Vladimir Voevodsky has died

https://www.ias.edu/news/2017/vladimir-voevodsky

by slbenfica • 9 years ago

397 62 9 years ago

danharaj3• 9 years ago

This is a massive loss for mathematics and the world :(

Although I've never met him, I've been strongly influenced by his writings and contributions to math, especially his down to earth blog posts.

auggierose• 9 years ago

It is. I wonder what this will mean for Homotopy Type Theory.

zitterbewegung• 9 years ago

I think that people will still develop the theory. It still needs a bunch of work but it seems popular enough to stay around.

defen• 9 years ago

That's two Fields Medalists taken entirely too early in the past 3 months (the other being Maryam Mirzakhani). Very sad.

SomeStupidPoint2• 9 years ago

A great loss for mathematics!

I became familiar with his work through HoTT --

More recently he became interested in type-theoretic formalizations of mathematics and automated proof verification. He was working on new foundations of mathematics based on homotopy-theoretic semantics of Martin-Löf type theories. His new "Univalence Axiom" has had a dramatic impact in both mathematics and computer science.

And some of his online lectures outlining his reasoning and motivations became greatly influential on my own interests.

saganus• 9 years ago

Could you expand on his work, related to CS and/or his influence in your work?

I've never heard of him so I'm curious, being a Field medalist and all.

danharaj3• 9 years ago

Voevodsky won the Fields medal for A^1 homotopy theory: https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory

It's quite technical to describe what that is, but the general idea is that he imported homotopy theory, a fundamental concept in mathematics which allows you to describe topology with an algebra of paths in that geometry, to algebraic geometry. This allowed him to solve some major open problems in the field.

Topology is essentially the study of continuity and the properties that are invariant of objects under continuous deformation. The prototypical example of a topological space is the continuum although the concept of continuity has been generalized a great deal. Homotopy is the study of continuous paths which are defined as continuous functions from the unit interval into topological spaces, as well as higher dimensional "paths". It turns out that these paths have a rich algebraic structure which give you a strong idea of what the "shape" of the space is like.

Classically algebraic geometry is the study of solutions to systems of polynomial equations over systems of numbers related to the integers, rationals, reals, and complex numbers. More modernly, it is the study of models of theories that resemble the previously mentioned theory in fundamental ways. For example, the theory of elliptic curves which underlies some of our modern cryptography is part of algebraic geometry.

throwaway5752• 9 years ago

I'm in a similar situation, I hope these couple of pieces about univalent foundations are useful: https://www.ias.edu/ideas/2014/voevodsky-origins, https://www.ias.edu/ideas/2013/awodey-coquand-univalent-foun...

sddfd• 9 years ago

Not the op, but basically Voevodsky realized that the notion of equality in type theories as implemented in Coq or Agda is fundamentally more fine grained than what mathematicians are used to thinking of. This mismatch causes problems when formalizing mathematics in type theory.

Voevodsky proposed the univalence axiom which can be used to obtain more equalities and gave rise to the field of homotopy type theory (HoTT).

An intuition about the univalence axiom is that it allows to regard isomorphic types as equal. (This isn't entirely correct but gives a good intuition). The consequences of the axiom are severe (probably in a good way) but a lot more research is needed.

The hopes are that the work on HoTT will make it easier to formalize mathematics and in turn make it easier to verify software.

grondilu• 9 years ago

That's young. What happened?

j-pb• 9 years ago

F*. This is an unfatomable loss both him as a amazing person and him as an outstanding mathematician.

We just lost the Hilbert of the new Hilbert program.

tuxguy• 9 years ago

Does anyone know what happened ?

Was he sick ? Was it cancer ?

shivak• 9 years ago

He struggled deeply with alcoholism, but the cause of his death has not been announced.

AnkhMorporkian• 9 years ago

I cannot confirm this in any way, but one of my Russian friends told me he had Cirrhosis and was being treated for it.

downandout• 9 years ago

It’s a frightening testament to the power of addiction that even some of the smartest, most logical people in the world cannot control some of their own extremely illogical decisions.

sillysaurus33• 9 years ago

Can we not? Do you think that they would have wanted the thread about their death to be filled with speculation about whether he killed himself or drank himself to death? No one knows anything, and even if they did it would be impolite to offer up that information.

