A brief somewhat stream-of-consciousness commentary is in order on this of all days:

LANGUAGE! LANGUAGE! LANGUAGE! I'm doing insane things this term with professional development. We're back a few weeks into it now, but for some reason, with my book's page proofs and index now in print (book in November!) I feel like I have time. I don't have time, but it feels that way, because talking with students feels more like my own personal sustenance than work.

So I'm applying for new research grants left and right, while taking another new African language--the train leaves once a year on that track, so I have to start now--and it's rather hectic. But I can't recommend the latter highly enough for grad students and even junior scholars. I hadn't intended it, but my tenure committee sort of lit up with interest when they found out I was taking a new language aimed at future projects. I was really doing it because I hate going places where I can't even be courteous properly--and maybe because I'm hoping to encounter some colonial-era petitions that are in early forms of those local languages.

I'm also finding out just how many Africanists do not have any African language. There are some very, very senior South Africanists--with named chairs--who have English, French, and German, and that's it. Nothing else. Not even Dutch or Afrikaans. It kind of boggles the mind, but it underscores again just how incredibly useful it is to have language skills. One of my students in South African history is an academically accomplished woman who wants to do work in the region, was born in Namibia, and speaks four languages already--English, Afrikaans, and two of the major Bantu languages of the north--but she's also fully American, having been here for three decades, and is concerned about her chances at getting into programs of graduate study. I do not think she will have a problem--and as a dual citizen, can even do research without the $500 clearance processes they require. So yeah, history students? GET LANGUAGE.

I just have to gush for a minute-- I got my extended reader badge at the Getty Research Institute on Monday (along with the rest of my class) and a tour of the library (HOLY SHIT IT'S AWESOME-- if you live in the LA area it is well worth having and anyone can get a badge with references). After brief lecture and discussion on Bauhuas, our teacher took us to a special collections reading room where we got to handle and look through a ton of ephemera from Bauhaus Dessau, including students' notebooks, photographs, lecture notes and color charts from Kandinsky and Klee. One of my classmates can read German and she was attempting to translate for us (turns out Kandinsky's handwriting is difficult) and the bit she was able to pick up was so methodical and fascinating. So effing cool-- we were even allowed to take photos. (To my knowledge it's okay for me to be posting these here but if mods or anyone else disagree please let me know and I'll take them down.)

If anyone wants to take a stab at one of Kandinsky's notebooks...

Bonus: An unnamed student's constructions with a deutsche mark and chocolate bar wrapper.

I'd be curious to know if anyone could identify that mark by sight-- I'm not sure if it's a Papiermark, Rentenmark, Reichsmark or what.

I wrote a little bit on the history of Fermat's Last Theorem for the Maths department at Uni if you'd like to read it. I couldn't put in all the information that I wanted to, because they wanted to keep in less than a page (which I went over anyway) and it goes a little over the 20 year rule so I'll remove it if you want (I don't know if that's allowed in this thread.) At some point maybe I'll edit it and put it into a proper /r/askhistorians quality post, but this is basically a rough outline of it. Also tell me if any of the formatting fucked up. I just copied and pasted from the weird software I wrote it on.

Brief Biography of Fermat

Pierre de Fermat, born in the early 17th Century (the exact date and year of which is disputed, however he was said to have been born on 17 August 1601) in Beaumont-de-Lomagne, France, where his father, a wealthy leather merchant, had been one of the one of the four consuls. The problem is many details about his early life are very sparse, however he apparently spent his childhood and early school years in his birthplace. In similar sparse detail he may have attended the University of Toulouse, however all that is certain is that he stayed in Bordeaux in the later 1620’s before finally receiving the Bachelor of Civil Laws degree from the University of Orleans in 1631. ^1

After finishing his degree, Fermat served in the local parlement at Toulouse, first as a lawyer and later as a councillor. However while he performed this busy role, he also managed to make time to enjoy classical literature, science and most importantly working as an amateur mathematician. This meant that by 1629 he had began to make discoveries of importance in mathematics, such as the restoration of works of antiquity, examples of this being how he undertook the task to reconstruct the Plane Loci of Apollonius. Fermat however refused to publish the majority of his work, because he never wanted to put it into a polished form. ^2

Fermat's Last Theorem

It was because of Fermat's refusal to publish his work that people feared that it would be forgotten. Hence his son, Samuel, undertook the task of collecting all his work, including letters, comments written in books and other mathematical papers, with the intention of publishing his work. Fermat's Last Theorem was discovered in this way, in the form of a note which Fermat has written in a copy of the Greek book Arithmetica by Diophantus. ^3

Translated from what he wrote in originally in Latin, Fermat claimed "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."

This note is stating that x^(n) + y^(n) = z^(n) has no solutions for for non-zero integers when n>(2) . This is related to Pythagoras' Theorem, which is "x^(2)+y^(2) = z^(2)." This is why the n >(2) is a necessary restriction, because for n = 2 there are a number of formulas which can generate an infinite number of Pythagorean Triples, satisfying the equation. ^3

Proof of Fermat's Last Theorem

When Fermat wrote his last theorem he claimed "I have discovered a truly remarkable proof which this margin is too small to contain." Fermat however left no details of his proof apart from for the special case n = 4 , and then never mentioned it. This could mean that his complete proof may have been wrong. ^3

Many well known mathematicians later tried to attempt a proof, such as Euler who is credited with working it out for n = 3 . Euler's original proof however contains a fallacy, but there is a way of fixing this that appears in other proofs discovered by Euler. Much later on, by 1993, computers managed to show that the theorem holds for values up to n = 4000000 . This still does not constitute a proof though, yet it was the only place progress seemed to be happening hence why the theorem holds the dubious distinction of being the theorem with the largest number of published false proofs. For example over 1000 false proofs were published between 1908 and 1912.

