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szottesfolditanyak · 7 months ago

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Alexander Grothendieck

Eszményem a koktélparti-beszélgetés; amikor a mély gondolatot szórakoztató módon, a lényegre lecsupaszítva közvetítjük egy érdeklődő barátnak (esetleg egy gyors rajzzal is kísérve a szalvétán). A cél az, hogy az újonc fejében világosságot gyújtsunk, de vigyünk a témába egy olyan csavart, amellyel a szakértő tetszését is elnyerjük. És persze soha ne untassunk. - írja Jim Holt az Amikor Einstein Gödellel sétált című könyve előszavában. Sikerült is ebben a szellemben megírnia az egész könyvet.

Egyik matematikai fejezetben szentel pár oldalt Grothendiecknek. Íme (a képeket én tettem közé):

Az 1930-as években ragyogó fiatal párizsi matematikusok - köztük André Weil - elhatározták, hogy a matematika házát biztonságosabbá teszik, újra felépítve azt a halmazelmélet logikai alapjain. A projekt a Bourbaki kollektív álnév alatt évtizedekig folytatódott, s egyik vastag értekezést szülte a másik után. Ennek egyik következménye - eléggé esztelen módon - az „új matematika" nevű oktatási reform bevezetése volt még az 1960-as években, amely a számokról való intuitív beszédet a halmazok idegen zsargonjával helyettesítve teljesen összezavarta az amerikai iskolás gyerekeket és szüleiket.

A fizikusok a „minden elméletének" megtalálásáról beszélnek; s a halmazelmélet annyira elsöprően általános, hogy akár a „minden elmélete elméletének" is tűnhet. A Bourbaki-kör tagjai is biztosan így látták. De néhány évtizeddel azután, hogy programjuk elindult, a rendkívüli Alexander Grothendieck vált a kör központjává, és túllépett rajta. Eközben létrehozta a tiszta matematika új stílusát, amely éppolyan gyümölcsözőnek bizonyult, mint amilyen szédítően elvontnak. Már jóval azelőtt, hogy 2014-ben a Pireneusokban egy távoli tanyán nyolcvanhat évesen meghalt, az utolsó fél évszázad legnagyobb matematikusának tekintették. Ahogy Harris megjegyzi, bizonyára a "legromantikusabb" is volt: „Élettörténete írói feldolgozásért kiált."

A nyers tények eléggé meglepőek. Alexander Grothendieck 1928-ban született Berlinben aktív anarchista szülőktől. Orosz zsidó apja részt vett a cári rezsim elleni 1905-ös felkelésben és az 1917-es forradalomban. A bolsevikok alatt megúszta a bebörtönöztetést; összecsapott a náci gengszterekkel Berlin utcáin; harcolt a republikánus oldalon a spanyol polgárháborúban (ahogy Grothendieck anyja is); és Franciaország eleste után Párizsból Auschwitzba deportálták, majd ott meggyilkolták.

Grothendiecket hamburgi nem zsidó anyja nevelte Franciaország déli részén. A fiú mind a számokhoz, mind a bokszhoz tehetséget mutatott. A háború után Párizsba ment, ment, hogy a nagy Henri Cartannál tanuljon matematikát. A Sao Paulóban és Kansasban, valamint a Harvardon elvégzett korai oktatási gyakorlat után Grothendiecket 1958-ban meghívták, hogy csatlakozzon az Institut des Hautes Études Scientifiques-hez, amelyet éppen akkor alapított egy magánvállalkozó Párizs mellett, a Bois-Marie erdeiben. Ott töltötte Grothendieck a következő tizenkét évet, megdöbbentve elit kollégáit és fiatalabb tanítványait azzal, ahogy a magasabb matematika tájképét újjáalkotta.

Grothendieck fizikailag impozáns, borotvált fejű, jóképű férfi volt; éppolyan karizmatikus, mint puritán. Kegyetlen minimalizmusa kiterjedt a pénz megvetésére és szerzetesi ruhatárára. Következetes pacifista és antimilitarista lévén 1966-ban nem volt hajlandó Moszkvába menni (ahol a matematikusok nemzetközi kongresszusát tartották), hogy átvegye a matematikában legnagyobb kitüntetést, a Fields-érmet. Ugyanakkor a következő évben elutazott Észak-Vietnamba, ahol a dzsungelben tiszta matematikára tanította azokat a diákokat, akiket Hanoiból evakuáltak az amerikai bombázás elkerülése végett. Életének nagy részében (önként) hontalan maradt, három gyermeke volt egy nőtől, akit feleségül vett, és még kettő házasságon kívül. Megalapította a Survivre et Vivre radikális ökológiai csoportot, és egyszer letartóztatták, mert egy politikai tüntetésen Avignonban leütött néhány csendőrt.

Kérlelhetetlen és néha paranoiás integritásérzése miatt Grothendieck végül elidegenedett a francia matematikusok intézményi világától. Az 1990-es évek elején eltűnt a Pireneusokhan, ahol - mint azt maroknyi csodálója jelentette, akiknek sikerült nyomon követni őt - a fennmaradó éveiben pitypanglevesen élt, és azon elmélkedett, hogy egy rosszindulatú metafizikai erő pusztítja a világ isteni harmóniáját, alkalmasint picit módosítva a fény sebességén. Azt mondták, a helybeli falusiak gondoskodtak róla.

Grothendieck átalakította a modern matematikát. Azonban ennek az átalakulásnak nem kis részét egy kevésbé ismert előfutárának, Emmy Noethernek kell a javára írni. Az 1882-ben Bajorországban született Noether volt az, aki a kategóriák elméletét inspiráló absztrakt megközelítést nagyrészt létrehozta. Azonban nőként egy férfiak által uralt egyetemi világban el volt zárva előtte annak lehetősége, hogy professzor legyen Göttingenben; a klasszicisták és a történészek a karon azt is megpróbálták megakadályozni, hogy fizetés nélküli előadásokat tartson. Erre föl jegyezte meg David Hilbert, a német matematika doyenje: "Nem látok okot arra, hogy neme akadálya legyen kinevezésének. Utóvégre egyetem vagyunk, nem fürdő." ...

