{"id":544050,"date":"2010-03-12T18:36:11","date_gmt":"2010-03-12T22:36:11","guid":{"rendered":"tag:typepad.com,2003:post-6a00d8341d17e553ef0120a92e623e970b"},"modified":"2010-03-12T18:36:11","modified_gmt":"2010-03-12T22:36:11","slug":"a-radical-shift-in-the-practice-of-mathematics-and-a-radical-shift-in-stories-about-mathematics-took-place-at-exactly-the-same-time-a-conversation-with-amir-alexander","status":"publish","type":"post","link":"https:\/\/mereja.media\/index\/544050","title":{"rendered":"“A radical shift in the practice of mathematics and a radical shift in stories about mathematics took place at exactly the same time”: A conversation with Amir Alexander"},"content":{"rendered":"
\n

<\/o:smarttagtype>\"ALEDUE\"<\/a> It\u2019s a story that has been
\ntold and re-told over two centuries: A young man steps into the Paris dawn of May 30,
\n1832, dueling pistol in hand. Long haunted by a premonition of early death, he
\nhas spent the night bent over his desk, unburdening his mind of the
\nmathematical insights that teem there, pausing only to scrawl a protest\u2014I have not time<\/em>\u2014in the margin. On this
\nfoggy morning, his premonition comes terribly true: shot in the stomach, the
\nyoung man dies the next day, cradled in his brother\u2019s arms. \u00c9variste Galois\u2019s
\nmathematical insights, cruelly rebuffed during his short life, will be
\nappreciated only after his death. <\/span>
<\/span><\/p>\n

\"Alexander.tif\"<\/a>  The only trouble with this
\nfoundational story of modern mathematics is that it\u2019s not true. The posthumous
\nGalois, an innocent whose groundbreaking ideas were neglected by an obstinately
\nignorant academy during his short lifetime, bears only a passing resemblance to
\nthe real Galois, an intemperate
\nrevolutionary who had already published his most important discoveries on
\nalgebra by the time of his death, and who attracted mentors in the Paris
\nmathematical establishment in spite of his twin gifts for giving offense and
\nfor self-destruction. In Duel at Dawn: Heroes, Martyrs, and the Rise of Modern
\nMathematics<\/a>, Amir Alexander tells the story of how the real Galois became the
\nlegendary one– and how a similar transformation was wrought on mathematicians Niels
\nHenrik Abel<\/a> and J\u00e1nos Bolyai<\/a>. The transformation, Alexander shows, was a
\ncultural one, and reveals the deep connections between mathematics and its
\ncultural setting. <\/span>
<\/span><\/p>\n

<\/span>Alexander spoke with us
\nabout how he came to write the book, his findings, and the challenges and
\nrewards of writing about math for a general audience.<\/span><\/p>\n

<\/span>Q. When
\ndid you first hear the story of Galois<\/a>? What did you think of it then?<\/em><\/span><\/p>\n

I first heard the story of Galois from a professor
\nwhen I was a mathematics undergraduate in college. I think that\u2019s how most
\nmathematicians learn the story \u2013 it is told by teachers to students, and all
\nmathematicians know it. <\/span>
<\/span><\/p>\n

Even when I first heard the story it struck me as
\nsomething more than an amusing anecdote. 
\nIt seemed to suggest that mathematics is for the young, that only a
\nselect few can understand and appreciate its beauty, and that those who pursue
\nit run the risk of being lost to our world. 
\nThose are deeply held beliefs among many mathematicians, and so the
\nstory of Galois has become something of a founding myth of modern mathematics,
\npassed on from one generation to the next.<\/span>
<\/span><\/p>\n

Q. How and when did you link his story to the
\nlarger narrative you draw out in Duel at Dawn<\/strong>\u2014the idea that mathematics exists as part of the larger culture, and
\nthat the stories we tell about (or impose upon!) the lives of mathematicians
\nreveal something about the practice of mathematics?<\/em><\/span><\/p>\n

It\u2019s very hard to say when exactly I noticed the
\nrelationship between the story of Galois and the actual practice of
\nmathematics. I\u2019ve been living with mathematics and stories about mathematics
\nfor a long time, and the awareness of these interconnections came slowly. But I
\nthink I can say something about how I
\narrived at the idea, the basic thought process that led to it.<\/span>\n<\/p>\n

First of all, after learning the story of Galois I
\nsoon found that it did not stand alone. Only slightly less famous are the
\nlegends of Abel, the Norwegian genius who died in poverty at age 26, and
\nBolyai, the young Hungarian discoverer of non-Euclidean geometry, who was
\ncrushed by the indifference of established mathematicians. The basic outline of
\nall these stories is strikingly similar\u2014 and even more strikingly, all three
\nlived and work at precisely the same time. Galois, Abel, and Bolyai all
\nproduced their mathematics between the mid 1820s and the early 1830s. So it
\nseemed there was a new and dramatic story about mathematicians that appeared at
\na very specific time. This was the first piece of the puzzle.<\/span>  <\/span>\"Fellas_duelling\"<\/a>
<\/span><\/p>\n

