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An AI editorial illustration of Viazovska with an E8 projection, a layered 24-dimensional lattice, an auxiliary function touching its bound, and coauthors' hands in an invented Lausanne-style study
AI editorial portrait of a living person

After finding the densest pattern, build the function proving none can do better

A public photograph of the living Viazovska was used only for recognizable facial and hair features. This is not an actual EPFL lecture, Fields Medal ceremony, or 2016 proof moment. The lattices are nonliteral projections of higher dimensions, and the hands at right preserve the coauthors of the 24-dimensional result.

MathVoyage editorial direction · OpenAI image generation · living-person photograph reference · local candidate gate · 2026-08-07

A mathematical scene preserving a public likeness

Maryna Viazovska

AD 1984 - ?
Thinking ground · Berlin
Born · Kyiv
Modern EraThe exceptional symmetry of E8 in dimension 8An auxiliary function exactly attaining the boundA collaborative proof in dimension 24

The idea to carry forward

Optimality needs more than a good arrangement: it needs a bounding function proving that none can do better.

Enter through one scene

AD 2016

arXiv 1603.04246 — sphere packing in dimension 8

Using modular forms and Fourier transforms, she constructed an auxiliary function that exactly attains the Cohn–Elkies bound and proves E8 optimal. With four coauthors she then proved the 24-dimensional optimality of the Leech lattice.

Questions this person helps open

Concept ports to revisit, not another achievement list

These are reverse projections of existing editorial routes, not claims of direct influence or sole invention.

No concept port has yet been reviewed for this person.

Browse every concept route

PROFILE 02 · DEEP VOYAGE

How Maryna Viazovska’s ideas moved

Instead of memorizing more dates, follow the world that shaped this mind, the scenes that changed its direction, and the questions carried onward.

CHAPTER 01 · PERSON AND PERIOD

What questions surrounded Maryna Viazovska?

Before the finished achievement, read what this person treated as a problem and where the surviving evidence reaches its limit.

About 1 min read

A mathematician who captured the exceptional symmetries of dimensions 8 and 24 with exact functions in a problem that becomes harder as dimension grows. In 2016 Viazovska built an auxiliary function from modular forms that attains the linear-programming bound exactly, proving the E8 lattice is the densest sphere packing in dimension 8. Soon afterward, with Cohn, Kumar, Miller, and Radchenko, she proved optimality of the Leech lattice in dimension 24. This did not single-handedly finish a “four-century generalization” of the three-dimensional Kepler problem: optimal packing is a separate problem in each dimension, and 8 and 24 are exceptional because of the symmetries of E8 and the Leech lattice. The proof built on the Cohn–Elkies bound and earlier modular-form theory. For this and related work, Viazovska received the 2022 Fields Medal, becoming its second woman recipient.

CHAPTER 02 · TURNING SCENES

3 turning scenes

Follow the moments when the idea moved one step further. Every scene continues through an evidenced place or an honestly labelled time context.

  1. Scene 1 / 3

    AD 2016Berlin

    arXiv 1603.04246 — sphere packing in dimension 8

    Using modular forms and Fourier transforms, she constructed an auxiliary function that exactly attains the Cohn–Elkies bound and proves E8 optimal. With four coauthors she then proved the 24-dimensional optimality of the Leech lattice.

    Continue from this scene's place

  2. Scene 2 / 3

    AD 2017Lausanne

    EPFL Lausanne professorship

    She joined EPFL in Lausanne and continued research linking number theory, discrete geometry, and modular forms while extending the methods to new problems.

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  3. Scene 3 / 3

    AD 2022Helsinki· Geographic context

    Fields Medal — the second woman

    The official citation recognized the eight-dimensional sphere-packing proof and related extremal and interpolation problems in Fourier analysis. She became the second woman recipient after Mirzakhani.

    Continue from this scene's time

THOUGHT EXPERIMENT · NOT A FACT CLAIM

Erase Maryna Viazovska from the map

This is a thought experiment about influence, not a verified historical fact.

Beginners arrange coins or circles in the plane and compare gaps. Intermediate learners calculate lattice density. Advanced learners study the linear-programming bound through Fourier transforms. Experts verify how an auxiliary function built from modular forms for E8 satisfies every equality condition and investigate why the construction does not automatically repeat in other dimensions.

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