When last we left my humble post, I’d attempted to do the student community a favor by making more widely known the short proof by Moran and Doyle of the existence of a triangulation for a compact 2 manifold. Feeling proud of the service I performed, I went back to my studies and pathetic excuse for a life until my friend JS (his name is being withheld to protect the innocent from harm-namely ME) brought up during a discussion about a possible student conference we’re discussing for Queens College that the matter was quite a bit murkier then it initially looked. Quote from the math society message board:

That's interesting. I was confused because I heard that all surfaces are compact and I believed it without looking at any proofs. Also when I looked at it on wikipedia, they were unclear as to whether or not the surfaces had to be compact.I imagine that since every 2-manifold has a differentiable structure, and every manifold that has a differentiable structure has a piecewise linear triangulation you should be able to triangulate every surface regardless of whether or not it is compact.I could be wrong about a lot of things though, since I don't know the proofs for any of these things and I haven't even glanced at the papers. It would be awesome if you could clarify all this stuff for me and even more awesome if you could talk about it in August.

Leave it to JS to point out the gaping hole in the ceiling. He was right,though-I’d seen Rado’s proof stated for noncompact and compact surfaces, something clearly wasn’t clear here. Does an arbitrary surface admit a triangulation or not? It turns out it depends on what you call a surface-and mathematicians are not of a single mind on this.

This is the definition of a manifold I was always taught: An n dimensional manifold is a Hausdorff topological space that is locally homeomorphic to an open subset of R n . That definition clearly does NOT require n dimensional manifolds to be compact: consider the very simple example of a hyperplane in R n . This is clearly a manifold of dimension n-1, but it’s not compact. It turns out the necessary condition for 2-manifolds to be triangulable is that they must be 2nd countable (i.e. have a countable basis). This in turn implies that the spaces are separable (i.e. has a countable dense subset). If the surface is 2nd countable, then every surface is triangulable by the aforementioned VERY lengthy proof by Rado. ( Yes, to make sure, I DID read Rado’s original proof. There is an excellent statement and discussion of the proof in Zieschang, Vogt and Coldewey’s Surfaces And Planar Discontinuous Groups, Springer-Verlag, 1980). The proof hinges on a decomposition of the surface into disjoint closed regions which are then separated using carefully selected arcs and the Jordan-Shoenflies theorem. It turns out without second countability, there are counterexamples to this construction, namely the so-called Prufer surface, which is a seperable but NOT second countable and therefore non-triangulable complex surface. (Note that for a manifold, second countability implies separability but not vice versa.) A terrific discussion of this counterexample can be found in the paper linked HERE:

http://arxiv.org/PS_cache/math/pdf/0609/0609665v1.pdf

(It turns out this surface is also nonmetrizable ,which has deep consequences for both the general theory of Riemann surfaces and homotopy group of an associated CW complex, namely it doesn’t HAVE one. )

So all we have to do is assume all manifolds are second countable and end of problem, right? WRONG. It turns out differential geometers always define manifolds to be second countable partly to avoid this problem and algebraic topologist and algebraic geometers usually drop the condition since the counterexamples such as a Prufer surface is useful to them. (I’m too damn tired at this point to answer why, just trust me, they like the wacko manifolds……….) So as usual in mathematics-context, context ,context. This is why we need to DEFINE everything carefully people. Since most of us are a lot more interested in the geometry of manifolds then their topology per se-I’m inclined to give them all countable bases and be done with it.

By the way, the geometers have found there’s an even better reason to assume all manifolds are 2nd countable spaces: Since manifolds that are not 2nd countable are not necessarily seperable, the result is that the smooth structure on said manifold MAY NOT BE UNIQUE. That kind of ruins your day if you plan to do differential geometry on them, doesn’t it………….?

Off to bed. Discuss this among yourselves and no need to thank me………………..