He was a great mathematician. RIP.

widdma• 9 years ago

I think if he did have mental health problems, like many others in the field, it's now more than ever to raise the point. If he didn't it doesn't hurt to raise the issue, because it is genuine.

If you suffer from anxiety and/or depression, there is help. Talk to someone. You're not alone, and you don't need to suffer alone.

dsacco2• 9 years ago

Can we not?

He was a great mathematician. But I'm still interested in how he died. So actually, can we? You're free not to participate in that which you find distasteful, but we're adults here.

mathgenius2• 9 years ago

The name Voevodksy comes from two old russian words: vodit, which means "to lead", and voena which means war. So, voevod, would mean something like "war leader", or general. (Source: russian friend that I just consulted.)

pandaman• 9 years ago

The word is voevoda (воевода) and, indeed, originally meant "a general". https://en.wikipedia.org/wiki/Voivode

avenoir• 9 years ago

It seems like the word "Voevoda", at least in Ancient Rus, was the highest military rank given to someone who exceled in very specific areas of warfare.

For instance, the Voevoda of Defense (modern minister of defense?) would figure out how to fortify and defend a city from assault. Similarly, a Reconnaissance Voevoda would be sent to figure out the position and the size of an enemy. So it's not necessarily the general, although it looks like the highest class of Voevoda "Bolshoi Voevoda" or "Big Voevoda" could probably be compared to modern day Generals. I'm not entirely sure if one could progress up the ranks or if they just sort of branched out. Very interesting read here (in Russian) [1]

[1] https://ru.wikipedia.org/wiki/воевода

robotomir• 9 years ago

old russian words

That word "voevoda" existed before Russians were even a thing.

iagooar• 9 years ago

In Polish, there is the word "wojewoda" (Polish uses "w" where in English or Latin languages you would use a "v"). Historically it meant the same as in Russian, but nowadays it is the title of the governor of a province.

To make things even more interesting, Poland is actually divided in regions / provinces called "województwa" (plural), or literally "lands that belong to the wojewoda". A "województwo" (singular) is more or less the equivalent of a German "Land" or US American "states".

dkural• 9 years ago

:( Such a huge loss to the world. What a terrible year, to lose such bright and young mathematicians.

robinhouston• 9 years ago

This interview (link below) gives some interesting insight into his work and motivations. It’s in Russian, but Google Translate does a pretty good job with it.

http://baaltii1.livejournal.com/198675.html

Among many other things, he describes some unusual experiences in 2006–7 that clearly had a powerful impact on his thinking:

[Translation by Google] “I had in a few months acquired a very considerable experience of visions, voices, periods when parts of my body did not obey me and a lot of incredible accidents. The most intense period was in mid-April 2007 when I spent 9 days (7 of them in the Mormon capital of Salt Lake City), never falling asleep for all these days.

Almost from the very beginning, I found that many of these phenomena (voices, visions, various sensory hallucinations), I can control. So I was not scared and did not feel sick, but perceived everything as something very interesting, actively trying to interact with those "creatures" in the auditorial, visual and then tactile spaces that appeared (themselves or by call) around me. I must say, probably, to avoid possible speculations on this topic, that I did not use any drugs during this period, tried to eat and sleep a lot, and drank diluted white wine.”

gtt• 9 years ago

I'm getting access denied on this entry. Could you copy-pase it somewhere else?

jlgaddis• 9 years ago

Try this (may have to run it through Translate): http://archive.is/b4gHd

coffeemug• 9 years ago

Thank you for posting this! I'm lucky to be able to read the interview in the original (for those who can't, google translate does a reasonable job). Part I: http://archive.is/b4gHd. Part II: http://archive.is/NtBiy.

Well worth reading.

carlob• 9 years ago

During grad school I had to spend a year at IAS, because my advisor was there on sabbatical.

The Institute is not very grad-student-friendly (by design): there are a lot of cultural and bureaucratic hurdles a student might find there, such as refusing any affiliation, both for visa and academic purposes, not offering proper office place, and a certain aloofness of the faculty.

My experience was a bit better than the norm at the then-new School for System Biology, but I have a lot of great memories of discussion with Voevodsky over lunch. He had found in me and another grad student from the same group two people interested in the use of computers in science, and he didn't care that we completely out of our depth discussing the foundations of mathematics. We were both just very interested in how computers were transforming science, and he kept telling us that the same revolution was going to happens for mathematics as well, despite the resistance of some of his colleagues.

