**Mathematical Elitism: A Discussion**

Mathematicians are often perceived as elitist, and this perception can be both true and misleading. The notion that mathematics is inherently elitist stems from the fact that many mathematical texts, particularly those considered rigorous and complex, are written with the intention of challenging readers to think deeply about abstract concepts. These books often require a significant amount of effort and dedication to fully comprehend, which can create an impression that only a select few can appreciate them.

I recently came across a book on duty cuts in an appendix of a more modern edition of "Complex Analysis" by Henri Cartan. This text is considered extremely rigorous and complex, making it inaccessible to all but the most dedicated readers. However, this does not mean that mathematicians are elitist; rather, it highlights the challenges inherent in writing about abstract mathematical concepts.

To illustrate this point, I drew upon my personal experience with a friend who has a PhD in mathematics. He is an accomplished individual who can easily grasp complex ideas, but he chose to read "Complex Analysis" from start to finish without attempting any of the exercises. This anecdote demonstrates that even those with advanced mathematical knowledge can find certain texts daunting and unapproachable.

Furthermore, I encountered another classic text on complex variables, "Elementary Theory of Analytic Functions of One or Several Complex Variables," written by Henri Cartan. The book is intense and requires a high level of dedication to understand its contents. However, the rigors of this text do not necessarily imply elitism; rather, they underscore the complexity and nuance of mathematical concepts.

In conclusion, while some mathematicians may be perceived as elitist due to their focus on rigorous and complex texts, this perception is not entirely accurate. Mathematics can be beautiful and rewarding, even for those who struggle with its more challenging aspects. As the author suggests, sitting down with a book like "Complex Analysis" or another rigorous text and working through it slowly can yield significant insights and understanding.

**A Closer Look at Classic Texts**

To gain a deeper understanding of mathematical elitism, let us examine four classic texts on various subjects: "Complex Analysis" by Henri Cartan, "Elementary Theory of Analytic Functions of One or Several Complex Variables," as well as two other notable works. These books are considered classics in their respective fields and offer a glimpse into the challenges faced by mathematicians who pursue rigorous and complex mathematical knowledge.

**Book Recommendations**

For those interested in delving deeper into mathematical texts, I recommend the following four books:

1. "Complex Analysis" by Henri Cartan

2. "Elementary Theory of Analytic Functions of One or Several Complex Variables"

3. "Advanced Calculus" (also known as Undergraduate Analysis)

4. "Real and Complex Analysis"

These texts offer a range of challenges, from the rigorous and complex to the more accessible and introductory.

**The Elitism Debate**

To address the question of whether mathematicians are elitist, we must consider various perspectives and experiences. Some may argue that mathematics is inherently elitist due to its complexity and rigors. Others may contend that this perception stems from the fact that certain texts are written with challenging audiences in mind.

As for my own stance on the matter, I believe that mathematics can be beautiful and rewarding, even for those who struggle with its more challenging aspects. However, it is also true that some mathematicians may become carried away by their intellectual pursuits and neglect to appreciate the beauty of mathematical concepts outside of the realm of rigorous theory.

Ultimately, whether or not mathematicians are elitist depends on one's perspective and definition of elitism. Mathematics can be both beautiful and challenging, and those who pursue it must develop a deep appreciation for its complexities and nuances.

**A Legacy of Excellence**

The author of "Complex Analysis" by Henri Cartan was a renowned mathematician who made significant contributions to the field. Although I do not know his exact lifespan, it is clear that he lived a long and distinguished life. This legacy of excellence serves as a testament to the power of mathematics and its ability to inspire and captivate those who study it.

The fact that this book was written for a government agency speaks to the author's reputation as an expert in their field. The dedication required to work on such high-level projects underscores the importance of mathematical rigor and attention to detail.

**A Rare Book**

My final note is about an unusual book, "Elementary Theory of Analytic Functions of One or Several Complex Variables," which was written by Henri Cartan but has been removed from this particular edition. I am not certain if it will be included in future editions of the text.

The section on duty cuts is actually located in the appendix.

Mathematics can indeed be complex and challenging, but it also holds a beauty that captivates those who study it. Whether or not mathematicians are elitist depends on one's perspective and definition of elitism.