Emmy Noetherben természetesen alakult ki az az intellektuális szokás, hogy egy problémával az általánosság egyre magasabb szintjein birkózzon meg. Ezt osztotta Grothendieck is, aki azt mondta, hogy nem a „kalapács-véső" módszerrel szeret megoldani egy problémát, hanem hagyja, hogy az absztrakció tengere „elárassza és feloldja" azt. A matematikusok által kezelt ismerős dolgok, mint például az egyenletek, függvények és még a geometriai pontok is az ő víziójában jóval összetettebb és sokoldalúbb struktúrákként születtek újjá. A régi dolgok az újak puszta árnyékainak - vagy, ahogy Grothendieck szívesebben hívta őket, „avatárjainak" - bizonyultak. (Egy avatár eredetileg egy hindu isten földi megnyilvánulása; sok francia matematikus talán a szanszkrit nyelvben is szakértő André Weil befolyása miatt merít előszeretettel a terminológiában a hindu metafizikából.)

Ez nem egyszeri folyamat. Végül minden új absztrakcióról kiderül, hogy egy még magasabb absztrakció avatárja. Ahogy Michael Harris mondja: „A rendelkezésre álló fogalmak az általunk megragadni próbált, elérhetetlen fogalmak avatárjaként értelmezhetők." Ezen új fogalmak megragadásával a matematika a növekvő absztrakció egyfajta „létráján" halad felfelé. És Harris szerint ez az, amire a filozófusoknak figyelniük kell: „Ha a mai matematika egyetlen jellegzetességére kérdeznél rá, amely filozófiai elemzés után kiált, azt tanácsolnám, hogy a szilárd alapok keresése helyett gyakorold a fogalmi és avatárlétrák megmászását."

És mi van a létra tetején? Harris játékos komolysággal azt állítja, hogy „talán van egy nagy tétel", minden matematika végső eredete — „valami samsara = nirvana-hoz hasonló". De mivel a megmászásra váró lépcsők száma végtelenül sok, ... ...

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A pireneusos rész miatt elkezdett érdekelni. Utánanéztem.

Ezeket a következő idézeteket nem szerkesztem, csak hangulatképek; akit érdekel, úgyis utánaolvas. Ezek azok az időkből valók, amikor már otthagyta az akadémiai világot.

A legvégére teszek két beszámolót két egyetemi hallgatótól, akik ad hoc meglátogatták a Pireneusokban. Ebben az egész posztban az első emlékezés a legmeghatóbb.

"Between June 1983 and February 1986, Grothendieck wrote Récoltes et Semailles: Réflexions et témoignage sur un passé de mathématicien (Reapings and Sowings: Reflections and testimony about the past of a mathematician). It is a work that defies categorization. The title suggests a memoir, but Récoltes et Semailles is something more and less than a memoir. It is more, in that it contains not only memories of events in his life but also analyses, often quite deep and minute, of the moral and psychological significance of those events and his attempts to reconcile their meaning with his view of himself and the world."

"In the years prior to and following his retirement, Grothendieck began sending strange letters to former colleagues and friends, expressing his spiritual beliefs. For instance, in the period 1987–88 he wrote a 300-page manuscript (accompanying 500 pages of notes) entitled La Clef des Songes ou Dialogue avec le Bon Dieu (“The Key to Dreams or Dialogue with the Good Lord“) in which he expressed his conviction that “God exists and that he speaks to people through their dreams” (Jackson, 2004b). A few years later, in 1990, he wrote a letter entitled La Lettre de la Bonne Nouvelle (“The Letter of Good News”) which he addressed to 250 people, declaring that the “Age of Liberation will commence on the Day of Truth, 14 October 1996”.

Around the same time, he burned approximately 25,000 pages of his own writing, including various works in mathematics, letters between his parents in the 1930s and unpublished manuscripts in an attempt to “lighten himself of all things”

...

... described Grothendieck not as arrogant, but as “Just friendly, and at the same time rather naive and childlike […] Many mathematicians are childlike, unworldly in some sense, but Grothendieck more than most. He just seemed like an innocent — not very sophisticated, no pretense, no sham. He thought very clearly and explained things very patiently, without any sense of superiority.” "

Grothendieck:

Today I am no longer, as I once was, the prisoner of interminable tasks, which so often prevented me from leaping into the unknown, mathematical or otherwise. The time of tasks for me is over. If age has brought me anything, it is lightness. —Esquisse d’un Programme

David Mumford méltatása 2014-es halála után, főleg szakmai.

A fenti két jó életrajzon kívül még egy matekra kihegyezett címszavas zanza életrajz.

Récoltes et Semailles, Part I - el tudom képzelni, hogy létezik annyi fű, hogy ez énekeljen; anélkül nehéz.

Tisztelői gyűjteményes oldal:

És a két beszámoló a látogatásokról. Módfelett tanulságosak az amilyen az adjonisten szemszögéből. Idekopizom őket egészükben is a linkek után, ha esetleg eltűnnének idővel.

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Visiting Alexander Grothendieck Mohammad Hadi Hedayatzadeh

On February 18, 2011 I met Alexander Grothendieck at the gate of his house in Lasserre, France. The idea of meeting Grothendieck was on my mind ever since I learned about his beautiful Mathematics and his charismatic character as a student in Iran about 10 years before. At that time the idea was raw and more a fancy than something that could one day be realized.

The more I studied Algebraic Geometry the more I admired Grothendieck's mind and genius. I was determined to meet him. Towards the end of my graduate studies, at ETH Zurich, while at the Journées Arithmétiques in Rennes, France, I met Prof. Michel Raynaud. Our conversation soon converged toward Grothendieck. I explained to him how I felt about Grothendieck and that I really needed to meet him. He instructed me to contact Prof. Leila Schneps. I did. Prof. Schenps was very kind to share with me Grothendieck's home address. She warned me not to expect a kind response from him, and told me the stories of people with sad experiences. The decision was instantly made: I would go to the south of France as soon as I defended my PhD thesis.