These discussions sparked an interest I still have for proof verification, automatic theorem proving, and type systems.

Here's to hoping his legacy lives on and that the revolution he helped start brings on a new era in mathematics.

mathgenius2• 9 years ago

https://github.com/vladimirias

monort• 9 years ago

Amusing anecdote from the life of Voevodsky (https://lj.rossia.org/users/tiphareth/2097217.html):

Voevodsky was too lazy to search for an apartment, so he lived in his office (at Harvard each graduate student gets a personal office) and slept on the roof. Unfortunately, the windows of dean office (Willy Schmid) had direct view at that roof. Volodya didn't adhere to the usual day routine (and didn't adhere to anything at all), sometimes he slept during the dean office hours. Some day Schmid looked through the window and saw a roof and Voevodsky was sleeping at the roof. It has to be said, that living and sleeping in the office is a terrible taboo and social stigma in America, so Schmid was outraged. Voevodsky was almost expelled, but everything turned out well, though he was forced to rent an apartment and he has lived there from then on.

wolfgke2• 9 years ago

It has to be said, that living and sleeping in the office is a terrible taboo and social stigma in America

I am not a US-American, so can you elaborate?

aswanson2• 9 years ago

Not having a home in general is looked down upon here. Everyone is expected to have their place of work/study to be separate from the place where they bathe, sleep, etc.

umanwizard• 9 years ago

There is no stigma against homeless people in your country?

ynotyman• 9 years ago

I was a grad student at Harvard... let me correct a few things. First, Wilfred Schmid would probably never be called Willy. It's a funny idea though. Like calling the Queen of England Lizzy. He wasn't the dean... he might have been the dept chair at the time. As for living/sleeping at the office -- it's not a "terrible taboo and social stigma in America". (I'm American). But it's not allowed due to problems with hygiene (no showers in most bathrooms), smell, clutter, disruption at odd hours, etc.. So it's not allowed in any workplace. When it happens, the response of most departments is sympathy and an effort to find the cause and find the person a place to live. And grad students at Harvard are financially supported well enough to afford a decent room in the area. I mean... I wasn't rich, but lived comfortably in apartments shared with a few other grad students.

arkvet• 9 years ago

I was a grad student at Harvard in the math department too. In my time there was a student who decided he was going to sleep in his office (I don't think sleeping outside is such a great option in the New England winter). These offices are small - there's a desk, then room for a chair, and shelves for books above the desk. They are essentially for solo work. Anyway, this student was handling it fine - showering in the university gym and doing laundry in the basement of the nearby graduate residence halls, and rolling his bed up in the morning so as not to be reported by the cleaning staff. Then his girlfriend visited from abroad and she was so appalled with the suggestion that they bed down together essentially under his desk, that he ended up having to pay for them to stay for a week in a decent hotel. After that he found himself an apartment-share pretty quick.

anticodon• 9 years ago

His own words in this interview: http://www.polit.ru/article/2006/08/22/voevod/ (in Russian)

trhway• 9 years ago

As for living/sleeping at the office -- it's not a "terrible taboo and social stigma in America". (I'm American). But it's not allowed due to problems with hygiene (no showers in most bathrooms), smell, clutter, disruption at odd hours, etc.. So it's not allowed in any workplace.

And as a Russian, my impression is somewhat similar to the original - in order to avoid all the problems that you mentioned it was made into that "terrible taboo". I mean many (if not pretty much any) taboo had pretty reasonable rationale at the time and place of its creation.

fermigier2• 9 years ago

From http://www.mathunion.org/ICM/ICM2002.1/Main/icm2002.1.0099.0... (2002):

"Among his main achievements are the following: he defined and developed motivic cohomology and the A1-homotopy theory of algebraic varieties; he proved the Milnor conjectures on the K-theory of fields."

