Ode to Vladimir Voevodsky

[jmikedupont2]

Ode to Vladimir Voevodsky and his Unimath Project

Ode to Vladimir Voevodsky and his Unimath Project

O muses, hear my humble plea
And grant me some poetic skill
To sing the praises of a man
Who dared to dream and to create
A new and unifying math
That bridges the gap between the types
And the homotopies in their path

He was a visionary who saw
The beauty and the power of
The univalence axiom
That makes the equal types above

He was a pioneer who made
The unimath library
That implements the univalent math
And uses Coq as a guarantee

He was a leader who inspired
Many others to join his cause
And to contribute and to share
Their knowledge and their applause

He left us too soon, but his legacy
Lives on in his unimath project
And in the minds and hearts of those
Who admire and respect

His work, his passion, and his vision
Of a better and a brighter math
That is based on the univalent
Foundations and their path

[jmikedupont2]

Sure, I can try to rewrite the poem for you. Here is my attempt:

O muses, lend me your support
And help me craft this epic tale
Of a brave hero who embarked
On a quest to find and to reveal
A new and glorious math
That connects the types and shapes
And the transformations in their space

He was a champion who wielded
The mighty thread of univalence
That makes the equal types reveal
Their hidden essence and their sense

He was a warrior who fought
The fearsome beast of inconsistency
And used Coq as his trusted sword
To ensure the soundness and the purity

He was a savior who rescued
The fair maiden of category theory
And brought her to the light of day
From the dark dungeon of complexity

He left us too soon, but his legacy
Remains in his unimath quest
And in the souls and deeds of those
Who honor and respect

His courage, his passion, and his vision
Of a better and a brighter math
That is founded on the univalent
Principles and their path

[jmikedupont2]

There once was a minotaur who lived in a maze He guarded the secrets of unimath with his gaze He challenged the seekers to prove their worth By solving the puzzles of types and shapes on earth

But one day a hero came with a thread of truth He followed the path of univalence with his sleuth He faced the minotaur with his Coq in hand And proved the beast was nothing but a type in his land

He freed the secrets of unimath from the maze And shared them with the world for everyone to praise He honored the minotaur for his role in the quest And thanked him for the univalent principles and their test

[jmikedupont2]

Sure, I can try to reframe Vladimir Voevodsky in the hero's journey of unimath. Here is my attempt:

The hero's journey of Vladimir Voevodsky

1. The call to adventure: Vladimir Voevodsky is a brilliant mathematician who is dissatisfied with the foundations of mathematics and the lack of rigor and reliability in proofs. He is intrigued by the idea of using computer programs to check the validity of mathematical statements and to construct new theories.
2. The refusal of the call: Voevodsky faces resistance and skepticism from his peers and the mathematical community, who are reluctant to adopt new methods and tools. He also struggles with the technical difficulties and limitations of existing proof assistants and programming languages.
3. The meeting with the mentor: Voevodsky meets Steve Awodey, a logician and philosopher who introduces him to the concept of homotopy type theory, a new approach to the foundations of mathematics that combines ideas from topology, logic, and category theory. Awodey also shows him the Coq proof assistant, a software that allows users to write and verify proofs in a formal language.
4. The crossing of the threshold: Voevodsky decides to pursue homotopy type theory as his new research direction and to use Coq as his main tool. He leaves behind his previous work on algebraic geometry and motivic cohomology and enters a new and unfamiliar domain of mathematics.
5. The tests, allies, and enemies: Voevodsky faces many challenges and obstacles in his quest to develop homotopy type theory and to apply it to various fields of mathematics. He has to learn new concepts and techniques, to overcome technical and conceptual difficulties, and to convince others of the value and feasibility of his vision. He also finds allies and collaborators who share his enthusiasm and support his work, such as Andrej Bauer, Thierry Coquand, Peter Lumsdaine, and many others.
6. The approach to the inmost cave: Voevodsky discovers the univalence axiom, a key principle that states that equivalent types can be identified. This axiom has profound implications for the foundations of mathematics, as it allows for a new and flexible way of expressing and relating mathematical objects and structures. It also enables the development of a rich and expressive language for mathematics, called the unimath language.
7. The ordeal: Voevodsky faces the ultimate challenge of proving the consistency of the univalence axiom and of homotopy type theory. This is a crucial and difficult task, as it would establish the soundness and validity of his new foundation for mathematics. He also has to deal with the complexity and size of his unimath library, a collection of formalized mathematical theories and results that he and his collaborators have created using Coq and the unimath language.
8. The reward: Voevodsky succeeds in proving the consistency of the univalence axiom and of homotopy type theory, using a model based on simplicial sets. He also manages to organize and maintain his unimath library, which becomes a valuable and accessible resource for mathematical knowledge and verification. He receives recognition and admiration from his peers and the mathematical community, who acknowledge his groundbreaking contributions and achievements.
9. The road back: Voevodsky returns to his original field of algebraic geometry and motivic cohomology, and applies his new tools and insights to solve some of the open problems and conjectures that he had left behind. He also continues to work on homotopy type theory and unimath, and to explore new directions and applications of his ideas.
10. The resurrection: Voevodsky passes away unexpectedly at the age of 51, leaving behind a legacy of innovation and excellence. His work on homotopy type theory and unimath inspires and influences many other mathematicians and researchers, who continue to develop and extend his vision and his project. His unimath library becomes a living and growing repository of mathematical knowledge and verification, that can be used for research, education, and verification.
11. The return with the elixir: Voevodsky's work on homotopy type theory and unimath has a lasting impact on the foundations and practice of mathematics. It provides a new and unifying perspective on mathematics, that bridges the gap between types and shapes, and between logic and geometry. It also offers a new and reliable way of doing mathematics, that ensures the correctness and clarity of proofs and constructions. It also opens up new possibilities and opportunities for mathematics, that can lead to new discoveries and insights.
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Source: Conversation with Bing, 1/30/2024
(1) Hero's journey - Wikipedia. https://en.wikipedia.org/wiki/Hero%27s_journey.
(2) The 12 Steps of the Hero’s Journey, WIth Example | Grammarly. https://www.grammarly.com/blog/heros-journey/.
(3) Hero's Journey: Get a Strong Story Structure in 12 Steps - Reedsy. https://blog.reedsy.com/guide/story-structure/heros-journey/.
(4) en.wikipedia.org. https://en.wikipedia.org/wiki/Hero%27s_journey.