**Classic Texts: A Review**

To delve deeper into the world of mathematics, let us examine four classic texts:

1. "Complex Analysis" by Henri Cartan

2. "Elementary Theory of Analytic Functions of One or Several Complex Variables"

3. "Advanced Calculus" (also known as Undergraduate Analysis)

4. "Real and Complex Analysis"

These books represent the breadth and depth of mathematical knowledge, offering challenges and insights for readers seeking a deeper understanding of mathematics.

**Mathematical Elitism: A Reality**

Mathematicians often face criticism for writing texts that are too complex or challenging for general audiences. However, this does not necessarily imply elitism; rather, it highlights the complexities inherent in mathematical concepts.

To illustrate this point, I can share a personal anecdote about my friend with a PhD in mathematics who chose to read "Complex Analysis" without attempting any exercises. This experience demonstrates that even those with advanced knowledge can find certain texts daunting and unapproachable.

Furthermore, Henri Cartan's "Elementary Theory of Analytic Functions of One or Several Complex Variables" is an intense text that requires dedication to comprehend its contents. The rigors of this text underscore the complexity and nuance of mathematical concepts but do not necessarily imply elitism; rather, they highlight the challenges inherent in writing about abstract mathematical ideas.

In conclusion, while some mathematicians may be perceived as elitist due to their focus on rigorous texts, this perception is not entirely accurate. Mathematics can be beautiful and rewarding, even for those who struggle with its more challenging aspects.