On February 15, 2011, my spouse, Sepideh Farmani, and I left Zurich to go to the Pyrenees. On February 16 we arrived in Aurignac, France, about 35 km from Grothendieck's home in Lasserre. The next morning, we drove to Lasserre. We entered the little town, with tiny streets. Even though we had the postal address, finding the right house was by no means trivial; there was no number or name tag. We finally found the house, which had a rather big garden. As you can imagine the house did not have a door bell. We didn’t know what to do. We talked to his neighbors. They were very nice people. They told us that Grothendieck would very rarely leave the house, maybe once a month to collect and send mail at the post office. They also told us that few months earlier a young lady had tried to meet him. Their advice was to shout his name, wait patiently, hope, and prepare for disappointment. We followed their instructions. I never shout. I never talk loudly in public places. It was hard to shout "Monsieur Grothendieck" in an unknown place! After some hours, Grothendieck came out. The excitement was high! I called out his name again from behind the garden fence. He was about four meters away. He turned, but did not pay any attention. He looked at some of the plants in the garden. I'm not sure what he did. But after few minutes he went back in. It was getting dark. We waited a little longer in vain. I was a little hurt, just a little; why would he not answer me? Why total ignorance? Sepideh suggested that I write a letter to him, where I introduce myself, tell him what I wanted to tell him, and explain what happened that day. I had a portrait of him printed on an A4 paper. On the back I wrote the letter. I put the letter in his mailbox. We drove back to our hotel in Aurignac. That night I wrote to Prof. Winfried Scharlau, to tell him that I was there and asked him if he had any tips for increasing my chances of meeting Grothendieck.

The next morning, we drove back to Lasserre. There is a school in the town. There were about five children and two teachers. We met them and talked to them. We told them why we were there and they told us they knew that a great mathematician lived there, but they had never met him. We also talked to the lady at the post office. She told us that from time to time Grothendieck would come to the post office. Another friendly neighbor told us that Grothendieck's phone worked only in one direction and that usually he ordered his groceries on the phone. The neighbor with whom we had spoken the night before had told us that Grothendieck usually worked until late at night (about 3 or 4 in the morning) and he would wake up late in the morning, around noon. Of course they didn't know the exact time, but this was his lifestyle for a long time and this family had lived there for a long time, before the time Grothendieck had abandoned all social interactions. So, not expecting to see him in the next couple of hours, we studied the little town.

It was early in the afternoon. I was pacing in front of his garden, hopelessly, and regularly checking his door. All of a sudden, Grothendieck came out of the house. He checked his plants and then moved towards the gate, where his mailbox was located. I rushed towards him. When there was only a fence between us, I called his name. He greeted me. He was checking his mail. Instead of introducing myself —which I had done in the letter— I told him that I had written something for him. He took the letter and started reading it.

He would stop now and then to answer a question or address a point in the letter. He apologized for not having answered my call the day before, because his hearing was not very good (something that became obvious the instant we started our conversation). I had said in the letter that I was a mathematician working in Arithmetic Algebraic Geometry, that I had just finished my PhD and that I was about to start a Postdoc position at the California Institute of Technology. But I had made a point not to discuss Mathematics. He had decided to leave Mathematics and I didn't want to violate his decision. And I didn't want to meet Grothendieck to "learn" Mathematics or to get "inspirations". For sure, I came to know him through Mathematics, but after reading more about him and his non-mathematical work, my admiration for him only grew. He was no longer just a great mathematician for me. Well, if I have to talk about my feelings about Grothendieck, I would have to write pages and pages. All I want to say here is that I didn't talk about Mathematics because he probably didn't want to and also it was not the reason why I wanted to meet him in the first place.

I had written about my background. That I was a Muslim from Iran. He said that he also believed in God, but he didn't follow any "traditional" religion. I had written about my feelings towards the mathematical community and that I shared some of the feelings he had when he left the community.

When the letter was finished and he saw his portrait on the verso, he was quick to ask where I had obtained his picture. I was not sure how much he knew about Internet. I told him that I had downloaded it from the website Grothendieck- Circle. He was very displeased to hear it. He told me that he had requested the responsible people to take down the site. I assured him that the site was indeed inactive. I wanted to tell him that it was thanks to this site that many people (including myself) got to know more about him and that it was such a valuable source for his legacy, but I decided to let him be the speaker. He asked how I had obtained his address. I explained. He also asked if I was alone and if I had driven all the way from Zurich. When I told him that my spouse and I (and only the two of us) drove from Zurich to meet him, he was very touched, and thanked us. I think he did not realize what position he occupied in the heart of so many passionate mathematicians, for whom Mathematics was not everything, and saw Grothendieck not just as a great mathematician, but as an activist, a rebel and a person of principles.

He apologized that he could not invite me inside his house. He told me that back in the days, his door was always open and everybody was welcome to go inside his house whenever they wanted. I could sense sorrow in his blue eyes and deep voice. "But now, it would be better for your own well-being not to come inside", he said. He just said that there were des êtres occultes that could harm me (maybe I should mention that our conversation was in French, so I'm translating, and neither French nor English being my mother tongue, I hope I have understood what he said and am able to translate it to English the best I can). I didn't press him to elaborate. I believe that because of my Eastern spiritual heritage I was not shocked by what he said. But I am also a mathematician hit by the passion of Mathematics when I was 12. So, it was in my nature to examine these unexaminable claims.

He said: "you know, nobody loved Mathematics the way I did". It was clear that it was not one of those easy and cheap claims some people make. He said that he suffered for his amour of Mathematics like nobody else. I don't know how one measures these emotions, but it was evident that he had pondered over them for a very long time.

He talked about pain and the importance of suffering; la douleur et la souffrance. When he was instructing me to write to him, he emphasized on the fact that he would only reply my letters if I had written them "with pain" (and that he would know if I had suffered). This was how he did Mathematics, he declared.

He told me that he was not anymore doing Mathematics in the "traditional" sense, but was "using" or "applying" Mathematics in order to describe the "Universe". He would often need to invent new Mathematics for that, he added. He was not doing a physicist's job; rather a philosopher's. It is easy to dismiss this effort as futile, but from what I knew about Grothendieck and the serious air, with which he was speaking, I believe one should expect something profound in his “forthcoming” oeuvre (that we might never see!).

From the accounts I heard from his neighbors, of people trying to meet him and the way he spoke of some letters he had received, it was clear that he was wary of people meeting him. He stressed on several times that this was for their own good. He didn't ask me, but I assured him that I would not recount to anyone this visit, in order to save him (or them) from the ordeal of such visits. I kept my promise and I revealed my secret only after Grothendieck's passing.

