March 10, 2007 6:23 AM Subscribe

Alain Connes has a blog. Terry Tao also has a blog. Two Fields medalists blog on open problems, their views on mathematics, and Tomb Raider. Timothy Gowers doesn't have a blog, but does have a compendium of informal essays on topics like Why is multiplication commutative? If you prefer pictures to words: Faces of Mathematics.

posted by escabeche (15 comments total) 9 users marked this as a favorite

posted by escabeche (15 comments total) 9 users marked this as a favorite

Read that as Alan Colmes, was wondering why hannity didn't post there too, in really big font.

posted by furiousxgeorge at 6:40 AM on March 10, 2007

posted by furiousxgeorge at 6:40 AM on March 10, 2007

posted by kliuless at 6:39 AM PST

one of the consistently perplexing things about foreigners is that they often refuse to speak in English, prefering their own native tongue, or some such...

posted by geos at 6:59 AM on March 10, 2007

geos: "*one of the consistently perplexing things about foreigners is that they often refuse to speak in English, prefering their own native tongue, or some such...*"

The joke, translated, and adapted:

The joke, translated, and adapted:

An old mathematician, is nearing his death, is considering the worthlessness of his life. He will die unknown, having never solved any of the world's great problems. He decides that it would be worth it to sell his soul to the devil in exchange for being remembered after his death. When he meets with the devil, he asks "Is the Riemann hypothesis true?" The devil quickly responds "I don't know what the Riemenn hypothesis is." After a lengthy explanation, the devil furrows his brow and says "It will take som time to find the answer. Return here at midnight, in exactly one month."posted by Plutor at 7:29 AM on March 10, 2007

One month later the mathematician waits at the same place. Midnight comes and goes, and the devil is still nowhere to be seen. Around 2am, the mathematician decides that the devil has given up or forgotten, and begins to leave. Suddenly, the devil appears, disheveled, sweaty, and depressed.

"I cannot accept your soul. I was unable to find the answer. But I have succeeded in finding an equivalent conjecture which will perhaps be easier to solve!"

Technically I guess Connes' blog isn't Connes', but rather was originally Arup Pal's, who later handed it over to Masoud Khalkhali, who got Connes to post on it. Or something. Still, very cool.

Too many of us are afraid to rattle on in public about things that may turn out to be false, or (worse) ill-posed, or (much much worse) trivial. I've always liked Terry Tao's "short stories", in which he tries to isolate the key ideas in some topic, usually someone else's work, without any plan to publish them, but simply to explain something well. I wonder if he got the idea directly from John Baez's TWF.

posted by gleuschk at 7:32 AM on March 10, 2007

Too many of us are afraid to rattle on in public about things that may turn out to be false, or (worse) ill-posed, or (much much worse) trivial. I've always liked Terry Tao's "short stories", in which he tries to isolate the key ideas in some topic, usually someone else's work, without any plan to publish them, but simply to explain something well. I wonder if he got the idea directly from John Baez's TWF.

posted by gleuschk at 7:32 AM on March 10, 2007

Plutor:

Thanks! not a very good joke...

now, how about the grothendiek:

Google sez:

The interdict which strikes the mathematical dream, and through him, all that is not presented under the usual aspects of the finished product, ready with consumption. The little which I learned on the other natural science is enough to make me measure that an interdict of a similar rigour would have condemned them to sterility, or with a progression of tortoise, a little as at the Average Age where it was not question of écornifler the letter of the Holy Scriptures. But I well also know that the major source of the discovery, just like the step of discovered in all its essential aspects, is the same one in mathematics as in any other area or thing of the Universe which our body and our spirit can know. To banish the dream, it is to banish the source - to condemn to an occult existence

posted by geos at 7:37 AM on March 10, 2007

Thanks! not a very good joke...

now, how about the grothendiek:

Google sez:

The interdict which strikes the mathematical dream, and through him, all that is not presented under the usual aspects of the finished product, ready with consumption. The little which I learned on the other natural science is enough to make me measure that an interdict of a similar rigour would have condemned them to sterility, or with a progression of tortoise, a little as at the Average Age where it was not question of écornifler the letter of the Holy Scriptures. But I well also know that the major source of the discovery, just like the step of discovered in all its essential aspects, is the same one in mathematics as in any other area or thing of the Universe which our body and our spirit can know. To banish the dream, it is to banish the source - to condemn to an occult existence

posted by geos at 7:37 AM on March 10, 2007

sorry...

Metafilter: rattling on in public about things that may turn out to be false, or (worse) ill-posed, or (much much worse) trivial.

posted by geos at 7:40 AM on March 10, 2007 [1 favorite]

Metafilter: rattling on in public about things that may turn out to be false, or (worse) ill-posed, or (much much worse) trivial.

posted by geos at 7:40 AM on March 10, 2007 [1 favorite]

Since I was enjoying the remarks on linear algebra, here's a little 3-dimensional vector problem - it's not really a linear algebra problem, though. It's about the vector cross product. Bear with me.

Write down a cross-product of some number of unspecified vectors (go ahead). For example, a 4-fold product:

v_{1}×v_{2}×v_{3}×v_{4}

Now wait a minute; we all know cross product isn't associative. So go ahead and parenthesize that so that it's well-defined. In fact, parenthesize it two different ways. For example:

(v_{1}×v_{2})×(v_{3}×v_{4}) and (((v_{1}×v_{2})×v_{3})×v_{4}

(There are still other ways to parenthesize a four-fold product, and if you have a longer product, you'll have many many choices of different choices of ways to fully parenthesize!)