## Dealing In Triangles Part Deux: Revenge Of The Sugarman

## Dealing In Triangles Part Deux: Revenge Of The Sugarman

When last we left my humble post, I’d attempted to do the student community a favor by making more widely known the short proof by Moran and Doyle of the existence of a triangulation for a compact 2 manifold. Feeling proud of the service I performed, I went back to my studies and pathetic excuse for a life until my friend JS (his name is being withheld to protect the innocent from harm-namely ME) brought up during a discussion about a possible student conference we’re discussing for Queens College that the matter was quite a bit murkier then it initially looked. Quote from the math society message board:

That's interesting. I was confused because I heard that all surfaces are compact and I believed it without looking at any proofs. Also when I looked at it on wikipedia, they were unclear as to whether or not the surfaces had to be compact.I imagine that since every 2-manifold has a differentiable structure, and every manifold that has a differentiable structure has a piecewise linear triangulation you should be able to triangulate every surface regardless of whether or not it is compact.I could be wrong about a lot of things though, since I don't know the proofs for any of these things and I haven't even glanced at the papers. It would be awesome if you could clarify all this stuff for me and even more awesome if you could talk about it in August.

Leave it to JS to point out the gaping hole in the ceiling. He was right,though-I’d seen Rado’s proof stated for noncompact and compact surfaces, something clearly wasn’t clear here. Does an arbitrary surface admit a triangulation or not? It turns out it depends on what you call a surface-and mathematicians are not of a single mind on this.

This is the definition of a manifold I was always taught: An n dimensional manifold is a Hausdorff topological space that is locally homeomorphic to an open subset of R n . That definition clearly does NOT require n dimensional manifolds to be compact: consider the very simple example of a hyperplane in R n . This is clearly a manifold of dimension n-1, but it’s not compact. It turns out the necessary condition for 2-manifolds to be triangulable is that they must be 2nd countable (i.e. have a countable basis). This in turn implies that the spaces are separable (i.e. has a countable dense subset). If the surface is 2nd countable, then every surface is triangulable by the aforementioned VERY lengthy proof by Rado. ( Yes, to make sure, I DID read Rado’s original proof. There is an excellent statement and discussion of the proof in Zieschang, Vogt and Coldewey’s Surfaces And Planar Discontinuous Groups, Springer-Verlag, 1980). The proof hinges on a decomposition of the surface into disjoint closed regions which are then separated using carefully selected arcs and the Jordan-Shoenflies theorem. It turns out without second countability, there are counterexamples to this construction, namely the so-called Prufer surface, which is a seperable but NOT second countable and therefore non-triangulable complex surface. (Note that for a manifold, second countability implies separability but not vice versa.) A terrific discussion of this counterexample can be found in the paper linked HERE:

http://arxiv.org/PS_cache/math/pdf/0609/0609665v1.pdf

(It turns out this surface is also nonmetrizable ,which has deep consequences for both the general theory of Riemann surfaces and homotopy group of an associated CW complex, namely it doesn’t HAVE one. )

So all we have to do is assume all manifolds are second countable and end of problem, right? WRONG. It turns out differential geometers always define manifolds to be second countable partly to avoid this problem and algebraic topologist and algebraic geometers usually drop the condition since the counterexamples such as a Prufer surface is useful to them. (I’m too damn tired at this point to answer why, just trust me, they like the wacko manifolds……….) So as usual in mathematics-context, context ,context. This is why we need to DEFINE everything carefully people. Since most of us are a lot more interested in the geometry of manifolds then their topology per se-I’m inclined to give them all countable bases and be done with it.

By the way, the geometers have found there’s an even better reason to assume all manifolds are 2nd countable spaces: Since manifolds that are not 2nd countable are not necessarily seperable, the result is that the smooth structure on said manifold MAY NOT BE UNIQUE. That kind of ruins your day if you plan to do differential geometry on them, doesn’t it………….?

Off to bed. Discuss this among yourselves and no need to thank me………………..

## Dealing in Triangles:A Little Known Short Proof Of The Existence of A Triangulation Of A Compact Surface And Other Matters Mathematical...........

Holla. Back on the chain gang with my girl bitching I'm broke ass and wondering why she gives me the time of day. OoOoOoO,I can't wait until she's in England next year getting her Master's. She thinks she's going to go to class and work part time since "school is so much easier then working."I can't wait until she calls me at 3 am long distance crying..................LOL

Before we get to the first mathematical post of the blog-I should introduce myself formally. My name is Andrew L. As for the rest:

Name: Oh,wouldn't you like to KNOW..............

Location:The City That Never Sleeps And Hates King George For Letting 9/11 Happen..................

Age:As old as my tongue and a little older then my teeth.

Gender:Male

Marital Status::If you can ask,you've never seen a picture of me.......................

