AliceVision is a Photogrammetric Computer Vision Framework providing 3D Reconstruction and Camera Tracking algorithms. It allows creating a 3D textured model from the analysis of a set of unordered images of a static scene taken with any type of cameras, from professional cameras to smartphones. Meshroom is the graphical user interface built around AliceVision. It has a nodal-based interface, with a default reconstruction pipeline that can be customized for specific acquisition systems or industrial workflows. The nodal pipeline is split into small tasks that can be computed on multiple machines in parallel on render farm. This nodal pipeline also allows the end user to customize the workflow for a specific acquisition setup or to add dedicated nodes to run any task from another script or piece of software. Meshroom has been used since 2014 in digital environment creation for the Visual Effects industry and now in many other industries including manufacturing, medical, cultural heritage, tourism, archeology, biology, surveillance and 3D printing. During this session, we will present the technology behind AliceVision, illustrated by some concrete examples of production pipelines built around it. Check out our website : alicevision.org

1. francois@rudder.io @fanf42
Towards
collaborative, open science
in Maths
- with the help of computers -
2021-11

2. Hi!
secops automation/compliance app
manage ten of thousands servers
2
François ARMAND
CTO
Free Software Company
“Stay Up”
Stand B14

3. Mathematics proofs are hard.

4. Mathematics proofs are hard.
Today proofs are hundreds of pages long.
And because of high specialization, there is routinely less than 10 people on
Earth able to barely understand them.

5. Mathematics proofs are hard.
Today proofs are hundreds of pages long.
And because of high specialization, there is routinely less than 10 people on
Earth able to barely understand them.
↠ Grigori Perelman proof of Poincaré conjecture in 2002:
after several years of review - it seems ok

6. Mathematics proofs are hard.
Today proofs are hundreds of pages long.
And because of high specialization, there is routinely less than 10 people on
Earth able to barely understand them.
↠ Grigori Perelman proof of Poincaré conjecture in 2002:
after several years of review - it seems ok
↠ Shinichi Mochizuki proof of ABC conjecture in 2012:
500 pages of terse proofs and totally new concepts - nobody knows if ok

7. “The world of mathematics is becoming very
large, the complexity of mathematics is
becoming very high, and there is a danger of
an accumulation of mistakes.
Proofs rely on other proofs; if one contains a
flaw, all others that rely on it will share the
error.”
Vladimir Voevodsky

8. Vladimir Voevodsky
● In 1990, enters Harvard without applying
after publishing a major theorem proof.
● Proves Milnor’s conjecture in 1996.
● Fields Medal in 2002 at only 38 years
old for Milnor’s conjecture proof.
● After 10 years of work, proves
Bloch-Katos conjectures in 2009.

9. Building castle on sand
Sometimes, major proofs
are wrong.

10. Building castle on sand
Sometimes, major proofs
are wrong.
↠ Kenji Fukaya foundational theorem
on symplectic geometry proof was
mostly wrong (and it takes almost 15
years to get noticed and corrected)

11. Building castle on sand
Sometimes, major proofs
are wrong.
↠ In 1998, Carlos Simpson find an error in
Voevodsky’s 1990’s work.
It was an epiphany for Voevodsky.
↠ Kenji Fukaya foundational theorem
on symplectic geometry proof was
mostly wrong (and it takes almost 15
years to get noticed and corrected)

12. “I got worried. I stopped doing curiosity driven
research.
I might make a mistake. And, as I’ve just learned,
no one was likely to be checking up with any
diligence.” Vladimir Voevodsky

13. “I got worried. I stopped doing curiosity driven
research.
I might make a mistake. And, as I’ve just learned,
no one was likely to be checking up with any
diligence.” Vladimir Voevodsky
Machine checked proof ?

14. In software world - proof assistants
Goal: make interactive, formal, machine verified proof
of theorems
They are like a game:
● you have some basic rules (higher order logic)
● you defined goals (theorems), and steps to reach
them (lemma)
● and then you spend hours arguing with the
computer (the interactive proof part)
● in the end, you get a reusable machine checked
proof

15. In software world - proof assistants
Goal: make interactive, formal, machine verified proof
of theorems
They are like a game:
● you have some basic rules (higher order logic)
● you defined goals (theorems), and steps to reach
them (lemma)
● and then you spend hours arguing with the
computer (the interactive proof part)
● in the end, you get a reusable machine checked
proof
● Martin-Löf type theory
○ 1972
● Isabelle/HOL
○ 1986
○ Higher Order Logic
○ University of Cambridge &
Munich
● Coq
○ 1989
○ Calculus of Inductive
Constructions
(Coquant, Bertot, Leroy...)
○ INRIA 󰏃
● Lean
○ 2013
○ Calculus of Inductive
Constructions
○ Microsoft

16. Making proof assistants suitable for Maths
Proof assistant equivalence language is alien for mathematicians.
(type theory) (set theory)

17. Making proof assistants suitable for Maths
Voevodsky spent 7 years rebuilding Mathematics foundation to make them easy
to use in proof assistant: Homotopy Type Theory (HoTT)
Proof assistant equivalence language is alien for mathematicians.
(type theory) (set theory)

18. Making proof assistants suitable for Maths
And then, magic happened...
Then, he tries to convince people to use that foundation to build up things

19. HoTT book - Doing science in our Millennium
In 2012-2013, a special team is built. Achievement:
“collaborative open science”
- in less than 6 months
- more than 30 Mathematicians,
- from different backgrounds,
- created a new branch of Mathematics,
- with machine-checked proofs in Coq,
- reported in a 600 pages book,
- in github, under a Creative Common license !