In 1955 however progress was made in an unexpected, the field of elliptic curves and modular forms. Goro Shimura, Yutaka Taniyama and later on Andre Weil came up with the Shimura-Taniyama-Weil Conjecture that said every elliptic curve over rational numbers is modular. This wasn't thought of as being connected to Fermat's Last Theorem, until 1985 when Gerhard Frey at University of Saarbrücken observed that if the conjecture was true, it would imply Fermat's Last Theorem.

In 1993 Andrew Wiles, a British mathematician working at Princeton in the USA gave a series of three lectures at the Isaac Newton Institute in Cambridge. It was on 23 June 1993 in the final lecture that Wiles appeared to show that the Shimura-Taniyama-Weil Conjecture is true for semistable elliptic curves, and one of the corollaries of said result that Wiles wrote on the blackboard was Fermat's Last Theorem. While reviewing these lectures for publication though, he found a gap in his proof.

Wiles began to collaborate with Richard Taylor in 1994 in an attempt to fill the holes in this proof. By 1995 Wiles had managed to fix his proof and "Modular Elliptic Curves and Fermat's Last Theorem" appeared in the Annals of Mathematics. ^4

Sources

1. http://www.encyclopedia.com/topic/Pierre_de_Fermat.aspx#1-1G2:2830901403-full

2. A History of Mathematics - Carl B. Boyer, Uta C. Merzbach - Pg 320 - 329

3. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Fermat%27s_last_theorem.html

4. A History of Mathematics - Carl B. Boyer, Uta C. Merzbach - Pg 593 - 596

Can anyone recommend some reading material about what makes a revolution? When are the conditions right? When will it likely succeed or fail? Does a revolution need 100% of the people behind it or can it work with far less? Are they only a thing of the past and must they be violent?

Please and thank yous. :)

Also, meta-history question: As we all know, the most beloved part of the header text for the Friday Free-for-All thread concerns the Doge of Venice. Through deep and painstaking archival research, I have discovered the first attested instance of the Doge of Venice palling around with Foucault is on October 25, 2013. What socio-political factors led /u/lngwstksgk to adding that point? How did it effect class relations in Manchester?

Anyone know any good readings on ancient African warfare and the differences between it and European/Asian warfare around the same time period?

A couple weeks ago I posted a review of an episode of Michael Wood's Story of India, and after finishing the series I thought I may as well put a recommendation here, particularly of the excellent last episode on British India. The series has some problems from a strict historical sense--the first episode is very rough, the portrayal of Aurangzeb is expectedly unfair, and the narrative of south India is rather confused, for example--but it works very well as a general introduction to the often bewildering subject of the history of India. And it has all of the qualities you expect from a Michael Wood documentary.

The last episode also put in my mind a very interesting and I think somewhat fundamental truth about pre-1300 history of India, and that is the extent to which it all begins with Britain. There isn't much of a native historiographic tradition in India, so whenever you study a topic before the Muslim conquests you always read the phrase "beginning with the effort of nineteenth century British philologists/archaeologists/Indologists..." I think this goes a long way to describing the troubles India still has with its past, especially when you compare it to, say, China which has been able to much more easily shrug off the weight of Western orientalism (which arguably never really had a chance at gaining a strong foothold there).

Interloper entering: I found this video by Ray Laurence about teenage life in Rome and was just curious if anyone knew about this man's work and if he was any good. It was very interesting and learning about the day-to-day in history is always a lot of fun.

Speaking of fun, since, I'm not sure if these question would ever get any notice I had two things to ask and they are sort of meta questions. Here they go:

What are modern historian's views on Hegel?

What is that appeal of history? What is it about history that draws us near it to learn more? What is it that is something greater then aphorism like "Those who don't study history are doomed to repeat it"?

Both questions are rather philosophical. (And you guys can beat me up and take my lunch money later if you'd like) but those two questions have been really buzzing in my head.

Thanks.

Would anyone be able to provide sources to the rise of the water level of the Indian Ocean during the time of the mysterious disappearance of Mohenjo-Daro?

Anyone here suggest good reading materials covering the Library at Alexandria?

Here's a question I don't think merits it's own thread involving U.S. History:

Is it known who the first person born in the United States was following the Declaration of Independence?

I know Virginia Dare is speculated to be the first (Anglo-Saxon) child born in North America, but I strictly wonder about the first child born in the true "United States of America".

Last week, there was plenty of interest in trying to solve a mystery surrounding one of the letters in my collection and I must say that I am truly grateful for everyone who took time out of their day to reply.

Considering the amount of interest last time, I wondered if anyone would be interested in having it as a sort of recurring thing in the Friday Free-For-All thread? It's not often I get to share this wealth of never before seen letters and I would love for more people to see them.

Without further ado however, here is this weeks letter for those who are interested. Here's a German letter from 1941 which also came with a photograph showing a young man wearing what I imagine to be a Luftwaffe uniform, judging from the collar rank tabs. There is a possibility that he is a Fallschirmjager, but I am not completely certain. I will scan the photograph.

There are two things about this letter that catches my attention when I first saw it: the drawing on the back. I have no idea what it is depicting. Secondly, the stamp on the back is also very interesting. I'm not completely certain that purpose it serves and why it has been stamped inside of the letter and not on the cover where the usual feldpost and censor stamps can be found.

Real life is terrifying enough that I almost want to do that doctorate after all...

2 days to fill in a form which (might) get me shortlisted. Real life is haaard

Holy shit I hate Habermas and everything related to him.

Also, anyone know of any books/articles on independent slave production and marketing? This is all I have thusfar.

Can someone recommend a few good books about first contact between civilizations or some interesting anecdotes that took place during initial exchanges? It doesn't particularly matter which cultures are meeting I find it all fascinating.