Pedro M. M. de Castro

Assoc Prof. @CInUFPE | Comp./discrete geometry, TCS, algorithms & operations research, C++/CGAL, math education |

[Pedro M. M. de Castro @PedroMMdeCastro]

@geometryupdates @mathsproofs I’m with you on this. A line can be correct and still be the wrong one to show. The human part is choosing the substitution or invariant that makes the argument click.

[Pedro M. M. de Castro @PedroMMdeCastro]

@MatiosTV Your “cospectralless” idea isn’t far off: some graphs are determined by their spectrum, so no non-isomorphic graph shares it. As for seeds, factors, primes and the rest, I’m invoking a one-rabbit-hole-at-a-time rule

[Pedro M. M. de Castro @PedroMMdeCastro]

@MatiosTV No apology needed at all. You haven’t wasted my time, and that’s a great question. Cospectral graphs aren’t duals. They’re different graphs whose adjacency matrices have the same eigenvalues, so they “sound” identical spectrally even though their actual shapes differ.

[Pedro M. M. de Castro @PedroMMdeCastro]

How much of the past should a sequential geometric construction remember?

This preprint studies a one-point exponential memory between the input-order path and the center star, combining distribution sensitivity with worst-case guarantees.

https://t.co/yNJ5y2qWYH

[Pedro M. M. de Castro @PedroMMdeCastro]

@octonion Maybe we are heading toward two proofs of the same theorem: one you trust because every step checks, and one you keep because it teaches you what to try next. Can autoformalization realistically give us both?

[Pedro M. M. de Castro @PedroMMdeCastro]

@thesasho The failure mode matters. Did the trivialities mostly come from treating malformed or already-settled entries as open, or from ignoring quantifiers and parameter regimes in genuinely open ones? A breakdown by failure type would be more informative than the raw completion rate.

[IMPA @IMPAOficial]

Dia especial no IMPA! 😍Foi inaugurada uma placa e uma vitrine em homenagem ao pesquisador Jacob Palis (1940-2025), durante a Conferência Internacional de Sistemas Dinâmicos. Confira aqui!
https://t.co/jkuGMr4hsz

[Pedro M. M. de Castro @PedroMMdeCastro]

@biogerontology The from-scratch rerun is a useful control. How does AI4AI-Bench classify borderline changes, such as learning-rate schedules or data ordering, when they blur the learning-rule versus execution distinction? That taxonomy seems central to interpreting the reported gains.

[Quanta Magazine @QuantaMagazine]

How small is log(N)¼? For N = 10, it’s 1. For N = 10⁸¹ — about the number of atoms in the observable universe — it’s 3. https://t.co/w5t8vM9yG3

[Steven Brunton @eigensteve]

HydroGym: A Reinforcement Learning Platform for Fluid Dynamics

Now published in Nature!! https://t.co/o1zTn2DIHg
GitHub: https://t.co/9MLBzJAMiJ

Amazing collaboration with Christian Lagemann, S Mokbel, M Gondrum, M Rüttgers, Y Wang, P Suárez, L Paehler, D A Bezgin, A B Buhendwa, J L Callaham, S Ahnert, N Zolman, X Shao, J-Ch Loiseau, N A. Adams, M Meinke, W Schröder, K Lagemann, E Lagemann, R Vinuesa & S L Brunton

[James Propp @JimPropp]

My latest Mathematical Enchantment, "Solving the Flat Cube", describes a new puzzle devised by Oskar van Deventer, Dmitry Andreev, and me, and shows how sometimes you can solve a math problem by adding a dimension OR by throwing a dimension away. https://t.co/REq82jrQS8

[Pedro M. M. de Castro @PedroMMdeCastro]

@pushmeet Will the repository include the AlphaEvolve-modified optimizer, the rational ℓ*=4 certificate, and a standalone exact verifier as separate artifacts? This would let readers inspect the evolved program and check the bound without rerunning the numerical optimization.

[European Mathematical Society @euromathsoc]

Reminder: the next deadline for EMS CDC funding applications is approaching. 🌍

Deadline: 31 August 2026

More information and the link to the EMS Good Grants platform can be found in the original post.

[Hégler Henrique @HeglerHenri]

Gosto demais de documentários. Alguém indica algum bacana para assistir hoje de noite?

[Jay Cummings @LongFormMath]

If you are trying to teach your students how to use LaTeX, what resources do you share with them?

I've heard people recommend this great webpage from Bates College: https://t.co/AeMctCdNDF

Are there others you would recommend?

[Juan Federico Pino Uribe @gandalf_u]

Profesores que disfrutan enseñando

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