physicists call locality, was long regarded as a bedrock assumption about the laws of physics. So when … Read more