Hobbies & Interests:Just about EVERYTHING,really-with particular emphasis on anything mathematical or in the hard sciences.(I don't distinguish between pure and applied mathematics and to me,EVERYTHING other then theoretical mathematics is just applied math-biology,physics,chemistry-EVERYTHING.Sue me............) Studying(naturally),Research;tall,curvaceous girls with brains and hearts (a rare commodity to be sure,but worth the search);writing,debating,compassionate friend to the ungrateful masses and whatever else I can accomplish in this meaningless existence to fill up my time until I join the dinosaurs.

Favorite Gadgets:The internet on whatever PC I can steal...............

Occupation: WAS a double major in mathematics and biochemistry-have since entered Queens College of The City University Of New York as a pure mathematics Master's student and hoping to use it as a new beginning to an Ivy League PHD after wrecking my career caring for my late father.Studying topology with Dennis Sullivan next semester if all goes well,that should get me off on the right foot...............

Personal Quote:"God doesn't exist.GET OVER IT..........."

To that,I'd like to add 2 things:

a) I'm learning this career path is MUCH harder then I could have imagined without coffee, which I can't drink anymore. IBS be damned............

b) This past semester,I relearned my love of philosophy under the tutelege of the legendary Saul Kripke in his philosophy of mathematics lectures at the Graduate Center of the City University Of New York.

To expand on these endeared memories-I remember the first day.I showed up with my friend Joey-probably the department's most talented mathematics major-to hear the giant speak. (Check that-I dunno if I'd go so far as to say Joey's the most TALENTED.We have a half a dozen really talented students in our mathematics club. But he's certainly the most advanced of us in his studies and research-and none of us are as dedicated or focused as he is.) Dr.Kripke went on about matters I remembered little about from my philosophy days in his unique,soft spoken and sometimes halting manner-he would stop to think about what he wanted to say and when it did come out,it was amazingly profound. It was clear to me this was a man who cared not only about what he was saying,but took time to stop himself and make sure he got it right.

Joey didn't agree-he looked at me perplexed and disappointed in Kripke's style-and he left and never came back. It was his loss. I'll talk more about it in future posts-but Joey, you missed an experience in this course. Dr.Kripke is giving a second semester by popular demand next semester-sadly,it's at the same time as the deformation theory research seminar myself and several others are already committed to. Unless it can be moved to a half-hour earlier, I'll have to make some hard choices before the fall. It will agonize me to not attend the second semester. But I am a mathematics graduate student and my heart must follow that path for now. I'm torn between my past love and my current path. The fork in the road will have some of my heart's blood on it either way I choose.

Today, I was engrossed with algebraic topology,a subject I swore a blood oath to conquer this summer before I went back. I raced through it last time trying to make a deadline for completion the department forced on me-and ended with a less then stellar grade of B+. Under the circumstances,though-I really should be estatic with it.Considering I crammed most of homology theory in in ONE WEEK,I should be thanking all the Fates and giving my professor John Terilla a kiss for that grade. I'm mad at myself because I know I can do better. Be that as it may-I was looking over Massey's presentation proof of the classification theorum of surfaces. I've always thought it was a beautiful tour-de-force: An incredibly deep result (all compact orientable surfaces(2-manifolds) are homeomorphic to either a) a connected sum of tori ,b) a connected sum of spheres or c) the projective plane) proved with "bare hands" by folding, glueing and pasting carefully selected edges and points on the surface S and showing the resulting quotient spaces have to be equivelent to one of those three. This proof is pretty long-it takes up most of chapter 1 of Massey's *Algebraic Topology:An Introduction *( or *A Basic Course In Algebraic Topology*, the first half of the second book is basically the first with the useless last chapter removed). But it always intrigued me that this proof relies on a fact most topology books take for granted-the fact that all compact surfaces have at least one triangulation. Classically,a trangulation of a surface was exactly that-a homeomorphic decomposition of the surface into a set of oriented disjoint triangles. This step is critical for the classical proof of the classification theorum-there's literally nowhere to begin without it. As I usually do when something mystifies me-I dig into history to see how a concept evolved. Apparently the idea of busting a surface up into a mass of triangles originated with the first rigorous "combinatorial" definition of a surface in the plane by Dehn and Heergard in 1907; they defined a surface S as a simplexical complex where each edge is incident with 2 triangles and each fixed vertex is incident on a set of ordered vertices where each vertex in the set and the fixed vertex define a unique edge of a triangle in S. ( Aren't you glad you're not a topologist living back then?) Classical topology then proceeded on this assumption until mathematicans began to question if the definition was valid i.e. can every surface be covered with edge-pairwise disjoint triangles? The answer turned out to be yes,as was shown by Tibor Rado in 1925-but the proof had 2 major drawbacks: First, it was LONG. 23 PAGES long to be exact. Not exactly the kind of thing you can do in a classroom in a few lectures. The other and much more serious problem was that Rado's proof showed that although a surface can be covered by a set of triangles defined as above, the set need not be finite. Indeed, some mathematicans had already succeeded in producing infinite triangulations of some surfaces before Rado's proof.