It was now time to say goodbye. I queried whether I could visit him again. He said that we would soon meet each other again, but not in this world. In the meantime, however, I should write to him, he advised. Hesitantly, I asked him if he would allow me to take a photograph with him. I said I wanted to keep it as a memento. In his gentle manner, he told me to come closer. He shook my hands and hugged me and said that this hug was a better memento. Of course it was. Still today, I cherish that memory; the smell of the grass, the golden light of the setting Sun, his kind smile and the echo of his captivating voice.

Then, I watched him fill some bowls at gate of his garden. They were for neighbors’ cats. Trying not to make him uncomfortable, I left and sat in the car, meters away from his garden. We watched him in high spirits, for the last time, as he was going back in, trying to engrave every millisecond in our memory…

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Katrina Honigs September 27, 2015

I met Alexander Grothendieck on January 2, 2012. As I made my way to a car rental center in the outskirts of Toulouse that morning, with the sky still dark, the displays on passing buses flashed between their numbers and “Bonne Ann´ee.

I was halfway into my third year of graduate school and had read a bit of Alexander Grothendieck’s mathematical work and felt a sense of connection with it. I found his writing to be generally very clear, and I liked his approach to algebraic geometry. In my own career, I was at a point where I was not only not making progress on solving any problems, but miserably unengaged by my work. But despite the burnout, Grothendieck’s work remained an island of enjoyment in an otherwise featureless sea. Grothendieck is unquestionably one of the most influential mathematicians of the 20th century, and to a graduate student all the way in California, his exit to live the life of a hermit, location unknown somewhere in the Pyrenees of France or Andorra, rendered him a practically mythical figure.

But I am driven to demystify – it is part of what motivates me to be a mathematician – and when we tell ourselves and others that our heroes are inhuman and on a pedestal that is not just high but unattainable, we are actually pushing ourselves down rather than climbing. And so, following a decision to attend a conference in France, some emails, a lesson driving with a manual transmission, a session of studying maps, and a long conversation at the rental car center made difficult by my limited French, that brisk but mild winter morning found me driving through rural France, wildly hoping for a conversation about mathematics, or that I might at least see that it was truly a real person who did all the work with the name Grothendieck on it.

Lasserre is small and remote, but Grothendieck’s house is by no means the isolated cabin in a dark forest that I had imagined when I first heard about him. That area of the Pyrenees is lovely, and the drive through a rolling land- scape down lanes lined with sycamore trees featured views of fallow winter fields and blue mountains swelling along the horizon that reminded me very strongly of where I grew up in the foothills of the Appalachians. The town is so small that the houses do not have numbers, which, judging by the dubi- ous looks and patient explanations that addresses really should have numbers that French postal workers gave me when I handed them my letters addressed to Grothendieck, is relatively uncommon. Since I didn’t know which house in Lasserre was Grothendieck’s, I chose to park in a convenient small gravel lot. I was faced with a very finite number of possible houses since Lasserre consists of the intersection of a few roads, and figured I would find my way after knocking on some doors and inquiring where I might find the person who proved the representability of the Quot functor. However, it wasn’t necessary to make in- quiries this way: my appearance in a rental car was a strange enough event in Lasserre that as soon as I put the car in park, a friendly man came out of a nearby house to ask if I needed any help. He appeared to be a bit puzzled by my pronunciation of “Alexander Grothendieck”, but after I further explained that the person I was seeking would be someone “vieux et ´etrange”, he was abruptly quite certain of who I had in mind, and we giggled like children whis- pering in the back of the classroom over having described Grothendieck this way. Grothendieck’s house was not 50 feet away from where I had parked. His neighbor walked me over to the locked gate, shrugged, and walked away.

I returned to the car to equip myself with a pair of shoes lighter than the boots I was wearing that I had brought along for fence-climbing, and some galettes du roi full of almond paste, a pastry made during the church season of Epiphany, which I had purchased that morning in preparation for fence- climbing-apologizing.

Some lights were on in the house, but there was no sign of movement when I approached the gate. I hopped easily over the fence, which was made of wood and stone and about waist-height, much more modest than it had loomed in my imaginings in the previous weeks. I stepped furtively across the slightly ramshackle yard, which had many plants and terra cotta pots in various degrees of wholeness, and walked up the steps. I knocked on the door and waited, and then I knocked again. Getting more nervous, but aware that this would likely be my only chance to meet him, I shouted “Monsieur Grothendieck!” and waited, but there was no response. Thinking of the baked goods in my bag, I called “Je vous apporte quelque chose de bon!” and then cringed as I realized that was an odd tactic, like something someone might say to entice children into a windowless van. What should one say to get Grothendieck’s attention? Maybe a new proof of a big conjecture, but I didn’t bring one. I tried calling his name a couple more times, but there was no sign that I was heard. Looking over at the windows to my right, I started to wonder how long I should stay. I had done my best to arrive at a likely time of day, about 11 am, and it occurred to me that I hadn’t decided what to do in the event that Alexander Grothendieck did not happen to be sitting right by the door, ready to greet me.

When I looked up from my reverie, I realized that a figure with a large white beard wearing a brown robe over his clothes had appeared utterly silently quite nearby on my left. I was so startled that I felt like I was outside myself watching the scene. My eyes widened, I jumped involuntarily, my heart pounded. I thought, wildly, “Oh no, what if I have accidentally come to the home of the wrong hermit?”. But as soon as I looked at his face, I recognized it from photos I had seen. Oddly enough, it was not the more recent photos where I saw the resemblance, but to a much older black and white photo of him when he was young. “It’s you!” I managed, idiotically. Grothendieck stood impassively. In one hand, he held a short pitchfork loosely at his side. It reminded me of his doodle of devils with pitchforks around the Grothendieck–Riemann–Roch formula. His free hand rose, brandishing an admonitory finger. “Il ne faut pas entrer,” he said, advancing slowly toward me. I tried to form some sentences about visiting, but Grothendieck did not react. He continued to walk slowly toward me, wagging his finger, telling me that I shouldn’t be in here disturbing him, and asking me how I got in here.

