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The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields

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The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering is a mathematics book by Piper Harron (also known as Piper H and Piper Harris), based on her Princeton University doctoral thesis of the same title. It has been described as "feminist",[1] "unique",[2] "honest",[2] "generous",[3] and "refreshing".[4]

The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering
AuthorPiper H
PublisherBirkhäuser Basel
Publication date
2016
ISBN978-3-319-76531-0

Thesis and reception

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Harron was advised by Fields Medalist Manjul Bhargava, and her thesis deals with the properties of number fields, specifically the shape of their rings of integers.[2][5] Harron and Bhargava showed that, viewed as a lattice in real vector space, the ring of integers of a random number field does not have any special symmetries.[5][6] Rather than simply presenting the proof, Harron intended for the thesis and book to explain both the mathematics and the process (and struggle) that was required to reach this result.[5]

The writing is accessible and informal, and the book features sections targeting three different audiences: laypeople, people with general mathematical knowledge, and experts in number theory.[1] Harron intentionally departs from the typical academic format as she is writing for a community of mathematicians who "do not feel that they are encouraged to be themselves".[1] Unusually for a mathematics thesis, Harron intersperses her rigorous analysis and proofs with cartoons, poetry, pop-culture references, and humorous diagrams.[2] Science writer Evelyn Lamb, in Scientific American, expresses admiration for Harron for explaining the process behind the mathematics in a way that is accessible to non-mathematicians, especially "because as a woman of color, she could pay a higher price for doing it."[4] Mathematician Philip Ording calls her approach to communicating mathematical abstractions "generous".[3]

Her thesis went viral in late 2015, especially within the mathematical community, in part because of the prologue which begins by stating that "respected research math is dominated by men of a certain attitude".[2][4] Harron had left academia for several years, later saying that she found the atmosphere oppressive and herself miserable and verging on failure.[7] She returned determined that, even if she did not do math the "right way", she "could still contribute to the community".[7] Her prologue states that the community lacks diversity and discourages diversity of thought.[4] "It is not my place to make the system comfortable with itself", she concludes.[4]

A concise proof was published in Compositio Mathematica in 2016.[8]

Author

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Harron earned her doctorate from Princeton in 2016.[9] In the academic year 2023-2024 she was a teacher at Philips Exeter Academy. She has changed her name to Piper Harris. In 2017 in an American Mathematical Society blog she asked white cisgender men to leave their job, because they are "taking up room that should go to someone else".

References

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  1. ^ a b c Molinari, Julia (April 2021). "Re-imagining Doctoral Writings as Emergent Open Systems". Re-imagining doctoral writing (preprint). Colorado Press.
  2. ^ a b c d e Salerno, Adriana (February–March 2019). "Book review: Mathematics for the People" (PDF). MAA Focus. 39 (1): 50–51.
  3. ^ a b Ording, Philip (2016). "Creative Writing in Mathematics and Science" (PDF). Banff International Research Station Proceedings 2016. p. 7. Retrieved June 18, 2021.
  4. ^ a b c d e Lamb, Evelyn (December 28, 2015). "Contrasts in Number Theory". Scientific American. Retrieved June 18, 2021.
  5. ^ a b c "The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields". Springer Nature Switzerland AG. Retrieved June 18, 2021.
  6. ^ Harron, Piper (June 20–24, 2016). "Contributed Talks" (PDF). 14th Meeting of the Canadian Number Theory Association. University of Calgary. p. 26.
  7. ^ a b Kamanos, Anastasia (2019). The Female Artist in Academia: Home and Away. Rowman & Littlefield. p. 21. ISBN 9781793604118.
  8. ^ Bhargava, Manjul; Harron, Piper (June 2016). "The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields". Compositio Mathematica. 152 (6): 1111–1120. arXiv:1309.2025. doi:10.1112/S0010437X16007260. MR 3518306. S2CID 118043017. Zbl 1347.11074.
  9. ^ "Grad school experiences | Department of Mathematics". September 24, 2016. Retrieved January 31, 2024.
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