It's because of all this BS that modern topologists have come to define triangulations in a much more abstract way: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a *homeomorphism** *h:K to X. Unsurprisingly,even with this definition, most topologists have been reluctant to directly decompose manifolds like they did in the old days;most stick with homology group(or for those sharper tools in the shed. groupoids) based analyses and call it a day. Still-it would be fascinating to have a short,clear proof of the fact to convince oneself that the classification of surfaces isn't mere combinatorial slight of hand.

*blaring of trumpets in the background in anticipation of startling revelation*

Such a simple 2 PAGE proof HAS in fact been found-it was published by P.H. Doyle and D.A. Moran,then both of Michigan State, in an obscure journal in 1968. It's like most good things in life, pretty simple mathematically-and it relies on a very easy generalization of the Jordan curve theorum to convert a covering of 2-cells (open disks) of a surface S into a countably infinite set of simplexical complexes.(Note,though,sadly it hasn't reduced the triangulation to finitely many complexes.Oh well.) I am proud to present the link to the proof,which I have found posted online. It shocks me that this proof is not more commonly known-most mathematicans I've asked referred me with pained expressions to Rado's proof when I asked about taking triangulations on faith. The only mathematican I was able to find in the textbook literature refer to it was James R.Munkres in his book.

So the mystery is no longer so intractable,students! Go forth and add this beautiful result to your toolbox-we no longer need to take this fact on faith! Spread the word, that this momentously practical result can now be shared by all!

http://www.digizeitschriften.de/contentserver/contentserver?command=docconvert&docid=374534

Andrew L.

The Mad Mind

## Dealing in Triangles:A Little Known Short Proof Of The Existence of A Triangulation Of A Compact Surface And Other Matters Mathematical...........

Holla. Back on the chain gang with my girl bitching I'm broke ass and wondering why she gives me the time of day. OoOoOoO,I can't wait until she's in England next year getting her Master's. She thinks she's going to go to class and work part time since "school is so much easier then working."I can't wait until she calls me at 3 am long distance crying..................LOL

Before we get to the first mathematical post of the blog-I should introduce myself formally. My name is Andrew L. As for the rest:

Name: Oh,wouldn't you like to KNOW..............

Location:The City That Never Sleeps And Hates King George For Letting 9/11 Happen..................

Age:As old as my tongue and a little older then my teeth.

Gender:Male

Marital Status::If you can ask,you've never seen a picture of me.......................

Hobbies & Interests:Just about EVERYTHING,really-with particular emphasis on anything mathematical or in the hard sciences.(I don't distinguish between pure and applied mathematics and to me,EVERYTHING other then theoretical mathematics is just applied math-biology,physics,chemistry-EVERYTHING.Sue me............) Studying(naturally),Research;tall,curvaceous girls with brains and hearts (a rare commodity to be sure,but worth the search);writing,debating,compassionate friend to the ungrateful masses and whatever else I can accomplish in this meaningless existence to fill up my time until I join the dinosaurs.

Favorite Gadgets:The internet on whatever PC I can steal...............

Occupation: WAS a double major in mathematics and biochemistry-have since entered Queens College of The City University Of New York as a pure mathematics Master's student and hoping to use it as a new beginning to an Ivy League PHD after wrecking my career caring for my late father.Studying topology with Dennis Sullivan next semester if all goes well,that should get me off on the right foot...............

Personal Quote:"God doesn't exist.GET OVER IT..........."