When he seemed totally unmoved by my getting out the bakery box from my bag and told me again to leave, I returned to the gate. I explained that I had climbed the gate to get in, but when he didn’t react at all, I thought (nonsensically, I now realize) that he wanted me to climb back over the gate to prove to him that this was indeed how I entered his yard. But, the ground under the gate was sloped so that the fence was significantly higher from the inside, and I was shaking from the huge influx of adrenaline that I was experiencing. After a few horribly embarrassing failed attempts at pushing myself back over the gate, during which all I could think, over and over, was “Alexander Grothendieck is watching me” (which he was, with what I might describe, in retrospect, as detached bemusement), I asked him to unlock the gate. However, he stood totally still and silent, like my own personal Ghost of Christmas Future, and then told me, once more, to get out. I thought I had better not fail at this next attempt. I tossed my bag, hat, and scarf over, did a bit of a run up, and vaulted inelegantly over, smacking my shin hard on the gate on the way. Seeing the bruise later helped me convince myself that I had not dreamed up this entire episode.

Once he had seen me leave his yard, I thought that Grothendieck might just walk off, but I decided to wait. He did as well, and we studied each other from opposite sides of the gate for a moment. We were a similar height, and his blue eyes were alert and focused. Grothendieck asked me not angrily, but a bit sternly, in French, how I knew his address and how I had gotten there. He told me again that I should not have come in, and should not have disturbed him in his “cloˆıtre”, which reinforced the impression given by the brown robe he wore that he thought of himself, in some sense, as a monk. When I was given the address, I had said I wouldn’t tell Grothendieck how I came by it, so I just watched him silently during this monologue, looking shocked.

Then, he asked me my name, and explained that he could not hear very well anymore and so I must shout into his ear, a piece of information that abruptly made sense of our interaction thus far. It was quite disconcerting to need to get so close to him, and after I said my name I started to spell it to be helpful, but he stopped me partway in since he had already recognized it: a couple of weeks before, I had sent what I now realize was a very enthusiastic fan letter. He then switched to English and, irritably, asked me why I included a French translation. “To be polite? La politesse?” Everything I had seen of Grothendieck’s was written in French or German, and so it had seemed appropriate to me, but it was very apparent that he found my explanation unsatisfactory. Of course he knew English, and I had offended him a little.

He told me he had responded to my letter, explaining that my reasons for contacting him were insufficient, and that I should not visit. I felt a bit deflated as I realized the content of my letter was of course in no way interesting to him, but I also couldn’t help but be a little amused. Trust a mathematician to tell me that my reasons for writing were “not sufficient”. I hadn’t received his response, and realized that including my own name on the return address (rather than the name on the mailbox at the place I was staying) must have been an error. Later, I went to a post office to try to retrieve the letter, but had no luck. Actually, my inquiries ended with the woman working there getting very angry and shouting at me that if the letter was so important I should have addressed it properly – how could it be delivered without the correct name? The people delivering the mail aren’t mind-readers! I made the mistake since US postal workers, also not mind-readers, deliver mail to the address on a letter regardless of the name listed. Trying to explain the reason for the mix-up in my politest French, in the hopes that the worker would feel sympathetic and help me to navigate the system, only brought forth more ire. I’ve still never gotten the letter.

After Grothendieck discovered that I had not received his response to my letter, he seemed to decide that this explained my presence in part, but was still dissatisfied and asked again why I had visited. He told me repeatedly that I should have announced myself. It seemed lost on him that I had no idea how I might have done this. I certainly don’t have his phone number, and would have struggled to provide the information far enough in advance to put in a letter. Did he take carrier pigeons? Clearly a bit suspicious that I had some unsavory motive, he said he thought that my visit must indicate that I wanted something. I told him that maybe he didn’t realize, but he is very famous and I just wanted to meet him. He shrugged and said again that I didn’t have any satisfactory reason for visiting, but I could tell that he was a bit amused by being told that he was famous, and he relaxed a bit.

He told me that he could see from my face that I didn’t have any bad intentions, and that he would never want to harm anyone. I didn’t notice it before, but I saw then that the pitchfork was no longer in his hand, but propped against the fence. He said that he had some bad experiences, and he could not invite me in, though he would like to. If you had received my reply, he said, you would have understood that I am not taking visitors and you should not disturb someone in their retirement. He expected, though, to receive a letter from me soon explaining how I got his address. “C’est la moindre des choses,” he intoned, switching back to French for a moment. He used to receive all his visitors, he said, but he had two very bad experiences and no longer did it, though he was very sorry that I came such a long way to not be invited in, and that he was sorry for himself as well that he was not able to invite me in. He took my hand and shook it. The conversation took a maudlin turn. He told me that he thought we would meet again, very soon, though not in this life. He told me he thought that he would die within the year, though this prediction was made with a practiced air that suggested this was not the first time he had made it.

After these heavy declarations, he turned his attention back to my visit. For all his bluster about not wishing to be disturbed, a part of him was curious about his visitor. How did I get here? On a train? No, in a car. Am I rich? No. Am I poor? Of course I’m poor! I’m a graduate student! I laughed, and he chuckled good-naturedly. Am I alone? Yes. Didn’t I have something for him? The bakery box reemerged, and I opened it to show him the contents. He looked at the pastry inside. What is it? Galettes. What? Galettes! Did you make them? No, I bought them. What? I bought them! Oh, thank you for making them. He took the box from me, and said he wanted to get something for me too, and then went back into his house. I was glad for my instinct to bring baked goods. They smooth everything over in the American midwest, where I’m from.

This conversation had all developed in an unforeseen direction. I had not been able to discuss math with him at all. At one point, when I tried to make our conversation more detailed by writing on a piece of paper, he waved it away. But we spoke more than I had thought we might, and when he came back out of his house he presented me with a tomato and a packet of almond paste. The tomato was large and fresh and came from his garden – impressive for January – and he told me to eat it in good health. He also said I should remember that it was his friend; likely something was lost in translation. The packet of almond paste was very large. A kilo. I was not sure what to make of this generosity, and later, when I baked with it, it was good, though I realized that it had already expired when it was given to me. Almond paste has a very long shelf-life, so Grothendieck had likely had it for quite some time.

