Pi Day - School of Maths 2026

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Across
  1. 5. Axioms defining natural numbers.
  2. 6. p-adic analytic study of cyclotomic fields, class groups, and growth of invariants over infinite towers of number fields.
  3. 9. Ordinals that lead to contradiction.
  4. 15. The closed unit ball of the dual space of a normed vector space is compact in the weak topology.
  5. 16. Algebraic structure with associative multiplication and identity.
  6. 17. Fundamental equivalence used in perfectoid geometry.
  7. 18. The set everyone meets before they know what a set really is.
  8. 22. Property where future evolution depends only on present state.
  9. 24. Group characters and matrices.
  10. 25. Combinatorial theorem guaranteeing monotone subsequences.
  11. 27. Measure-theoretic theorem allowing interchange of integrals.
  12. 28. Logarithm pioneer whose tables saved astronomers centuries of calculation.
  13. 29. Hotel always has room.
  14. 31. Spectral sequence computing derived functors of a composite functor.
Down
  1. 1. Polynomials orthogonal under Gaussian weight, used in probabilistic expansions, quantum mechanics, and spectral PDE methods.
  2. 2. Function that keeps coming back to haunt complex analysts.
  3. 3. The theorem relating elliptic curves over ℚ to modular forms.
  4. 4. Grand unifying program linking automorphic forms with Galois representations.
  5. 7. Category-theoretic generalization of a topological space used in algebraic geometry.
  6. 8. Conjectures relating regulators, K-theory, and special values of L-functions.
  7. 10. Circles and randomness conspire.
  8. 11. Combinatorial paradoxes and dynamical systems.
  9. 12. Limit of scaled random walks converging to Brownian motion.
  10. 13. Cohomology theory used to study algebraic varieties over arbitrary fields.
  11. 14. Conjecture describing the location of nontrivial zeros of the zeta function.
  12. 16. Hypothetical objects intended to unify cohomology theories of algebraic varieties.
  13. 19. Cohomology theory obtained from differential forms on manifolds.
  14. 20. Non-Archimedean analytic spaces generalizing rigid analytic geometry.
  15. 21. Property of a function whose derivative changes sign infinitely often near a point.
  16. 23. Property of Banach spaces where the canonical embedding into the double dual is surjective.
  17. 26. Conjecture predicting a bound relating sums and products of coprime integers.
  18. 30. Paradoxical decomposition of a sphere using group actions.