To that,I'd like to add 2 things:

a) I'm learning this career path is MUCH harder then I could have imagined without coffee, which I can't drink anymore. IBS be damned............

b) This past semester,I relearned my love of philosophy under the tutelege of the legendary Saul Kripke in his philosophy of mathematics lectures at the Graduate Center of the City University Of New York.

To expand on these endeared memories-I remember the first day.I showed up with my friend Joey-probably the department's most talented mathematics major-to hear the giant speak. (Check that-I dunno if I'd go so far as to say Joey's the most TALENTED.We have a half a dozen really talented students in our mathematics club. But he's certainly the most advanced of us in his studies and research-and none of us are as dedicated or focused as he is.) Dr.Kripke went on about matters I remembered little about from my philosophy days in his unique,soft spoken and sometimes halting manner-he would stop to think about what he wanted to say and when it did come out,it was amazingly profound. It was clear to me this was a man who cared not only about what he was saying,but took time to stop himself and make sure he got it right.

Joey didn't agree-he looked at me perplexed and disappointed in Kripke's style-and he left and never came back. It was his loss. I'll talk more about it in future posts-but Joey, you missed an experience in this course. Dr.Kripke is giving a second semester by popular demand next semester-sadly,it's at the same time as the deformation theory research seminar myself and several others are already committed to. Unless it can be moved to a half-hour earlier, I'll have to make some hard choices before the fall. It will agonize me to not attend the second semester. But I am a mathematics graduate student and my heart must follow that path for now. I'm torn between my past love and my current path. The fork in the road will have some of my heart's blood on it either way I choose.

Today, I was engrossed with algebraic topology,a subject I swore a blood oath to conquer this summer before I went back. I raced through it last time trying to make a deadline for completion the department forced on me-and ended with a less then stellar grade of B+. Under the circumstances,though-I really should be estatic with it.Considering I crammed most of homology theory in in ONE WEEK,I should be thanking all the Fates and giving my professor John Terilla a kiss for that grade. I'm mad at myself because I know I can do better. Be that as it may-I was looking over Massey's presentation proof of the classification theorum of surfaces. I've always thought it was a beautiful tour-de-force: An incredibly deep result (all compact orientable surfaces(2-manifolds) are homeomorphic to either a) a connected sum of tori ,b) a connected sum of spheres or c) the projective plane) proved with "bare hands" by folding, glueing and pasting carefully selected edges and points on the surface S and showing the resulting quotient spaces have to be equivelent to one of those three. This proof is pretty long-it takes up most of chapter 1 of Massey's *Algebraic Topology:An Introduction *( or *A Basic Course In Algebraic Topology*, the first half of the second book is basically the first with the useless last chapter removed). But it always intrigued me that this proof relies on a fact most topology books take for granted-the fact that all compact surfaces have at least one triangulation. Classically,a trangulation of a surface was exactly that-a homeomorphic decomposition of the surface into a set of oriented disjoint triangles. This step is critical for the classical proof of the classification theorum-there's literally nowhere to begin without it. As I usually do when something mystifies me-I dig into history to see how a concept evolved. Apparently the idea of busting a surface up into a mass of triangles originated with the first rigorous "combinatorial" definition of a surface in the plane by Dehn and Heergard in 1907; they defined a surface S as a simplexical complex where each edge is incident with 2 triangles and each fixed vertex is incident on a set of ordered vertices where each vertex in the set and the fixed vertex define a unique edge of a triangle in S. ( Aren't you glad you're not a topologist living back then?) Classical topology then proceeded on this assumption until mathematicans began to question if the definition was valid i.e. can every surface be covered with edge-pairwise disjoint triangles? The answer turned out to be yes,as was shown by Tibor Rado in 1925-but the proof had 2 major drawbacks: First, it was LONG. 23 PAGES long to be exact. Not exactly the kind of thing you can do in a classroom in a few lectures. The other and much more serious problem was that Rado's proof showed that although a surface can be covered by a set of triangles defined as above, the set need not be finite. Indeed, some mathematicans had already succeeded in producing infinite triangulations of some surfaces before Rado's proof.

It's because of all this BS that modern topologists have come to define triangulations in a much more abstract way: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a *homeomorphism** *h:K to X. Unsurprisingly,even with this definition, most topologists have been reluctant to directly decompose manifolds like they did in the old days;most stick with homology group(or for those sharper tools in the shed. groupoids) based analyses and call it a day. Still-it would be fascinating to have a short,clear proof of the fact to convince oneself that the classification of surfaces isn't mere combinatorial slight of hand.