The second piece of the puzzle was that the period
\nin question, the early 19th century, was a time of dramatic change
\nin the practice of mathematics. So dramatic, in fact, that some historians have
\ncalled it the \u201cre-birth\u201d of mathematics, and it is often acknowledged as time
\nin which the modern practice of pure mathematics was born.  Whereas the old mathematics was focused on
\nstudying the physical world, the new practice was concerned with studying a
\npure mathematical world, separate from our own and governed solely by
\nmathematical laws. <\/span>
<\/span><\/p>\n

Overall then, a radical shift in the practice of
\nmathematics and a radical shift in stories about mathematics took place at
\nexactly the same time\u2014in the early 19th century. It seemed to me
\npractically inescapable that these two developments are related.<\/span><\/p>\n

<\/span>When I thought about it the connection between the
\ntwo seemed obvious: The new mathematics required a new kind of heroic
\npractitioner, one who would pursue it wherever it led, even beyond earthly
\nreality. Dramatic heroes like Galois and Abel, who were lost to the world in
\ntheir pursuit of mathematics, expressed this ideal perfectly. An \u201cotherworldly\u201d
\nmathematics went hand in hand with romantic practitioners, \u201cotherworldly\u201d beings
\nwho are strangers in our imperfect world.<\/span><\/p>\n


<\/span><\/p>\n

Q. Could you say a little about how this work
\nrelates to your earlier book, Geometrical
\nLandscapes<\/a>?<\/em><\/span><\/p>\n


<\/span><\/p>\n

Both books are parts of a larger project of writing
\na new kind of history of mathematics, one in which even highly technical
\npractices are deeply embedded in their cultural setting. In both cases I show
\nthat mathematics is part of broader history by looking at it through the lens
\nof stories told about the mathematics and its practitioners.<\/span><\/p>\n

Now mathematical stories, like all stories, are the
\nproduct of their cultural setting: in 17th century we have stories
\nabout geographical exploration, in the 18th century stories are told
\nabout \u201cnatural\u201d men, in the 19th century we have tales of tragic
\nromantic heroes, and so on. At the same time these same stories tell us
\nsomething about what people thought mathematics is, and who practiced it: the
\nmathematics of a 17th century explorer is very different from the
\nmathematics of a 19th century romantic outcast. Because they are
\npart of both the historical setting and technical mathematical practice,
\nstories are wonderful at connecting higher mathematics to the broad cultural
\ntrends of its times. Instead of a separate island of abstraction, mathematics
\nbecomes a part of the cultural mainstream.<\/span><\/p>\n

After Geometrical
\nLandscapes <\/strong>came out, some of the comments I got went something like this:
\n\u201cOK, you showed that in the early 17th century mathematics was
\nanchored in its cultural context. But that is relatively simple mathematics.
\nYou couldn\u2019t possibly show cultural connections for modern mathematics, which
\nis far more complex and abstract.\u201d I took that as a challenge: I wanted to show
\nthat modern mathematics too has cultural and historical underpinnings. The
\nresult was Duel at Dawn.<\/strong><\/span>  \"Guy_dead_from_duel\"<\/a> <\/p>\n

\nQ. How do you, as an author and educator, deal
\nwith (some) laypeople's aversion to math? Do you think it makes it more
\ndifficult to tell stories about math than about other fields, like science? How
\ndo you work around and overcome this obstacle?<\/em><\/span> <\/p>\n

\nI am very much aware that many people feel
\ncompletely alienated from math. Part of my purpose in this book is to try and
\nreverse this, engage people in mathematics, and return it to the mainstream of
\ncultural life. I think stories are a wonderful way of doing that, and from its
\nearly beginnings mathematics has always been accompanied by a treasure-trove of
\nstories and anecdotes. They are witty and amusing, and they also carry a moral
\nabout the practice and meaning of mathematics. Everyone loves a good tale, and
\nI think people will be willing to follow it to both its historical origins and
\nto its mathematical implications.<\/span><\/p>\n

<\/span>It\u2019s interesting that you use the term \u201claypeople,\u201d
\nsuggesting that mathematicians are a select priesthood possessing a secret
\nknowledge. I think many people see things in exactly these terms, and that\u2019s
\npart of the problem: mathematics is perceived as the domain of \u201cgeniuses,\u201d and
\nset on such a high pedestal as to be effectively irrelevant to many people.<\/span>\"GRANAM\"<\/a> <\/p>\n

It was not always this way. In the Enlightenment,
\nfor example, mathematical concepts were at the heart of public debates about
\nthe nature of knowledge and faith. A wonderful recent book called Naming Infinity <\/a>by Loren Graham and Jean-Michel Kantor <\/span>shows that advanced mathematics carried religious and
\npolitical meaning in early 20th century Russia. I want to make mathematics relevant to most people once again by showing that it is part of the world and part of life. Telling stories is my way to do this. <\/span><\/p>\n<\/div>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

It\u2019s a story that has been told and re-told over two centuries: A young man steps into the Paris dawn of May 30, 1832, dueling pistol in hand. Long haunted by a premonition of early death, he has spent the night bent over his desk, unburdening his mind of the mathematical insights that teem there, […]<\/p>\n","protected":false},"author":6896,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-544050","post","type-post","status-publish","format-standard","hentry","category-news"],"_links":{"self":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts\/544050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/users\/6896"}],"replies":[{"embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/comments?post=544050"}],"version-history":[{"count":0,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts\/544050\/revisions"}],"wp:attachment":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/media?parent=544050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/categories?post=544050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/tags?post=544050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}