Vladimir Voevodsky has died
ias.edu
ias.edu
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.
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.”
Well worth reading.
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.
I am not a US-American, so can you elaborate?
Quite the opposite: If you keep in mind that in many large German cities (such as Munich, Stuttgart and Berlin) it is hard to find an apartment, in particular if it is supposed to be affordable, I can imagine quite well that "living to the logical consequences that it is not worth the time to look for an apartment" could easily give him lots of sympathizers in Germany.
On the other hand Voevodsky would probably get in trouble with German law (Meldegesetz (https://de.wikipedia.org/wiki/Meldegesetz) - I don't know an "official" English translation of this word, but perhaps "registration law" might fit). But always keep in mind when talking about Germany, what Germans think and what the German laws say are two very different animals.
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Concerning your point
> There is no stigma against homeless people in your country?
monort's description of Voevodsky's lifestyle does not sound like the lifestyle of a homeless person. So the argument void. But to give nevertheless a point: I don't think there is a lot of a stigma against homeless people in Germany. The stigma is rather against things that accompany being homeless like drinking, rarely showering etc.
EDIT: To elaborate on the point that I don't think there is a lot of a stigma against homeless people in Germany: I (as an academic) actually know someone who was homeless for a longer time in life (at least 6 months, probably much more) and also had an interesting discussion about homeless people face in Germany with a homeless person who was begging for money when I was waiting for a train that was massively delayed.
The text " living and sleeping in the office is a terrible taboo and social stigma" is not phrased well. The issue with living at your office is much more due to liability reasons. If someone is allowed to live at their office, then the organization might be liable for anything that person does, or anything that happens to that person, even when not working. Also, as an organization it looks bad to have your graduate students / researchers be homeless, not to other grad students or researchers on an individual level, but in the sense that outsiders will react "I do not want to work at Harvard because they work their researchers so hard / pay their researchers so little that they have to live at their office."
This also happened about 25 years ago, when there was more of a stigma in the US for living an untraditional lifestyle. It's much, much more common these days for people in their 20s to live semi-homeless (e.g. in a car) and housing usually costs a lot more know, adjusted for inflation.
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.
We just lost the Hilbert of the new Hilbert program.
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.
One of Voevodsky's views was that all the foundation for a dependently typed formalization of maths is already there, and that it mainly needs to be organized in a better way (cf his unimath project).
"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...
French transcription here: http://smf4.emath.fr/Publications/Gazette/2014/142/smf_gazet...
https://groups.google.com/forum/#!topic/homotopytypetheory/K...
> 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...
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.
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.
Was he sick ? Was it cancer ?
"Vladimir Voevodsky alcohol" gives zero results.
Can we let one person's death be a little respectful? Just once.
Regards
A friend of mine died when he was only 24 due to a sudden brain aneurysm in his sleep, and in that same year I had two other friends commit suicide (in fairness one was questionable, but it was by a train). I grappled with that for well over a year, to the point that it caused me a great deal of anxiety and insomnia for someone apparently healthy to die that young. It fundamentally crushed a lot of my own personal sense of control and security. One of the most difficult things for me to process was the utter lack of information - how did he die? Did he have chronic headaches and didn't check? Is there a way I could consider him accountable for it? Something to understand the situation would give me greater closure than the reality that people simply die, sometimes quite suddenly, for no predictable reason at all.
This is an extreme example for me to give, but the message is this: I understand that you're upset by this individual dying and the way others reacted to it (take a look at a comment I made here when John Nash died in a car accident in 2015: https://news.ycombinator.com/item?id=9597349). But what you're doing is policing other peoples' emotions, and they have a right to react to the death by speculating about its causes. That is a natural and very common response that you cannot artificially remove.
Thanks for putting this into perspective. My comments in this post are pretty embarrassing. I wish I could delete them. But mistakes are too easy to run from. Apologies regardless.
It was quite selfish to make a ruckus like that, so I think I was the disrespectful one. The focus should be on Vladimir and his life.
He was a great mathematician. RIP.
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.
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.
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.
I've never heard of him so I'm curious, being a Field medalist and all.
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.
I once attended a talk on the subject by Michael Freedman who is with Microsoft Station Q. They are trying to build just such a computer.
Not sure who else might have a device that can instantiate in some physical way a Quantum Superposition, but Microsoft showed such a device during that discussion: https://youtu.be/d7f_GZsQMpA?t=1h3m6s
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.
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]
In Ancient Rus, it was strictly a military rank, and simply meant "general" (or something roughly equivalent - a commander of a large military force, at the level where large-scale strategic considerations are as important as battlefield tactics).
That word "voevoda" existed before Russians were even a thing.
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".