20. HoTT book - Doing science in our Millennium
In 2012-2013, a special team is built. Achievement:
“collaborative open science”
- in less than 6 months
- more than 30 Mathematicians,
- from different backgrounds,
- created a new branch of Mathematics,
- with machine-checked proofs in Coq,
- reported in a 600 pages book,
- in github, under a Creative Common license !
“Truly open research
habitats cannot be
obstructed by copyright,
profit-grabbing
publishers, patents,
commercial secrets, and
funding schemes that
are based on faulty
achievement metrics.”

21. End of story? Proof assistants don’t have it easy
Most mathematicians don’t like nor use proof assistants:
● "they remove the human creativity and insights"
● "they force to tediously prove each and all little aspects of a theory, obscuring
the bigs ideas behind a heap of irrelevant technical details" *
Plus:
● UnivMath effort stalled, its legacy is not clear yet
● Voevodsky died in septembre 2017 after difficult years
● HoTT needs some time to be more broadly assimilated
* If you are a developer, it may sound familiar (yes,
that holy war between statically and dynamically
typed language :)

22. Peter Scholze
● maths prodigy (but don't call it like that)
○ 3 gold / 1 silver medal in International
Mathematical Olympiad,
○ license in 3 semesters, master in 2
semesters, PhD done at 24y old...
● youngest Fields medal en 2018 at
30 for “the revolution that he
launched in arithmetic geometry.”

23. ● Scholze main work: Condensed Sets
○ new foundations for topology
● July 2019: works on a central theorem
○ (a complicated equivalence: "real functional analysis still works if you replace
topological spaces with condensed sets")
○ make the proof in his head with few notes for 4 days
Proving theorem in his head

24. ● Scholze main work: Condensed Sets
○ new foundations for topology
● July 2019: works on a central theorem
○ (a complicated equivalence: "real functional analysis still works if you replace
topological spaces with condensed sets")
○ make the proof in his head with few notes for 4 days
Proving theorem in his head

25. ● Scholze main work: Condensed Sets
○ new foundations for topology
● July 2019: works on a central theorem
○ (a complicated equivalence: "real functional analysis still works if you replace
topological spaces with condensed sets")
○ make the proof in his head with few notes for 4 days
○ not sure about one central part of the proof
○ even after writing it down 4 months latter
Proving theorem in his head

26. ● Scholze main work: Condensed Sets
○ new foundations for topology
● July 2019: works on a central theorem
○ (a complicated equivalence: "real functional analysis still works if you replace
topological spaces with condensed sets")
○ make the proof in his head with few notes for 4 days
○ not sure about one central part of the proof
○ even after writing it down 4 months latter
● Asked Kevin Buzzard and Johan Commelin, from Lean community, for help
↠ Liquid Tensor Experiment: "help me prove that hard theorem in Lean"
Proving theorem in his head

27. The Liquid Tensor Experiment - success
In december 2020, the Liquid Tensor experiment is started. Achievement:
“collaborative open science”
- in less than 6 months
- more than 12 Mathematicians,
- from different backgrounds,
- proved a hard theorem in a new branch of Mathematics,
- with machine-checked proofs in Lean,
- in github !

28. Maths as Collaborative open science
Formal, machine-checked proof
allowed to build on sound ground,
to scale-up the team and push
forward quickly.
Distributed collaborative work
improved efficiency: multiple
backgrounds, different expertise
and insights, more reviewers and
helps, more docs and async tasks.
Open processes created commons:
helped to spread the theory, get
feedbacks, removed virtual toll and
IP risk.
Massive gains for Human knowledge
3
1
2

29. Collaborative open science
Machine-checked automation
allows to build on sound ground,
scale-up the team and push
forward quickly.
Distributed collaborative work
improves efficiency: multiple
backgrounds, different expertise
and insights, more reviewers and
helps, more docs and async tasks.
Open processes creates commons:
help to spread the theory, get
feedbacks, remove virtual toll and
IP risk.
Massive gains for Human knowledge
3
2
1

30. … for massive gains for Human knowledge !
Let's bring it everywhere ...
Collaborative open science

31. References (Amazing pictures and quotes also mainly taken from following links *)
● On Shirishi’s ABC proof:
○ http://projectwordsworth.com/the-paradox-of-the-proof/
○ https://www.quantamagazine.org/hope-rekindled-for-abc-proof-20151221/
● On Perelman’s proof:
○ https://www.newyorker.com/magazine/2006/08/28/manifold-destiny
● On Kenji Fukaya foundational theorem problems:
○ https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/
● On Voevodsky error revealed by Carlos Simpson:
○ https://nautil.us/issue/24/error/in-mathematics-mistakes-arent-what-they-used-to-be
● Actually, the HoTT book (and author’s feedback on open science):
○ https://homotopytypetheory.org/
○ http://math.andrej.com/2013/06/20/the-hott-book/
● A superbe, must read article about Voevodsky, univalent foundation, set theory, and Maths roots:
○ https://www.quantamagazine.org/univalent-foundations-redefines-mathematics-20150519/
● On Peter Scholze Liquid Tensor Experiment:
○ https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-experiment/
○ https://www.quantamagazine.org/lean-computer-program-confirms-peter-scholze-proof-20210728/
○ https://github.com/leanprover-community/lean-liquid
* please let me know if it’s not ok!
● The Coq Proof assistant:
○ https://coq.inria.fr/
● Lean theorem prover:
○ https://leanprover.github.io/about/
● Stay Up - Journey of a Free
Software Company
○ https://medium.com/@fanf42/stay-up-5
b780511109d