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In science, the art is in spreading the word. Explaining a result at different depths is not merely a teaching device: it is an extension of the research itself, because in translating an idea you discover which part you did not yet understand.

“In a world like this, where everything is told, the most easily available and at once the deadliest weapon is popularisation.”
— Milan Kundera

Essays

  1. Castañeda (2025) Velarias y cáusticas Laberintos e Infinitos 56: 36--40
    PDF
    @article{castaneda2025velarias,
  author  = {Castañeda, Pablo},
  title   = {Velarias y cáusticas},
  journal = {Laberintos e Infinitos},
  volume  = {56},
  pages   = {36--40},
  year    = {2025},
}
  2. R. Kaufman and Castañeda (2025) Any positive number is a factor of a number that descends to 1 in the $\omega x + 1$ problem, for odd $\omega$ The College Mathematics Journal 56: 200--202
    DOI
    @article{kaufman2025collatz,
  author  = {Kaufman, Richard and Castañeda, Pablo},
  title   = {Any positive number is a factor of a number that descends to 1 in the $\omega x + 1$ problem, for odd $\omega$},
  journal = {The College Mathematics Journal},
  volume  = {56},
  number  = {3},
  pages   = {200--202},
  year    = {2025},
  doi     = {10.1080/07468342.2024.2424127},
}
  3. C. Bosch Giral and Castañeda (2025) El billar a tres hojas Miscelánea Matemática 80: 115--131
    DOI · open access
    @article{bosch2025billar,
  author  = {Bosch Giral, Carlos and Castañeda, Pablo},
  title   = {El billar a tres hojas},
  journal = {Miscelánea Matemática},
  volume  = {80},
  pages   = {115--131},
  year    = {2025},
  doi     = {10.47234/MM.8009},
}
  4. V. F. Breña Medina, Castañeda, L. Fernández Román and M. Madriz Mendoza (2025) Alebrije matemático Miscelánea Matemática 80: 47--65
    DOI · open access
    @article{brena2025alebrije,
  author  = {Breña Medina, Víctor F. and Castañeda, Pablo and Fernández Román, Leobardo and Madriz Mendoza, Maira},
  title   = {Alebrije matemático},
  journal = {Miscelánea Matemática},
  volume  = {80},
  pages   = {47--65},
  year    = {2025},
  doi     = {10.47234/MM.8005},
}
  5. Castañeda (2022) Un determinante extraño, un breve aporte Laberintos e Infinitos 55: 43--47
    ResearchGate
    @article{castaneda2022determinante,
  author  = {Castañeda, Pablo},
  title   = {Un determinante extraño, un breve aporte},
  journal = {Laberintos e Infinitos},
  volume  = {55},
  pages   = {43--47},
  year    = {2022},
}
  6. Castañeda (2020) Un paso hacia los agujeros negros, generalización del colapso esférico Motivos Matemáticos 3: 1--18
    enlace
    @article{castaneda2020agujeros,
  author  = {Castañeda, Pablo},
  title   = {Un paso hacia los agujeros negros, generalización del colapso esférico},
  journal = {Motivos Matemáticos},
  volume  = {3},
  number  = {1},
  pages   = {1--18},
  year    = {2020},
  url     = {http://motivos.matem.unam.mx/vol3/num1/aplicadas.html},
}
  7. Castañeda and J. Martínez Villarroya (2017) Las matemáticas del mal Laberintos e Infinitos 44: 51--62
    ResearchGate
    @article{castaneda2017mal,
  author  = {Castañeda, Pablo and Martínez Villarroya, Javier},
  title   = {Las matemáticas del mal},
  journal = {Laberintos e Infinitos},
  volume  = {44},
  pages   = {51--62},
  year    = {2017},
}
  8. Castañeda (2016) Oleĭnik a través del espejo Miscelánea Matemática 62: 61--80
    ResearchGate
    @article{castaneda2016oleinik,
  author  = {Castañeda, Pablo},
  title   = {Oleĭnik a través del espejo},
  journal = {Miscelánea Matemática},
  volume  = {62},
  pages   = {61--80},
  year    = {2016},
}
  9. Castañeda (2016) Dogma: S-shaped. Ode to Ônibus 409 The Mathematical Intelligencer 38: 10--13
    DOIResearchGate
    @article{castaneda2016dogma,
  author  = {Castañeda, Pablo},
  title   = {Dogma: S-shaped. Ode to Ônibus 409},
  journal = {The Mathematical Intelligencer},
  volume  = {38},
  pages   = {10--13},
  year    = {2016},
  doi     = {10.1007/s00283-015-9611-4},
}
  10. Castañeda (2014) Laberinto Laberintos e Infinitos 34: 56--64
    ResearchGate
    @article{castaneda2014laberinto,
  author  = {Castañeda, Pablo},
  title   = {Laberinto},
  journal = {Laberintos e Infinitos},
  volume  = {34},
  pages   = {56--64},
  year    = {2014},
}
  11. Castañeda (2014) Primos distantes y parientes relativos Miscelánea Matemática 58: 67--76
    ResearchGate
    @article{castaneda2014primos,
  author  = {Castañeda, Pablo},
  title   = {Primos distantes y parientes relativos},
  journal = {Miscelánea Matemática},
  volume  = {58},
  pages   = {67--76},
  year    = {2014},
}
  12. Castañeda (2000) La leyenda del Califa: una travesía por los métodos de multiplicación Cuento didáctico, proyecto "Posprimaria", CONAFE
    PDF
    @booklet{castaneda2000califa,
  author       = {Castañeda, Pablo},
  title        = {La leyenda del Califa: una travesía por los métodos de multiplicación},
  year         = {2000},
  howpublished = {Cuento didáctico, proyecto "Posprimaria", CONAFE},
}

The Colloquium and the Seminar

  • ITAM Mathematics ColloquiumI coordinated it from August 2017 to December 2024: ninety-four talks, by students, faculty, people from industry and from other institutions. Whoever runs it fulfils their community service that way, and the posters in the proceedings came out of it.
  • ITAM Mathematics SeminarI ran it for four semesters, from autumn 2014 to spring 2016: fifty-three talks with researchers from around the world.

One word

On 5 March 2024, Javier Martínez Villarroya invited me to his podcast Una Palabra, where we talked about a single one: Juego — play.

The Caliph books

For CONAFE's Posprimaria project, which set up study centres in villages too small for a secondary school. What was needed were materials a student could follow alone. Out of that came the story of a caliph who must learn to multiply: in one chapter the vizier teaches him the Arabic method, in the next the caliph's son learns the Ethiopian one. Illustrations by Obal. Read it · printable version.