Cycling mathematician solves Kato's Conjecture

[Mike Kruger]

Prof Honored for Solving Old Math Problem
http://news.yahoo.com/s/ap/20051227...JkPLBIF;_ylu=X3oDMTA5aHJvMDdwBHNlYwN5bmNhdA--

KANSAS CITY, Mo. - A professor at the University of Missouri-Columbia is
being recognized for solving a math problem that had stumped his peers for
more than 40 years.

The achievement has landed Steven Hofmann an invitation to speak next spring
at the 2006 International Congress of Mathematicians in Madrid, Spain.
"It is like a baseball player being picked for the all-star team," Hofmann
said of the invitation to the event, which is held every four years.

The problem, known as Kato's Conjecture, applies to the theory of waves
moving through different media, such as seismic waves traveling through
different types of rock. It bears the name of Tosio Kato, a now-deceased
mathematician at the University of California-Berkeley, who posed the
problem in research papers first written in 1953 and again in 1961.

.... the problem began to take over his life in 1996. Until he solved it in
2000, it was the last thing he thought about before he went to bed and the
first thing he thought about when he woke. He spent two to eight hours each
day on the problem, working periodically with several colleagues.

"I could be out for a bike ride, and I would be thinking about it," Hofmann
told The Kansas City Star. "Sometimes I would be doing something, get an
idea and have to stop ... and write it down."

 

[[email protected]]

Mike Kruger writes:

> Prof Honored for Solving Old Math Problem

http://tinyurl.com/ba85y

I see why you didn't explain what that problem is or how it relates to
bicycling after looking into its definition:

# Abstract

# Kato's conjecture, stating that the domain of the square root of any
# accretive operator $L=-\dive(A\nabla)$ with bounded measurable
# coefficients in $\mathbb{R}^n$ is the Sobolev space
# $H^1(\mathbb{R}^n)$, i.e. the domain of the underlying sesquilinear
# form, has recently been obtained by Auscher, Hofmann, Lacey,
# M\texsuperscript^{c}Intosh and the author. These notes present the
# result and explain the strategy of proof.

> KANSAS CITY, Mo. - A professor at the University of
> Missouri-Columbia is being recognized for solving a math problem
> that had stumped his peers for more than 40 years.

> The achievement has landed Steven Hofmann an invitation to speak
> next spring at the 2006 International Congress of Mathematicians in
> Madrid, Spain. "It is like a baseball player being picked for the
> all-star team," Hofmann said of the invitation to the event, which
> is held every four years.

> The problem, known as Kato's Conjecture, applies to the theory of
> waves moving through different media, such as seismic waves
> traveling through different types of rock. It bears the name of
> Tosio Kato, a now-deceased mathematician at the University of
> California-Berkeley, who posed the problem in research papers first
> written in 1953 and again in 1961.

> ... the problem began to take over his life in 1996. Until he
> solved it in 2000, it was the last thing he thought about before he
> went to bed and the first thing he thought about when he woke. He
> spent two to eight hours each day on the problem, working
> periodically with several colleagues.

> "I could be out for a bike ride, and I would be thinking about it,"
> Hofmann told The Kansas City Star. "Sometimes I would be doing
> something, get an idea and have to stop ... and write it down."

My impression is that the bicycling connection is tenuous.

Jobst Brandt

 

[Rich Clark]

<[email protected]> wrote in message
news:[email protected]...

> My impression is that the bicycling connection is tenuous.
>
> Jobst Brandt

It was an interesting article, on topic by the definition of the newsgroup.
The tradition of cycling mathematicians is long and rich. Even the
mathematician-hero of the current CBS series "Numb3rs" has been shown
cycling at least once.

I'm aware of the fact that someone has been impersonating you recently, but
it's sometimes hard to tell the difference. Both you and the impersonator
seem to be equally sour lately.

RichC

 

[Tom Keats]

In article <[email protected]>,
[email protected] quotes:

> # Abstract
>
> # Kato's conjecture, stating that the domain of the square root of any
> # accretive operator $L=-\dive(A\nabla)$ with bounded measurable
> # coefficients in $\mathbb{R}^n$ is the Sobolev space
> # $H^1(\mathbb{R}^n)$, i.e. the domain of the underlying sesquilinear
> # form, has recently been obtained by Auscher, Hofmann, Lacey,
> # M\texsuperscript^{c}Intosh and the author. These notes present the
> # result and explain the strategy of proof.

Kewl!! TeX! And apparently composed in emacs! I'm almost tempted to
write a convertion program (in SNOBOL4 of course) that'll format the
above to a dvi-able .tex file. The PERL people could write something
screamingly faster, but mine would be prettier. And probably better
self-documenting.

I'm feeling a wistful, bittersweet nostalgia now.