*blaring of trumpets in the background in anticipation of startling revelation*

Such a simple 2 PAGE proof HAS in fact been found-it was published by P.H. Doyle and D.A. Moran,then both of Michigan State, in an obscure journal in 1968. It's like most good things in life, pretty simple mathematically-and it relies on a very easy generalization of the Jordan curve theorum to convert a covering of 2-cells (open disks) of a surface S into a countably infinite set of simplexical complexes.(Note,though,sadly it hasn't reduced the triangulation to finitely many complexes.Oh well.) I am proud to present the link to the proof,which I have found posted online. It shocks me that this proof is not more commonly known-most mathematicans I've asked referred me with pained expressions to Rado's proof when I asked about taking triangulations on faith. The only mathematican I was able to find in the textbook literature refer to it was James R.Munkres in his book.

So the mystery is no longer so intractable,students! Go forth and add this beautiful result to your toolbox-we no longer need to take this fact on faith! Spread the word, that this momentously practical result can now be shared by all!

http://www.digizeitschriften.de/contentserver/contentserver?command=docconvert&docid=374534

Andrew L.

The Mad Mind

## Re: A Brief Apology................

I needed to take a minute or so out to apologize to Dr.Fernando Gouvea for posting the small excerpt of his email at my blog. It was done VERY innocently to make a point-nothing private or personal is present in the selection. But I was just alerted by a friend-who's much more internet savvy then I am-that such is grounds for a lawsuit since an email is private communication. I was always under the impression emails, like everything else on the internet, was in principle accessible in the public domain by computer experts. I want to heartily apologize to Dr.Gouvea for my innocent error; the post will be edited appropriately and the excerpt removed.

Again,I'm so VERY sorry.

Next time,meaningful blogging (I HOPE).......................

Andrew L.

## Re: A Brief Apology................

I needed to take a minute or so out to apologize to Dr.Fernando Gouvea for posting the small excerpt of his email at my blog. It was done VERY innocently to make a point-nothing private or personal is present in the selection. But I was just alerted by a friend-who's much more internet savvy then I am-that such is grounds for a lawsuit since an email is private communication. I was always under the impression emails, like everything else on the internet, was in principle accessible in the public domain by computer experts. I want to heartily apologize to Dr.Gouvea for my innocent error; the post will be edited appropriately and the excerpt removed.

Again,I'm so VERY sorry.

Next time,meaningful blogging (I HOPE).......................

Andrew L.

## We Interrupt The Misery Of Human Existence For This Insignificant Blog To Light Meaning In The Darkness Of Mere Being..............

Yello, Netdwellers.

Welcome to my world-such as it is.Who am I? Good question. The answer will slowly emerge on this blog-along with many,many other things. What is this blog going to be about? Well, it'll be about MANY things. That my opinions will be part of the fabric of this place is nothing new-any jackoff with access to a keyboard or touchpad has a blog these days where they rant about everything What makes it unique besides the place where the mathematical sciences live and breathe through my voice. My voice is that of a first year graduate student in pure mathematics-with many issues,ideas and peeves.I decided if the imbeciles who believe George Bush is The Voice Of God and that price of gas is a conspiracy by environmentalists to wean America off gas and take thier precious SUVs from them could have blogs,why not me?

Actually,there was more to it then that. I've never really been a big fan of blogs. Yeah,they're useful for whining in public when no one else gives a damn what you're saying,but they have a tendency to become self-serving and obsessive. So why the sudden 180?

Blame Fernando Q. Gouvêa.

For those who don't know,Dr.Fernando Gouvêa is a professor of mathematics at Colby College in Maine,probably best known for writing the standard introductory text on p-adic analysis. Much more relevant to me,as I've been a native New Yorker all my life and wouldn't know Colby if you dropped me from a chopper into its main walkway-he's the editor,among other things,of the Mathematical Association Of America's Mathematical Sciences Digital Library

webpage. I've been writing for Professor Gouvêa's book review section for almost a year now. Among the books I've reviewed 5 textbooks to date, including Walter Rudin's *Principles Of Mathematical Analysis* and David Watkin's *Topics In Commutative Ring Theory. *For the most part, these reviews have gone pretty smoothly, with the exception of the usual grammar (which I don't care about) and me screwing up my facts (which I DO care about,but I'm not above admitting a screw up). He and I didn't really have a major issue until I tried to submit a review about Dover's wonderful new reissue in cheap paperback of Kenneth Hoffman's *Analysis In Euclidean Space.* I thought such a review would be a wonderful place for me to rant about the criminal cost of scientific textbooks in academia. I submitted the review. A few days later, I got an email from Dr. Gouvêa basically telling me that my review was no place for such commentary and that it exposed the MAA to litigation from the insulted parties i.e. the book publishers. (He DID offer to publish my comments in another forum intended for such commentary,such as FOCUS.)