After the exchange of gifts was over, it seemed we were finished. Grothendieck wished me well, shook my hand again, and, after entreating me once more to write a letter telling him how I came to know his address, told me goodbye and walked back to his house. I said goodbye as well, but his back was already turned to me and I realized right after I spoke that he likely didn’t hear me.

My experience of the rest of the day was odd and heightened. The drive back through the countryside. The primary colors of the public transit train in Toulouse. The tomato, when I ate it later that day. As the days and weeks went on, the visit was something I reflected on with enjoyment. My burnout faded and I got more excited about my work again.

A little while after my visit, I did write Grothendieck again, but my letter was returned unopened, even though he had requested I write it. I wrote to him a few further times, and my letters all came back unopened and labelled “retour a l’envoyeur” in his distinctive script. I knew from those returned letters that he did not die within a year of my visit, and I was glad to see his prediction was wrong, though after my letters continued to be returned, I gave up on writing. I was sad to learn of his recent death, and I have written about my visit to him as something of a memorial, though of course I am writing not as someone who knew Grothendieck at all, but someone who was interested by his life and work. As I look at the story of my visit, I hope it is clear that I didn’t write it to be disrespectful, or to claim any great insight into Grothendieck’s life, but I wrote it because I think it’s a story worth telling: a bit odd, a bit funny, and, at least to me, a bit meaningful. Despite all the headlines suggesting it would be impossible, I got to meet Alexander Grothendieck in person. Although my fantasies of having some magical conversation about math with him had to be swept aside in the face of the reality that he wasn’t really interested in me (though I have to say he handled my trespassing on his property very cordially), I am grateful to have had the chance to meet him.