> My impression is that the bicycling connection is tenuous.

Anyways, WYSIWYG and MS PageMaker, as well as bloated 3.n GL
database-building software has ruined the art of computer
programming. Anyone can monkey around with Oracle, if they've
got the storage. bTrieve took not only know-how, but know-where,
know-why, etc. I'm amused by attempts to similarly use high-tech
to dumb-down bicycling, with stuff like "automated" gear shifting
and re-reinvented "seats". People these days seem to fear knowledge,
or at least, the need to acquire and use it. Technology can be good,
but not when there's a lazy & complacent reliance on it.

I suppose bicycling can be a form of thought-condusive peripatism.
I enjoyed the PBS/Nova treatment of Richard Stoll's "The Cuckoo's Egg",
in which he rode his bicycle for a lot of his primary transportation.
I came away with the impression that that helped his investigative
thought processes.


cheers,
Tom

--
-- Nothing is safe from me.
Above address is just a spam midden.
I'm really at: tkeats [curlicue] vcn [point] bc [point] ca

 

[Claire Petersky]

"Mike Kruger" <[email protected]> wrote in message
news:C%[email protected]...
> Prof Honored for Solving Old Math Problem

> ... the problem began to take over his life in 1996. Until he solved it in
> 2000, it was the last thing he thought about before he went to bed and the
> first thing he thought about when he woke. He spent two to eight hours
> each day on the problem, working periodically with several colleagues.
>
> "I could be out for a bike ride, and I would be thinking about it,"
> Hofmann told The Kansas City Star. "Sometimes I would be doing something,
> get an idea and have to stop ... and write it down."


In the book, "The Origins of Consciousness in the Breakdown of the Bicameral
Mind" (a book I'd recommend, BTW), the author says that there are
traditionally three places, the three Bs, in which great discoveries are
made: Bed, Bath and Bus. In other words, when you are intellectually focused
on the problem, you are stuck. When you have the opportunity to relax, you
can then listen to the intuitive side, and make the leaps of insight needed.

Perhaps a fourth B could be added to the list where great discoveries are
made: the Bike.

--
Warm Regards,

Claire Petersky
http://www.bicyclemeditations.org/
Personal page: http://www.geocities.com/cpetersky/
See the books I've set free at:
http://bookcrossing.com/referral/Cpetersky

 

[[email protected]]

Claire Petersky writes:

>> Prof Honored for Solving Old Math Problem

>> ... the problem began to take over his life in 1996. Until he
>> solved it in 2000, it was the last thing he thought about before he
>> went to bed and the first thing he thought about when he woke. He
>> spent two to eight hours each day on the problem, working
>> periodically with several colleagues.

>> "I could be out for a bike ride, and I would be thinking about it,"
>> Hofmann told The Kansas City Star. "Sometimes I would be doing
>> something, get an idea and have to stop... and write it down."

> In the book, "The Origins of Consciousness in the Breakdown of the
> Bicameral Mind" (a book I'd recommend, BTW), the author says that
> there are traditionally three places, the three Bs, in which great
> discoveries are made: Bed, Bath and Bus. In other words, when you
> are intellectually focused on the problem, you are stuck. When you
> have the opportunity to relax, you can then listen to the intuitive
> side, and make the leaps of insight needed.

> Perhaps a fourth B could be added to the list where great
> discoveries are made: the Bike.

I find the attribution to the "B's" can be reduced to the "B" or
background processing. It is what we do when putting a problem aside
to do something else. When returning to the problem some or all of
the solution has been worked out in the subconscious. I don't believe
in the bus, bath and bed theory but rather in background processing.

The same occurs when bicycling and looking for certain objects such as
wildlife. While just riding along, the background processor monitors
things in peripheral vision and alerts the mind that the item is "over
there". Dreams are a form of background processing.

Jobst Brandt

 

[Rich Clark]

"Claire Petersky" <[email protected]> wrote in message
news:[email protected]...

> In the book, "The Origins of Consciousness in the Breakdown of the
> Bicameral Mind" (a book I'd recommend, BTW), the author says that there
> are traditionally three places, the three Bs, in which great discoveries
> are made: Bed, Bath and Bus. In other words, when you are intellectually
> focused on the problem, you are stuck. When you have the opportunity to
> relax, you can then listen to the intuitive side, and make the leaps of
> insight needed.
>
> Perhaps a fourth B could be added to the list where great discoveries are
> made: the Bike.

I've made no great discoveries in my life (and only the usual number of
rediscoveries), and I rarely feel comfortable moving my focus away from the
road and the surrounding traffic.

But I frequently find that immediately after a ride the solutions to
troubling problems present themselves easily, as if some part of my mind had
been freed to work them by my conscious mind removing focus from them
entirely.