I was livid and made my displeasure felt in no uncertain terms. In retrospect, I feel somewhat guilty about it. Dr. Gouvea was just doing his job-which,like it or not, it partly to protect the website from legal retaliation over an opinion. But the fact that this was even a real concern is truly tragic in what is supposed to be the Land Of The Free. To make a long story short, after a brief but somewhat heated exchange between us,I revised the review,removed all the commentary and the "safe" version was posted at the website.

I don't blame Professor Gouvea for the incident-he was doing the responsible thing for the website. It's the fact that he felt he HAD to that burned me. In the Land Of King George, Creationist Science, the Patriot Act and the most corrupt administration in our generation's lifetime, freedoms are what they say it is. I remember going to a diner with my late father a few weeks after 9/11-the diner owner was a Middle Eastern immigrant. The guy was practically in terror of any American coming through-he had the place loaded with American flags and said "God bless America" with every other sentence. His eyes looked like he was begging people not to call the police-and meanwhile, people were looking him up and down like he was wearing a .45 Magnum. I remember an Afgani friend of mine running for his life from a group of students throwing rocks at him for 4 blocks in Manhattan at about the same time. I also remember shopping in my local grocery store and a report coming over the radio of them shutting down JFK and beating the crap out of some guy who looked-and I quote-"vaguely Arabic". The time of Red State Rule finally is showing real resistance in the form of the Obama Movement (not so much the man, but the ATTITUDE that's made him the Democratic nominee) . But in the face of all this,the fears of intellectuals voicing thier opinions is a real threat.

We are not free anymore. We Are Property Of The Wealthy. So I can't feel anger towards my editor. Like I said, it's his job to protect the MAA from the dictatorship and the ignorance of those who worship them. As I've said-there's a very real sense of anger-driven change in the air-driven by homeless middle class people who can't heat thier homes and keep burying thier children before thier 25th birthday in a senseless war about ego and power. But change will not come if those who rage against the dying of the light stay silent.

Hence this blog. All opinions here are entirely mine. There is no fact here except those I identify, only passion and opinion, without which there can be no freedom. A change is trying to come. Whether or not it will actualize depends on what Bill Maher so beautifully called The Moron Factor in America. The Moron Factor saddled us with 4 more years of rule this planet will be paying for for centuries. Whether it dooms the Earth with ANOTHER 4 years is a story that will play itself out in the next 5 months.

Hence, the Beginning. There will be more-much more-here in the coming months. Next time-I'll formally introduce myself in a little more detail-and hopefully get to matters mathematical.

And of course,please feel free to contribute to the blog anything you want. And I mean ANYTHING. (Well, not porno, but you get the idea.................)

Ciao,all. A propo, I close with a quote from Kevin Smith:*" Don't have a belief-have an IDEA........................" *

Andrew L.

## We Interrupt The Misery Of Human Existence For This Insignificant Blog To Light Meaning In The Darkness Of Mere Being..............

Yello, Netdwellers.

Welcome to my world-such as it is.Who am I? Good question. The answer will slowly emerge on this blog-along with many,many other things. What is this blog going to be about? Well, it'll be about MANY things. That my opinions will be part of the fabric of this place is nothing new-any jackoff with access to a keyboard or touchpad has a blog these days where they rant about everything What makes it unique besides the place where the mathematical sciences live and breathe through my voice. My voice is that of a first year graduate student in pure mathematics-with many issues,ideas and peeves.I decided if the imbeciles who believe George Bush is The Voice Of God and that price of gas is a conspiracy by environmentalists to wean America off gas and take thier precious SUVs from them could have blogs,why not me?