#Alexander Grothendieck

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Arthur Lehning (1924). Traducido por Libertamen Fuente: L’idée anarchiste n°10-11 del 13 agosto y n°12 del 12 septiembre de 1924 Mientras el movimiento socialista moderno no fue parlamentario, tuvo un carácter antimilitarista y revolucionario. La primera internacional, la Asociación Internacional de Trabajadores, fue el primer gran intento de unir a los trabajadores de todos los países bajo la bandera de la lucha de clases y la liberación de la esclavitud del trabajo. Su idea motriz era que la liberación de los trabajadores debía ser obra de los propios trabajadores, y su arma era la solidaridad económica. Aspiraba a la emancipación del trabajo, y por esta emancipación entendía la igualdad económica, sin la cual la libertad política no es más que una apariencia engañosa. También declaraba que esta liberación no podía ser local ni nacional, sino internacional, y por eso llamaba a los trabajadores a luchar por la solidaridad internacional. A partir de ese momento, los trabajadores no debían tener otra patria que la gran Federación de Trabajadores de todo el mundo. Este espíritu revolucionario, este llamado a la fuerza y solidaridad económica de los trabajadores y a la acción directa se mostró luego en el III Congreso de la Internacional, celebrado en Bruselas en 1868, se debatió la cuestión de la guerra. Se presentó una resolución en la que se afirmaba que sólo hay una clase que tenga la fuerza y la voluntad real de dirigir la lucha contra la guerra: la clase obrera, y que el único medio eficaz de oponerse a la guerra es la paralización del trabajo, es decir, la huelga general. Desgraciadamente, este camino no se siguió durante mucho tiempo. Cuando, en el Congreso de Bruselas de 1891 y en el de Zurich de 1893, Domela Nieuwenhuis presentó una resolución a favor de la proclamación de la huelga general en caso de guerra, se le llamó utópico y exaltado, y se declaró que su resolución era mera fraseología. Domela Nieuwenhuis señaló en vano que su resolución estaba en consonancia con la concepción original de la Internacional y que el vago utopismo del que se le acusaba, mientras apelaba a la clase obrera, encontraba más bien su expresión en la resolución alemana que hacía a la burguesía irresponsable de la guerra.Si las palabras socialdemocracia y socialdemócrata las hubieran cantado Cristo y el cristianismo, el Ejército de Salvación o el Papa, nos habríamos puesto de acuerdo muy rápidamente. La huelga general es una estupidez general, se decía comúnmente en la socialdemocracia de la época. La única manera de conseguir el objetivo era trabajar para que la gente entrara en los cuarteles como socialistas. No parecían entender que el socialismo y los cuarteles eran dos cosas particularmente irreconciliables: al igual que incluso hoy hay gente entusiasmada con el militarismo proletario Scensa, el representante australiano, mostraba un estado de ánimo diferente. Junto con Francia y Noruega, fue el único país que votó a favor de la resolución holandesa. No puedo entender», dijo, «cómo los hermanos pueden permitir que se les ordene destrozarse unos a otros. Si me ordenaran cometer tales asesinatos, sería el primero en disparar a quien me lo ordenara. Por lo tanto, voto a favor de la resolución neerlandesa. Aunque esta concepción no representaba el punto de vista tolstoiano de la no resistencia absoluta a la fuerza (Domela Nieuwenhuis nunca representó tal punto de vista).Sin embargo, era más revolucionaria y realmente más antimilitarista que la concepción oportunista de la socialdemocracia alemana. La socialdemocracia se había adaptado por fin tan completamente a todo el sistema del Estado capitalista que era realmente parte integrante de ese Estado, y puesto que toda su táctica se reducía exclusivamente a ampliar esa influencia, era una imposibilidad absoluta que se posicionara jamás contra ese Estado. Fue la concepción que Marx tenía del Estado la que lo apartó del camino que él había seguido y lo vinculó cada vez más estrecha y exclusivamente a la política parlamentaria y a la lucha de clases «parlamentaria irreconciliable» con una táctica antimilitarista consecuente. La apoteosis de la conquista del poder político tuvo lugar el 1 de agosto de 1914, lo que demostró que en la lucha que la Internacional antiautoritaria había librado bajo la bandera de Bakunin, confió Marx, era Bakunin quien tenía razón.La Internacional Antiautoritaria podía continuar la tradición original de la Primera Internacional, porque siempre se apartó por principio de la política parlamentaria, porque no quería conquistar ningún Estado centralista para implantar el socialismo dictatorial, sino que consideraba que el primer deber del proletario era destruir ese Estado (si reconocía también el centralismo económico) y no esperaba otra salvación que la de la organización económica de los propios trabajadores. Frente al racionalismo y maquinismo preponderantes del autodesarrollo de las relaciones económicas, el anarquismo y el sindicalismo originarios siempre han defendido el elemento psíquico, la voluntad creadora. Por lo tanto, se continuó la tradición antimilitarista revolucionaria original que sólo conocían los anarquistas y sindicalistas, para quienes el antimilitarismo no era sólo un método táctico, sino parte de su visión del mundo, y que sentían que el militarismo era la mayor ofensa a la personalidad humana. Cuando, a principios de este siglo, el capitalismo moderno inició su ascenso sin parangón hacia la fase imperialista, los socialistas libertarios redoblaron sus esfuerzos para prevenir la amenaza de guerra. Así, Domela Nieuwenhuis, junto con algunos camaradas franceses, convocó un Congreso en Amsterdam en 1904, donde se fundó un grupo antimilitarista internacional, el «I.A.M.V.», cuya tarea era unir a todos los antimilitaristas lógicos para luchar contra el militarismo en todos los países [1]. Por diversas razones, la I.A.M.V. sólo pudo sobrevivir en Holanda. Por una serie de razones estrechamente ligadas al desarrollo histórico del pueblo holandés -y en las que no podemos entrar aquí, dado el estrecho alcance de este artículo- es comprensible que el antimilitarismo revolucionario se concentrara en el movimiento holandés. En 1917 se intentó restablecer los vínculos internacionales rotos por la guerra y convocar un congreso -en cuya preparación colaboró Domela Nieuwenhuis hasta su muerte en 1919- que finalmente se celebró en La Haya en Semana Santa de 1921.En vísperas del Congreso, una vez restablecidas las relaciones, se puso de manifiesto que en todos los países habían surgido organizaciones antimilitaristas como consecuencia de la guerra. Éstas tenían ya su propia historia, tradiciones y principios, lo que hacía difícil que pudieran afiliarse a la I.A.M.V. de forma organizada. A pesar de ello, el comité preparatorio del Congreso publicó un amplio trabajo sobre todas estas organizaciones, que era de la mayor importancia. Además, había organizaciones cuyo objetivo no era exclusivamente antimilitarista, como las organizaciones obreras anarcosindicalistas, las organizaciones juveniles, etc., pero que rendían tributo a un punto de vista revolucionario antimilitarista. Se decidió fundar una oficina internacional para concentrar todas las fuerzas revolucionarias antimilitaristas contra la amenaza de guerra y la reacción dominante. La Oficina Antimilitarista Internacional se fundó entonces en el Congreso de La Haya en Pascua de 1921, con la siguiente declaración de principios: La Oficina Antimilitarista Internacional contra la Guerra y la Reacción, compuesta por organizaciones antimilitaristas revolucionarias, Su objetivo es trabajar a escala internacional contra el militarismo. Hacer imposible la guerra y la opresión de las clases trabajadoras: Se esfuerza por fortalecer en la mente de los trabajadores la conciencia de su poder económico decisivo; Hace propaganda a favor de la huelga general y del rechazo masivo del servicio militar; Aboga por el cese inmediato de toda fabricación destinada a la guerra y por la no participación en el militarismo. Se esfuerza por hacer inútiles los ejércitos y las armadas; Rinde homenaje a los que rechazan individualmente todo servicio militar; Se opone con vehemencia a toda tentativa de nueva dominación, ejercida por una intervención querida contra un proletariado que ha roto el yugo capitalista; Contra todas las formas de explotación económica y de opresión militar de que son víctimas las razas de color; Fortalece la unión y la colaboración del proletariado revolucionario de Norte a Sur, de Este a Oeste. En la conferencia de la IAMV celebrada en Berlín en 1923, la Junta revisó su actitud hacia Rusia. Anteriormente, el IAMV había considerado el lado defensivo de la revolución frente a la política de intervención y el furioso terror blanco.Pero ahora se tiene la impresión de que, por diversas razones, la revolución ha llegado a una etapa definitiva y