For this reason, I try to schedule meetings for a half-hour after I arrive
at work. I don't do nearly as well at afternoon meetings.

The combination of a relaxed subconscious, a jolt of endorphins, and lowered
blood pressure seems to move my mental functioning to a higher level, at
least for a couple of hours.

RichC

 

[David L. Johnson]

On Tue, 27 Dec 2005 16:42:32 -0800, Tom Keats wrote:

> Kewl!! TeX! And apparently composed in emacs!

Umm, the difference between TeX composed in emacs, and TeX composed on any
other editor, would be what?


> I suppose bicycling can be a form of thought-condusive peripatism.

Y'know, when you try to use fancy words, you ought to turn on your
spellchecker.

--

David L. Johnson

__o | It is probably that television drama of high caliber and
_`\(,_ | produced by first-rate artists will materially raise the level
(_)/ (_) | of dramatic taste in the nation. -- David Sarnoff, 1939

 

[David L. Johnson]

On Tue, 27 Dec 2005 20:35:57 -0500, Rich Clark wrote:

> For this reason, I try to schedule meetings for a half-hour after I arrive
> at work. I don't do nearly as well at afternoon meetings.

If you are more productive in the mornings, by all means schedule meetings
for the afternoon.

--

David L. Johnson

__o | And what if you track down these men and kill them, what if you
_`\(,_ | killed all of us? From every corner of Europe, hundreds,
(_)/ (_) | thousands would rise up to take our places. Even Nazis can't
kill that fast. -- Paul Henreid (Casablanca).

 

[Mike Kruger]

<[email protected]> wrote in message
news:[email protected]...
> Claire wrote:
>> discoveries are made: Bed, Bath and Bus. ... Perhaps a fourth B could be
>> added to the list where great
>> discoveries are made: the Bike.
>
> I find the attribution to the "B's" can be reduced to the "B" or
> background processing. It is what we do when putting a problem aside
> to do something else. When returning to the problem some or all of
> the solution has been worked out in the subconscious. I don't believe
> in the bus, bath and bed theory but rather in background processing.
>
Yes, but 3 B's sounds so much better if you are trying to sell a book.
Just like the 4 P's in marketing (product, place, promotion, price) or the 4
C's (various versions).

The bicycling connection to the solution of Kato's conjecture is tenuous, I
admit.. I do find bicycling a form of background processing. I think it
works because the problem gets stripped down a bit in the background, so the
essential elements can come through without fluff.

While in grad school, I used to keep a pad and pen next to my bed in hopes
of writing down any brilliant thoughts that occured to me while sleeping.
None of these brilliant thoughts survived the cold light of day. I still
keep the pad there, but it's not for deep thoughts so much as stuff like
"buy milk tomorrow".

 

[Tom Keats]

In article <[email protected]>,
"David L. Johnson" <[email protected]> writes:
> On Tue, 27 Dec 2005 16:42:32 -0800, Tom Keats wrote:
>
>> Kewl!! TeX! And apparently composed in emacs!
>
> Umm, the difference between TeX composed in emacs, and TeX composed on any
> other editor, would be what?

Appropriacy.

>> I suppose bicycling can be a form of thought-condusive peripatism.
>
> Y'know, when you try to use fancy words, you ought to turn on your
> spellchecker.

I sincerely hope the rest of your life improovz from now on.


cheers,
Tom

--
-- Nothing is safe from me.
Above address is just a spam midden.
I'm really at: tkeats [curlicue] vcn [point] bc [point] ca

 

[Roy Zipris]

I am reminded of a story, possibly apocryphal, that I once read. A
reporter asked Einstein whether his theory of relativity came to him
all at once or over a long period of time. Einstein, replied, "Both."
Regards, Roy Zipris

 

[catzz66]

Mike Kruger wrote:
> Prof Honored for Solving Old Math Problem
> http://news.yahoo.com/s/ap/20051227...JkPLBIF;_ylu=X3oDMTA5aHJvMDdwBHNlYwN5bmNhdA--
>
> KANSAS CITY, Mo. - A professor at the University of Missouri-Columbia is
> being recognized for solving a math problem that had stumped his peers for
> more than 40 years.
>
> The achievement has landed Steven Hofmann an invitation to speak next spring
> at the 2006 International Congress of Mathematicians in Madrid, Spain.
> "It is like a baseball player being picked for the all-star team," Hofmann
> said of the invitation to the event, which is held every four years.
>
> The problem, known as Kato's Conjecture, applies to the theory of waves
> moving through different media, such as seismic waves traveling through
> different types of rock. It bears the name of Tosio Kato, a now-deceased
> mathematician at the University of California-Berkeley, who posed the
> problem in research papers first written in 1953 and again in 1961.
>
> ... the problem began to take over his life in 1996. Until he solved it in
> 2000, it was the last thing he thought about before he went to bed and the
> first thing he thought about when he woke. He spent two to eight hours each
> day on the problem, working periodically with several colleagues.
>
> "I could be out for a bike ride, and I would be thinking about it," Hofmann
> told The Kansas City Star. "Sometimes I would be doing something, get an
> idea and have to stop ... and write it down."
>
>
>
>

I overlooked this thread at first, not being a mathematician, thinking
it was going to be about the O J Simpson trial.