Quite an achievement, indeed...

marchdown• 9 years ago

Oh no! I was following his work closely and had high hopes for him delivering on his vision: type theory and constructive notion of equality not getting in the way of doing mathematics with computer, but helping us along. It will hopefully will be picked up by his collaborators.

cdetrio2• 9 years ago

Reading the story[1] about Voevodsky, I was reminded of how Bertrand Russell described Gottlob Frege as "almost superhuman":

As I think about acts of integrity and grace, I realise that there is nothing in my knowledge to compare with Frege’s dedication to truth. His entire life’s work was on the verge of completion, much of his work had been ignored to the benefit of men infinitely less capable, his second volume was about to be published, and upon finding that his fundamental assumption was in error, he responded with intellectual pleasure clearly submerging any feelings of personal disappointment. It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known. [2]

And how rare it is to see such "exceptionally honest" academic dialogue as Frege's:

Frege starts his analysis by this exceptionally honest comment : "Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr Bertrand Russell, just when the printing of this volume was nearing its completion" [3]

Voevodsky too, upon finding himself in the same position as Frege, reacted with a super-human level of integrity and intellectual honesty:

In 1998, the American mathematician Carlos Simpson published a paper indicating there might be a mistake in Voevodsky and Kapranov’s 1990 result. For years Voevodsky sifted through the details without making much progress. He remained convinced the result was right. Then, in the autumn of 2013, as the leaves changed color and summer gave way to autumn, he made a breakthrough. Of sorts. He confirmed the error. The important result was no longer quite so important.
“It is plainly wrong. The main theorem is incorrect,” he says. “It’s not that there is some gap in the proof. It’s that the main theorem is plainly wrong.” The mistake, he explains, was in failing to question the obvious. “We had proved that an assertion was indeed true in all of the difficult cases, but it turned out to be false in the simple case. We never bothered to check.” In confirming the error, he added an addendum to the original citation in his official publications list—“Warning: The main theorem of this paper was shown by Carlos Simpson to be false.” [1]

It is all the more remarkable that he spent years of working through painstaking details to prove to himself that he was wrong. And rather than quietly issuing a retraction, he shouted it from the rooftops, leading a heroic charge to get mathematicians to stop hand-waving with English-language proofs, and start writing code. [4]

And I now do my mathematics with a proof assistant. I have a lot of wishes in terms of getting this proof assistant to work better, but at least I don’t have to go home and worry about having made a mistake in my work. I know that if I did something, I did it, and I don’t have to come back to it nor do I have to worry about my arguments being too complicated or about how to convince others that my arguments are correct. I can just trust the computer. There are many people in computer science who are contributing to our program, but most mathematicians still don’t believe that it is a good idea. And I think that is very wrong.[5]

1. https://nautil.us/issue/24/error/in-mathematics-mistakes-are...

2. https://plato.stanford.edu/entries/russell-paradox/

3. https://en.wikipedia.org/wiki/Russell%27s_paradox#cite_note-...

4. https://www.quantamagazine.org/univalent-foundations-redefin...

5. https://www.ias.edu/sites/default/files/pdfs/publications/le...

cdetrio2• 9 years ago

Univalent Foundations is apparently controversial. It appeared to come to a head a couple years ago when a lively debate played out in the comments of a blog (including a comment by Voevodsky himself): https://mathematicswithoutapologies.wordpress.com/2015/05/13...

iheartmemcache• 9 years ago

(To contextualize [hopefully without misrepresenting their positions], Lurie and Vlad both think/thought that axiomatic set theory is not a proper mathematical foundation. Their disagreement lays in how to construct the reformalization of mathematics (Univalent Foundations vs Higher Topos Theory).

A (very rough) analogy would be the general consensus of climate change scientists agreeing on global warming being the result of the rapid re-release of fossil fuels into the ecosystem but disagreeing on whether the cause is from shipping container barges or the rapid industrialization of the BRIC nations.)

Here's what's regarded as the seminal resource[1] on Univalent Foundations. "Homotopy Type Theory: Univalent Foundations of Mathematics" which Vlad was working on at IAS. Not only mathematicians but logicians and computer scientists have made large contributions to this work. Names like Awodey and Robert Harper will certainly sound familiar to the C.S. crowd here.

[1]https://homotopytypetheory.org/book/

fermigier2• 9 years ago

A great video interview of VV (2014) discussing his career, in english (subtitled in French) is available here: https://vimeo.com/99586217

French transcription here: http://smf4.emath.fr/Publications/Gazette/2014/142/smf_gazet...

doall2• 9 years ago

What a huge loss :(

I have been dreaming that one day we will have a fully developed type system for programming languages based on HoTT and I can develop a new language based on that.

doall2• 9 years ago

Comments from the members of Homotopy Type Theory - Google Groups.

https://groups.google.com/forum/#!topic/homotopytypetheory/K...

Vladimir Voevodsky has died

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