que, desde el punto de vista revolucionario antimilitarista, hay que combatir a los representantes del Estado soviético. Por consiguiente, se decidió extender las actividades de la A.I.M.V. al fenómeno revolucionario ruso. Esta decisión se plasmó en la siguiente resolución: La Conferencia de la B.I.A. (Berlín 1923) considera como una de las consecuencias más peligrosas de la reacción mundial, inmensamente reforzada por la guerra, el hecho de que los revolucionarios de Rusia, en su lucha por la libertad, hayan llegado a emplear cada vez más métodos militaristas. La Conferencia expresa su firme convicción de que no se puede aniquilar la opresión capitalista y militarista, ni conquistar la libertad económica y social mientras se empleen métodos militaristas en la revolución social. Así como la B.I.A. ha protestado siempre contra el servicio obligatorio en los países capitalistas, la Conferencia protesta ahora contra el sistema de servicio obligatorio, que se está impulsando cada vez más en Rusia, y contra la política general de opresión que ha echado por tierra las primeras esperanzas de la revolución. El hecho es innegable: los propios trabajadores construyen sus propias prisiones y forjan sus propias cadenas. La obra de demolición de los cimientos de la esclavitud sólo podrá llevarse a cabo cuando los trabajadores se nieguen a trabajar al servicio de la destrucción y cuando estén dispuestos a realizar únicamente un trabajo humano. A este respecto, John Ruskin ya había declarado que sólo debemos realizar trabajos que beneficien a la humanidad. Y su axioma adquiere aquí de nuevo toda su importancia. Esta fue también la idea central del discurso de Max Nettlau en el Congreso de Londres de 1896, en el que planteó la cuestión de la responsabilidad de los trabajadores por el trabajo que realizan.Declaró que es indigno de un hombre hacer daño a sus semejantes, simplemente porque los capitalistas se lo exigen: Queremos liberar a los hombres ante todo en su mente, apartarlos de hacer aquellas cosas que perpetúan la miseria y la esclavitud de sus semejantes, y crear así una amplia corriente de simpatía y solidaridad que será la base de toda acción futura. Es fácil ver que este pensamiento se relaciona inmediata y esencialmente con el militarismo y lo que de él depende. Además, la idea de abstenerse de toda producción para la guerra y el militarismo ejerció una gran influencia en las tradiciones cristianas y, en particular, en las ideas de Tolstoi. Libertad también escribió: … Es este trabajo de la muerte el que, ocupando a más hombres que el trabajo de la vida, hace posible sobre todo el poder de la burguesía. Y, dirigiéndose a los que pensaban que de repente podría surgir un nuevo modo de vida en sociedad, dijo: La destrucción total va unida a la destrucción parcial. Rudolf Rocker también declaró en su discurso ante la Conferencia de Trabajadores Armamentísticos: No más armas para la guerra.Que el único medio de prevención para poner fin a las masacres organizadas es negarse a fabricar armas. Los congresos internacionales han proclamado con entusiasmo la necesidad de «deponer las armas», pero no han tenido el valor moral de deponer los martillos que las forjan. De nada sirve arrancar a la burguesía todo el aparato del Estado y los medios de producción; pero se trata de destruir estos medios de producción de máquinas asesinas, y este aparato de fuerza del Estado. Esta es la razón por la que los revolucionarios son también los oponentes de este frívolo militarismo rojo; porque en el militarismo están luchando no sólo contra una forma de asesinato colectivo y organizado, sino también contra un estado bárbaro del espíritu humano. Pues el militarismo domina no sólo en la guerra sino también en la paz, no sólo en los cuarteles sino también en la fábrica. La industria moderna ha introducido el sistema disciplinario de los cuarteles en la organización de la producción, tal y como lo formuló de Ligt. El capitalismo se opone tanto más al socialismo cuanto que está de acuerdo con el espíritu de guerra. De nada sirve acabar con el militarismo blanco si es sustituido por nuevas formas de militarismo.La revolución proletaria exige medios distintos a los de la guerra burguesa. Las relaciones obreras modernas han introducido por sí mismas medios de lucha y de liberación, como la huelga general, que no sólo golpean el corazón del capitalismo, sino que tienen una gran importancia moral para los trabajadores. Sobre todo, son el medio más adecuado para alcanzar el objetivo, ya que permiten a los trabajadores desplegar todo su poder, no en el terreno del militarismo y la guerra, sino en el terreno económico. El militarismo no sólo se utiliza contra el enemigo exterior en la batalla de los intereses económicos de los diversos grupos capitalistas dominantes y para la opresión de las razas de color, sino que también se utiliza contra el enemigo interior. Por consiguiente, el concepto de antimilitarismo burgués no es más que una broma, ¡ya que burguesía ya significa guerra! La paz en la sociedad burguesa es una guerra latente. Por lo tanto, no hay nada que esperar de aquellos movimientos que mantienen el sistema económico dominante, o que no quieren cambiar nada fundamental en él, y que, luchando contra las consecuencias de la guerra y del capitalismo, descuidan la lucha contra sus causas reales.No podemos elegir una posición intermedia entre la guerra y la revolución, porque no la hay. Lo mismo ocurre con la famosa Sociedad de Naciones, a la que esperamos hoy como esperábamos los Parlamentos antes de la guerra. La Sociedad de Naciones no es un vínculo de pueblos, sino un vínculo de Estados y gobiernos que, en realidad, representan los intereses de los grupos capitalistas que se agitan detrás de ellos, porque hoy no hay más política que la ordenada por el capitalismo. La socialdemocracia defiende hoy esta Sociedad de Naciones como defendía el parlamentarismo antes de 1914, fuera del cual, decía, no había salvación. Es fácil prever lo que podría esperarse, en caso de guerra, de esta Sociedad de Naciones y de esta socialdemocracia, mientras cuente en su seno con «dirigentes» de la II Internacional como el socialdemócrata chovinista Vandervelde, que es, además, ministro de Su Majestad y que todavía hoy declara que no podemos oponernos a una guerra defensiva. Esta mentira chovinista sobre la guerra defensiva es una de las principales razones por las que la guerra moderna sigue siendo posible. Pero, como ya se ha dicho, el militarismo no sólo sirve para hacer la guerra en el extranjero, sino que también es el apoyo más fuerte y eficaz del Estado. Puesto que la policía y la burocracia, los estatistas, representan diversas y particulares formas de militarismo, puede decirse con certeza que el poder del Estado se construye sobre la fuerza del militarismo; por otra parte, está claro que el militarismo desaparece si se destruye el Estado. Porque el Estado significa dominación y explotación, es decir, esclavitud, y el estado de ánimo militarista sólo es posible mediante la esclavitud. La dominación y la explotación significan la negación del socialismo, que es la colaboración fraternal de personalidades libres. El militarismo es la negación del socialismo. El ejemplo de Rusia ha demostrado que el Estado proletario está sometido a la ley de hierro de toda política. Necesita un militarismo, dedicado en apariencia a los intereses del pueblo, pero, en realidad, al servicio de la conservación del Estado. Quien quiera el Estado debe querer un Estado nacional. Y quien quiera un Estado nacional debe querer la guerra.El fascismo, esta organización militarista de la contrarrevolución, y esta contrarrevolución del militarismo, sólo ha podido sobrevivir en el terreno del Estado nacional. Por eso la Declaración de Principios de la I.A.M.V. afirma con razón que la creencia en el Estado debe ser combatida por encima de todo, porque convierte al hombre en esclavo del militarismo y amenaza incluso su derecho a la vida. El antimilitarismo tendrá una tarea que cumplir en la revolución, donde será una cuestión (todos los revolucionarios están de acuerdo en esto) de intensa humanidad, solidaridad voluntaria y libertad. El militarismo es la negación de la libertad, la negación de la solidaridad, la negación de la humanidad. La idea de revolución está estrechamente ligada a la idea de antimilitarismo, del mismo modo que el antimilitarismo es indisoluble de la revolución. Notas [1] Este año la I.A.M.V. conmemorará el vigésimo aniversario de su fundación. La influencia socialista-libertaria de esta organización antimilitarista es única en el movimiento obrero moderno. Tags: antimilitarismoEnlaces relacionados / Fuente: https://libertamen.wordpress.com/2024/11/27/el-antimilitarismo-revolucionario-y-la-internacional-antimilitarista-1924-arthur-lehning/

#anarchy #anarchism #social war #revolution #anarchie #anarchisme #anarquia #anarquismo #updates

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