 

[Paul Turner]

catzz66"

> I overlooked this thread at first, not being a mathematician, thinking it
> was going to be about the O J Simpson trial.

I thought Kato's conjecture was, "Shouldn't Britt Reid be the sidekick? I'm
the one who knows kung fu."

--
Paul Turner

 

[Leo Lichtman]

"Paul Turner" wrote: I thought Kato's conjecture was, "Shouldn't Britt
Reid be the sidekick? (clip)
^^^^^^^^^^^^^^^
And I confused it at first with Tonto's conjecture, but that was, "What do
you mean 'We,' Kimo Sabe?"

 

[Ron Hardin]

Tom Keats wrote:
> Kewl!! TeX! And apparently composed in emacs! I'm almost tempted to
> write a convertion program (in SNOBOL4 of course) that'll format the
> above to a dvi-able .tex file. The PERL people could write something
> screamingly faster, but mine would be prettier. And probably better
> self-documenting.

I have SNOBOL3 on my UNIX-PC, which may still work, at least
it was still working when it went into the closet.

man sno

--
Ron Hardin
[email protected]

On the internet, nobody knows you're a jerk.

 

[[email protected]]

Claire Petersky wrote:
> "Mike Kruger" <[email protected]> wrote in message
> news:C%[email protected]...
> > Prof Honored for Solving Old Math Problem
>
> > ... the problem began to take over his life in 1996. Until he solved it in
> > 2000, it was the last thing he thought about before he went to bed and the
> > first thing he thought about when he woke. He spent two to eight hours
> > each day on the problem, working periodically with several colleagues.
> >
> > "I could be out for a bike ride, and I would be thinking about it,"
> > Hofmann told The Kansas City Star. "Sometimes I would be doing something,
> > get an idea and have to stop ... and write it down."
>
>
> In the book, "The Origins of Consciousness in the Breakdown of the Bicameral
> Mind" (a book I'd recommend, BTW), the author says that there are
> traditionally three places, the three Bs, in which great discoveries are
> made: Bed, Bath and Bus. In other words, when you are intellectually focused
> on the problem, you are stuck. When you have the opportunity to relax, you
> can then listen to the intuitive side, and make the leaps of insight needed.
>
> Perhaps a fourth B could be added to the list where great discoveries are
> made: the Bike.

In my experience the bike beats the bus anyday I did some of my
best thinking for my master's thesis while cycling to and from the
university.
John Kane, Kingston ON Canada

 

[Tom Keats]

In article <[email protected]>,
"[email protected]" <[email protected]> writes:

> In my experience the bike beats the bus anyday

That's true in a number of ways. Not the least of
which is reduced exposure to germ-laden sick people.


cheers,
Tom

--
-- Nothing is safe from me.
Above address is just a spam midden.
I'm really at: tkeats [curlicue] vcn [point] bc [point] ca

 

[Tom Keats]

In article <[email protected]>,
Ron Hardin <[email protected]> writes:

> I have SNOBOL3 on my UNIX-PC, which may still work, at least
> it was still working when it went into the closet.
>
> man sno

A version is available here, but it's a Java implementation.
http://serl.cs.colorado.edu/~dennis/software/s3.html


cheers,
Tom

--
-- Nothing is safe from me.
Above address is just a spam midden.
I'm really at: tkeats [curlicue] vcn [point] bc [point] ca

 

[David L. Johnson]

On Wed, 28 Dec 2005 00:48:48 -0800, Tom Keats wrote:

> In article <[email protected]>,
> "David L. Johnson" <[email protected]> writes:
>
>> Y'know, when you try to use fancy words, you ought to turn on your
>> spellchecker.

> So, despite your momentary acerbity, I still like you, and I
> understand how life experience can take its toll. You're still
> a good guy, with good & valid things to say, ya grouch, ya!

Sorry to **** you off, Tom. I kinda thought that the "thought-condusive
peripatism" was a bit over the top. Forget I said anything.

BTW, I still don't see how you can tell whether or not TeX was composed in
emacs. But then, I hate emacs. I never could see the use of an editor
that required you to have a manual open on your lap, to use the darn thing.

Happy New Year, anyway.

--

David L. Johnson

__o | If all economists were laid end to end, they would not reach a
_`\(,_ | conclusion. -- George Bernard Shaw
(_)/ (_) |