"WEBVTTKind: captionsLanguage: enall math people are elitist this is something that people always say and in this video i'm going to tell you what i think about that and then we're going to take a look at four books that are actually in some small way maybe considered elitist by some people what these books all have in common though is that they are all extremely rigorous math books the thing is math is really really hard it takes a lot of work to get good at math i mean if you look here look at all of these papers you would think that maybe some of these papers don't have writing on them no they all have writing on them right they're all covered in math and that's what it takes to get good at math right stacks and stacks of problems hours of reading and so i think what happens is when people work really really hard on something they feel like i don't know like it's like a badge of honor there's like some glory to it for some people and it makes them perhaps come across as elitist but in my opinion i don't really think that's the case i think the most important thing you should take away from this discussion of math and being an elitist is to really be humble and remember you know math is hard for everyone these books are no joke all right so let's go ahead and talk briefly about each of these books because they're all relatively famous and very very well known this first book is real and complex analysis and it's by walter rudin and so this book is so famous it has a nickname people call it papa rudin apparently it was part of the mary grove college library the monroe campus i don't know where that is real and complex analysis so i bought this book even before taking a class on the subject this edition is from 1966 and this book is awesome you can see right away what you need to know in order to read this book you basically have to know a lot of math this is a graduate level book here it says this is undoubtedly the most important function in mathematics it is defined for every complex number z by the formula so that's the power series for e to the z they're defining it that way via the series which converges and it says it here the series 1 converges absolutely for every z and converges uniformly on every bounded subset of the complex plane thus it is a continuous function it goes on and talks more about it so a very rigorous book not for the faint of heart has no answers unfortunately i wish it did and it's basically graduate level real analysis very legendary book its counterpart is the much more gentle but still considered extremely rigorous principles of mathematical analysis and this is also by walter rudin so this one is called baby rudin and this one is called papa ruden so because this is what undergraduates take in an advanced calculus class or maybe like a mathematical analysis class and then this is what graduate students take after they already have a full math degree right so keep that in mind um if you buy this book and i'll try to leave links in the description to all of these books it's something that you might not really understand a lot of because it takes a lot of work to get here so let's talk a little bit more about this book one of the things i really like about this book is that it has a lot of information in it despite it being a fairly small book it's got a lot of really good math and really good examples i had a friend who actually read this entire book and he didn't do any of the problems but he read the entire book from the start to the finish and he's a really smart guy he has his phd in mathematics going through the contents here so you can see it yeah i mean tons of information in this book the exercises in this book can be pretty tough there's plenty of exercises that are easy slash medium but there's also some that are a little bit harder i would say it's a good mix but this book is still a tough read this is considered a rigorous book and it is not for the faint of heart i should mention that i think that the section on duty kind cuts is in the appendix on the newer versions of this book i'm not positive if i'm wrong please correct me but i believe this is in the appendix on newer editions this is an older edition of the text here we have another legendary book that is considered extremely rigorous it is complex analysis by alforz and again i picked books that are considered you know rigorous perhaps elitist right because they're so hard to read and they take so much work but what you get from sitting down with a book like this and a piece of paper and a pencil and slowly working through just a few pages is incredible if you sit down for an hour a day with one of these books and you just grind through what you can you're going to come out stronger you'll also probably come out with a lot of questions though because you won't understand a lot of the math it is a rigorous text here you can see the topics my copy smells really good i can't wait to give it a whiff i'm just going to go through the contents here quickly because oh oh i got to do it now oh what a classic and i have saved the most interesting book for last notice there's no writing on this book here and you can't even make out what it says there perhaps so let's go ahead and open it up so you can see this book this book was written by a member of borbaki borbaki was a group of elitist french mathematicians by the way the person who previously owned this copy works or worked for the government i looked it up on the internet i found them several years ago and they worked for the department of defense i believe anyways this is elementary theory of analytic functions of one or several complex variables by the legendary henry cartan and i wish i knew offhand how old he lived to be he died several years ago i think he lived to be 104 i don't know for sure but definitely over a hundred years old and he was a you know short little french man who was brilliant and wrote an incredible book this book is intense let me just show you how it starts so you can see how intense it is so this is actually chapter one of this book formal power series algebra of polynomials let k be a commutative field we consider the formal polynomials in one symbol or indeterminant x with coefficients in k for the moment we do not give a value to x then it talks about you know a vector space and you know i mean just right away there's no like this is a complex number this is the real part this is the imaginary part no no no i mean kartan just goes at it so very rigorous very classic text on complex variables so those are four classic texts on various subjects the kartan book being a complex variables book aka complex analysis along with the book by alforz and again these books are very rigorous you know you want to read these with a pen or paper and a pencil and read them slowly because it takes a lot of effort and we have this one which is basically an undergraduate analysis book aka advanced calculus and then we have real and complex analysis this one's baby ruden and this one's papa rudin so just a nice look at these books as far as the whole elitism thing what do you think do you think that mathematicians are elitist you know do you think that this is something that is true in general and if it is true you know if you do think that math people are elitist do you think that perhaps it's a bad thing right so again i really i really don't know what to think about it i think that math is beautiful and some people can work really hard on math and get carried away and feel smart and that's okay right i mean i think it's okay i think as long as you love math and you love what you're doing that's what matters the most anyways i hope this video has been helpful to someone out there and i hope you've enjoyed this video and maybe you've had some insight into some new subjects and really cool books good luck