Actually,there was more to it then that. I've never really been a big fan of blogs. Yeah,they're useful for whining in public when no one else gives a damn what you're saying,but they have a tendency to become self-serving and obsessive. So why the sudden 180?

Blame Fernando Q. Gouvêa.

For those who don't know,Dr.Fernando Gouvêa is a professor of mathematics at Colby College in Maine,probably best known for writing the standard introductory text on p-adic analysis. Much more relevant to me,as I've been a native New Yorker all my life and wouldn't know Colby if you dropped me from a chopper into its main walkway-he's the editor,among other things,of the Mathematical Association Of America's Mathematical Sciences Digital Library

webpage. I've been writing for Professor Gouvêa's book review section for almost a year now. Among the books I've reviewed 5 textbooks to date, including Walter Rudin's *Principles Of Mathematical Analysis* and David Watkin's *Topics In Commutative Ring Theory. *For the most part, these reviews have gone pretty smoothly, with the exception of the usual grammar (which I don't care about) and me screwing up my facts (which I DO care about,but I'm not above admitting a screw up). He and I didn't really have a major issue until I tried to submit a review about Dover's wonderful new reissue in cheap paperback of Kenneth Hoffman's *Analysis In Euclidean Space.* I thought such a review would be a wonderful place for me to rant about the criminal cost of scientific textbooks in academia. I submitted the review. A few days later, I got an email from Dr. Gouvêa basically telling me that my review was no place for such commentary and that it exposed the MAA to litigation from the insulted parties i.e. the book publishers. (He DID offer to publish my comments in another forum intended for such commentary,such as FOCUS.)

I was livid and made my displeasure felt in no uncertain terms. In retrospect, I feel somewhat guilty about it. Dr. Gouvea was just doing his job-which,like it or not, it partly to protect the website from legal retaliation over an opinion. But the fact that this was even a real concern is truly tragic in what is supposed to be the Land Of The Free. To make a long story short, after a brief but somewhat heated exchange between us,I revised the review,removed all the commentary and the "safe" version was posted at the website.

I don't blame Professor Gouvea for the incident-he was doing the responsible thing for the website. It's the fact that he felt he HAD to that burned me. In the Land Of King George, Creationist Science, the Patriot Act and the most corrupt administration in our generation's lifetime, freedoms are what they say it is. I remember going to a diner with my late father a few weeks after 9/11-the diner owner was a Middle Eastern immigrant. The guy was practically in terror of any American coming through-he had the place loaded with American flags and said "God bless America" with every other sentence. His eyes looked like he was begging people not to call the police-and meanwhile, people were looking him up and down like he was wearing a .45 Magnum. I remember an Afgani friend of mine running for his life from a group of students throwing rocks at him for 4 blocks in Manhattan at about the same time. I also remember shopping in my local grocery store and a report coming over the radio of them shutting down JFK and beating the crap out of some guy who looked-and I quote-"vaguely Arabic". The time of Red State Rule finally is showing real resistance in the form of the Obama Movement (not so much the man, but the ATTITUDE that's made him the Democratic nominee) . But in the face of all this,the fears of intellectuals voicing thier opinions is a real threat.

We are not free anymore. We Are Property Of The Wealthy. So I can't feel anger towards my editor. Like I said, it's his job to protect the MAA from the dictatorship and the ignorance of those who worship them. As I've said-there's a very real sense of anger-driven change in the air-driven by homeless middle class people who can't heat thier homes and keep burying thier children before thier 25th birthday in a senseless war about ego and power. But change will not come if those who rage against the dying of the light stay silent.

Hence this blog. All opinions here are entirely mine. There is no fact here except those I identify, only passion and opinion, without which there can be no freedom. A change is trying to come. Whether or not it will actualize depends on what Bill Maher so beautifully called The Moron Factor in America. The Moron Factor saddled us with 4 more years of rule this planet will be paying for for centuries. Whether it dooms the Earth with ANOTHER 4 years is a story that will play itself out in the next 5 months.

Hence, the Beginning. There will be more-much more-here in the coming months. Next time-I'll formally introduce myself in a little more detail-and hopefully get to matters mathematical.

And of course,please feel free to contribute to the blog anything you want. And I mean ANYTHING. (Well, not porno, but you get the idea.................)

Ciao,all. A propo, I close with a quote from Kevin Smith:*" Don't have a belief-have an IDEA........................" *

Andrew L.