Now here's a funny thing: in my example, I can**replace all the v's with standard basis vectors** - i's, j's, k's - **so that both products are equal and nonzero**. Viz, letting v_{1} = i , v_{2} = j, v_{3} = i, v_{4} = k, I have:

(i×j)×(i×k) = (((i×j)×i)×k = i.

Question: Is it always possible to this? For any length of product and any two parenthesizations?

posted by Wolfdog at 7:44 AM on March 10, 2007

Write down a cross-product of some number of unspecified vectors (go ahead). For example, a 4-fold product:

v

Now wait a minute; we all know cross product isn't associative. So go ahead and parenthesize that so that it's well-defined. In fact, parenthesize it two different ways. For example:

(v

(There are still other ways to parenthesize a four-fold product, and if you have a longer product, you'll have many many choices of different choices of ways to fully parenthesize!)

Now here's a funny thing: in my example, I can

(i×j)×(i×k) = (((i×j)×i)×k = i.

Question: Is it always possible to this? For any length of product and any two parenthesizations?

posted by Wolfdog at 7:44 AM on March 10, 2007

/begin{rant}

it sort of a paradox. there is alot of energy spent in science creating new "discoveries" but once something is already known it becomes sort of useless (unless someone thinks it can immediately lead to more new discoveries.) but that is sort of built into the US academic model anyway: research production over everything else.

people are fond of quoting newton's "shoulders of giants" but we spend little time trying to really understand the past, even the past 5 years much less what mathematicians were thinking gasp, 20 years ago... much less what happened 100 years ago : see Riemann.

/end{rant}

posted by geos at 7:48 AM on March 10, 2007

it sort of a paradox. there is alot of energy spent in science creating new "discoveries" but once something is already known it becomes sort of useless (unless someone thinks it can immediately lead to more new discoveries.) but that is sort of built into the US academic model anyway: research production over everything else.

people are fond of quoting newton's "shoulders of giants" but we spend little time trying to really understand the past, even the past 5 years much less what mathematicians were thinking gasp, 20 years ago... much less what happened 100 years ago : see Riemann.

/end{rant}

posted by geos at 7:48 AM on March 10, 2007

Seems a strange thing to say -- mathematicians think about math 20 years old and much older, all the time.

posted by escabeche at 8:00 AM on March 10, 2007

posted by escabeche at 8:00 AM on March 10, 2007

posted by Wolfdog at 7:44 AM PST on March 10

*(i×j)×(i×k) = (((i×j)×i)×k = i.*

but, ix((jxi)xk) = 0.

I'm not sure I understand your question... one way to think about the cross product is as the imaginary part of quaternionic multiplication (which is associative), considering 'vectors' as imaginary quaternions.

otherwise, that's why it's called a Lie bracket and not a product...

Seems a strange thing to say -- mathematicians think about math 20 years old and much older, all the time.

posted by escabeche at 8:00 AM PST on March 10

well, it was in rant tags. i think it is often like the joke with the devil, once phrased in terms of new technology, old questions become interesting because of what they say about the new techniques and I think 20 years is about the limit for a research topic... I stand by the assertion that there is very little 'scholarship' about non-antique topics: witness the History and Overview section in the arxiv.

my point was that not much energy is put into explaining what is already understood: if the goal is to get to the peak who cares what the mountain looks like... but it's a very general comment.

posted by geos at 9:10 AM on March 10, 2007

but, ix((jxi)xk) = 0.

I'm not sure I understand your question... one way to think about the cross product is as the imaginary part of quaternionic multiplication (which is associative), considering 'vectors' as imaginary quaternions.

otherwise, that's why it's called a Lie bracket and not a product...

Seems a strange thing to say -- mathematicians think about math 20 years old and much older, all the time.

posted by escabeche at 8:00 AM PST on March 10

well, it was in rant tags. i think it is often like the joke with the devil, once phrased in terms of new technology, old questions become interesting because of what they say about the new techniques and I think 20 years is about the limit for a research topic... I stand by the assertion that there is very little 'scholarship' about non-antique topics: witness the History and Overview section in the arxiv.

my point was that not much energy is put into explaining what is already understood: if the goal is to get to the peak who cares what the mountain looks like... but it's a very general comment.

posted by geos at 9:10 AM on March 10, 2007

I originally misread the post as saying that they had essays on topics such as "Why *isn't* multiplication commutative".

It only took a moment for me to realize that I had misread it, but that moment was shocking, in two different directions simultaneously:

It only took a moment for me to realize that I had misread it, but that moment was shocking, in two different directions simultaneously:

- These jokers won
*Fields Medals*? No way. - Maybe I
*don't*know what "commutative" means? Jeez.

geos: If I give you two parenthesized expressions, and you make a choice of i's, j's, k's to fill in for the v's, you'll usually get different results from plugging in to the two different parenthesizations (as you've shown). Also, your choice will very often make one or the other of the expressions zero.

The question is, if I give you two parenthesized expressions, can you always find a choice of i's, j's, and k's to fill in for the v's which gives the same, nonzero result in both parenthesizations?

posted by Wolfdog at 9:33 AM on March 10, 2007

The question is, if I give you two parenthesized expressions, can you always find a choice of i's, j's, and k's to fill in for the v's which gives the same, nonzero result in both parenthesizations?

posted by Wolfdog at 9:33 AM on March 10, 2007

posted by clevershark at 2:21 PM on March 10, 2007

Scientist at Work | Terence Tao: Journeys to the Distant Fields of Prime - At age 7, Terence Tao was taking high school math classes. At 31, he is one of the world’s top mathematicians, tackling an unusually broad range of problems.

posted by kliuless at 3:06 AM on March 13, 2007

posted by kliuless at 3:06 AM on March 13, 2007

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posted by kliuless at 6:39 AM on March 10, 2007 [1 favorite]