and take careall math people are elitist this is something that people always say and in this video i'm going to tell you what i think about that and then we're going to take a look at four books that are actually in some small way maybe considered elitist by some people what these books all have in common though is that they are all extremely rigorous math books the thing is math is really really hard it takes a lot of work to get good at math i mean if you look here look at all of these papers you would think that maybe some of these papers don't have writing on them no they all have writing on them right they're all covered in math and that's what it takes to get good at math right stacks and stacks of problems hours of reading and so i think what happens is when people work really really hard on something they feel like i don't know like it's like a badge of honor there's like some glory to it for some people and it makes them perhaps come across as elitist but in my opinion i don't really think that's the case i think the most important thing you should take away from this discussion of math and being an elitist is to really be humble and remember you know math is hard for everyone these books are no joke all right so let's go ahead and talk briefly about each of these books because they're all relatively famous and very very well known this first book is real and complex analysis and it's by walter rudin and so this book is so famous it has a nickname people call it papa rudin apparently it was part of the mary grove college library the monroe campus i don't know where that is real and complex analysis so i bought this book even before taking a class on the subject this edition is from 1966 and this book is awesome you can see right away what you need to know in order to read this book you basically have to know a lot of math this is a graduate level book here it says this is undoubtedly the most important function in mathematics it is defined for every complex number z by the formula so that's the power series for e to the z they're defining it that way via the series which converges and it says it here the series 1 converges absolutely for every z and converges uniformly on every bounded subset of the complex plane thus it is a continuous function it goes on and talks more about it so a very rigorous book not for the faint of heart has no answers unfortunately i wish it did and it's basically graduate level real analysis very legendary book its counterpart is the much more gentle but still considered extremely rigorous principles of mathematical analysis and this is also by walter rudin so this one is called baby rudin and this one is called papa ruden so because this is what undergraduates take in an advanced calculus class or maybe like a mathematical analysis class and then this is what graduate students take after they already have a full math degree right so keep that in mind um if you buy this book and i'll try to leave links in the description to all of these books it's something that you might not really understand a lot of because it takes a lot of work to get here so let's talk a little bit more about this book one of the things i really like about this book is that it has a lot of information in it despite it being a fairly small book it's got a lot of really good math and really good examples i had a friend who actually read this entire book and he didn't do any of the problems but he read the entire book from the start to the finish and he's a really smart guy he has his phd in mathematics going through the contents here so you can see it yeah i mean tons of information in this book the exercises in this book can be pretty tough there's plenty of exercises that are easy slash medium but there's also some that are a little bit harder i would say it's a good mix but this book is still a tough read this is considered a rigorous book and it is not for the faint of heart i should mention that i think that the section on duty kind cuts is in the appendix on the newer versions of this book i'm not positive if i'm wrong please correct me but i believe this is in the appendix on newer editions this is an older edition of the text here we have another legendary book that is considered extremely rigorous it is complex analysis by alforz and again i picked books that are considered you know rigorous perhaps elitist right because they're so hard to read and they take so much work but what you get from sitting down with a book like this and a piece of paper and a pencil and slowly working through just a few pages is incredible if you sit down for an hour a day with one of these books and you just grind through what you can you're going to come out stronger you'll also probably come out with a lot of questions though because you won't understand a lot of the math it is a rigorous text here you can see the topics my copy smells really good i can't wait to give it a whiff i'm just going to go through the contents here quickly because oh oh i got to do it now oh what a classic and i have saved the most interesting book for last notice there's no writing on this book here and you can't even make out what it says there perhaps so let's go ahead and open it up so you can see this book this book was written by a member of borbaki borbaki was a group of elitist french mathematicians by the way the person who previously owned this copy works or worked for the government i looked it up on the internet i found them several years ago and they worked for the department of defense i believe anyways this is elementary theory of analytic functions of one or several complex variables by the legendary henry cartan and i wish i knew offhand how old he lived to be he died several years ago i think he lived to be 104 i don't know for sure but definitely over a hundred years old and he was a you know short little french man who was brilliant and wrote an incredible book this book is intense let me just show you how it starts so you can see how intense it is so this is actually chapter one of this book formal power series algebra of polynomials let k be a commutative field we consider the formal polynomials in one symbol or indeterminant x with coefficients in k for the moment we do not give a value to x then it talks about you know a vector space and you know i mean just right away there's no like this is a complex number this is the real part this is the imaginary part no no no i mean kartan just goes at it so very rigorous very classic text on complex variables so those are four classic texts on various subjects the kartan book being a complex variables book aka complex analysis along with the book by alforz and again these books are very rigorous you know you want to read these with a pen or paper and a pencil and read them slowly because it takes a lot of effort and we have this one which is basically an undergraduate analysis book aka advanced calculus and then we have real and complex analysis this one's baby ruden and this one's papa rudin so just a nice look at these books as far as the whole elitism thing what do you think do you think that mathematicians are elitist you know do you think that this is something that is true in general and if it is true you know if you do think that math people are elitist do you think that perhaps it's a bad thing right so again i really i really don't know what to think about it i think that math is beautiful and some people can work really hard on math and get carried away and feel smart and that's okay right i mean i think it's okay i think as long as you love math and you love what you're doing that's what matters the most anyways i hope this video has been helpful to someone out there and i hope you've enjoyed this video and maybe you've had some insight into some new subjects and really cool books good luck and take care\n"