Time is scarce, and lately I’ve been devoting it mostly to things other than blogging — but I feel the need to emerge from hiding just long enough to acknowledge the shocking death today of the extraordinary mathematician Vladimir Voevodsky at the age of 51.
Voevodsky is best known for finding the right definition of motivic cohomology sometime around the year 2000. This was a Holy Grail, the quest for which had been set in motion by the earth-shattering vision of Alexander Grothendieck. I happen to have been leafing through my well-worn copy of Voevodsky’s book on Cycles, Transfers and Motivic Homology Theories (co-written with Andrei Suslin and Eric Friedlander) when I heard of his death.
More recently, Voevodsky had turned his attention to logic and the foundations of mathematics. Here is video of his talk “What if the Current Foundations of Mathematics Are Inconsistent?”
A brief obituary is here. A brief mathematical autobiography, written by Voevodsky, is here. I might return and add a few personal reminscences.
To what things have you been devoting your scarce time instead of blogging?
Al: I expect to be posting about that in the near future.
It is a little strange to think that the foundations of math might be inconsistent. I couldn’t figure out why he thought that, or how his proposals would somehow improve the situation.
Unrelatedly it seems Monty Hall also passed on this week :-(
http://time.com/4964286/lets-make-a-deal-host-monty-hall-dies-at-96/
https://xkcd.com/1282/
@Roger Schlafly,
The strangeness of VV’s inconsistency suggestion is even more extreme than you describe. In the video, he goes FAR beyond suggesting powerful theories like set theory (ZFC) may be inconsistent. He is actually suggesting first order arithmetic (Peano arithmetic) may be inconsistent.
For me at least, it is extremely hard to imagine how such a simple theory could be inconsistent. It is equally as hard to imagine (though also a bit fun) what the consequences would be, in many domains of intellectual life, if this turns out to be true.
In the section of Voevodsky’s video where he considers the three possible resolutions to the question of the consistency of arithmetic, it is unfortunate that he dismisses Options #2, transcendental knowledge, out of hand. Perhaps this is because he only had acquaintance with “superstitious” versions of this approach?
Husserl’s phenomenology addresses these issues in great depth, with tremendous success IMHO. Various books by Tragesser and Tieszen provide accessible introductions to Husserl’s transcendental phenomenology applied to foundational issues in mathematics.
This is another young death, reminding us of:
Maryam Mirzakhani (1977-2017),
Current Science, 113 (5), 982-983 (10 September 2017).
(Fortnightly Publication of the Indian Academy of Sciences).
http://www.currentscience.ac.in/Volumes/113/05/0982.pdf
Sameen
Sameen Ahmed KHAN
Assistant Professor
Department of Mathematics and Sciences
College of Arts and Applied Sciences (CAAS)
Dhofar University
Post Box No. 2509
Postal Code: 211
Salalah
Sultanate of OMAN http://www.du.edu.om/
http://scholar.google.com/citations?user=hZvL5eYAAAAJ
http://www.scopus.com/authid/detail.url?authorId=8452157800
https://www.researchgate.net/profile/Sameen_Ahmed_Khan
http://SameenAhmedKhan.webs.com/
http://www.imsc.res.in/~jagan/
My expectation is that pretty much all top mathematicians have a firm belief in the truth of what they are doing. It is just weird for someone like him to suggest that math is just one big blob of inconsistent logic.
“What if the Current Foundations of Mathematics Are Inconsistent?” If Zermelo-Fraenkel set theory is inconsistent then I promise to douse myself with gasoline and set myself on fire.
Google “witten milgrom”.