A (very) Brief History of Alexander Grothendieck

alexander grotendek was a 20th century mathematician who made wildly important contributions to topology algebra and logic earning a fields medal in 1966. amongst his many contributions to mathematics he's most notable for being the leading figure in the construction of contemporary algebraic geometry adding the following to its foundations commutative and homological algebra which studies algebraic structures in terms of their generators and relations sheaf theory with the sheaf being a tool for systematically tracking locally defined data attached to the open sets of a topological space and category theory a general mathematical theory of structures and of systems of structures groton deak is considered by many to be the greatest mathematician of the 20th century groton deak was born on march 28 1928 in berlin germany to anarchist parents alexander sasha shapiro and joanna honka grondik to understand groton dekemore it's important to go a bit more in depth into his parents backgrounds shapiro referred to generally as sasha was a russian man of jewish heritage born in novozibkov a town near the point where russia and the ukraine met at age 15 he fought for the revolutionaries against the russian czars being caught in 1907 and sentenced to death with his fellow comrades due to his age sasha ended up just being given life imprisonment instead of being killed he then spent 10 years in prison before escaping during the bolshevik revolution in 1917. after his escape he continued to fight for the anarchists being captured several times but always managing to escape he actually lost his left arm on one of these occasions sasha ended up marrying a woman named rachel and had a son with her named dodec due to his anarchist ties and the increasing oppression on anarchists in russia he ultimately had to evade russia in 1921 and ended up in berlin changing his name to alexander taneroff making a living as a street photographer joanna generally referred to as hanka was a woman of dutch origins born in hamburg germany who joined many left-wing groups working as a journalist for a progressive paper called der pronger she ended up marrying a journalist named alfred raddatz having a daughter in 1924 with him named froda but referred to as mighty on a visit honka made to berlin she ended up meeting sasha the pair had an affair which later resulted in the birth of alexander grondik our focus of this video as well as hanka leaving raditz to live with sasha the pair never married from 1928 to 1933 sasha honka maedi and groton deak lived in berlin together the family made money from owning and managing a photography studio but needless to say they lived in poverty in 1933 with hitler's takeover fear struck sasha due to his jewish heritage and he left for paris in may of 1933. honka stayed in berlin with groton deak and maiety until december 1933 where she then joined sasha in paris before leaving honka arranged for groton deak to live with a lutheran pastor wilhelm haydorn and his wife dagmar in hamburg and maidy was put into an institution for mentally handicapped children in berlin note that mayadi survived the war and eventually emigrated to the united states while living with the heydorns groton deacon attended elementary school and began studies at the local gymnasium but in april 1939 these studies were cut short due to rising fear of jewish persecution the haidorns felt they were in serious danger being a part of the hitler resistance so they located grotondig's parents in paris and put him on a train to go join them groton deak ended up spending the summer of 1939 and neem with his mother with the outbreak of world war ii groten deak and his parents were now in great danger even in france there was a law passed on november 12 1939 concerning undesirables requiring germans living in france to be sent to internment camps groton deak and his mother were interned in the hayuku camp near mund and sasha was interned in camp tu vergne it's almost certain that groton teak and hanka never saw sasha again while at huyuku groton deak was still allowed to get an education and he did so at a school in mullend about three miles from the camp also receiving private tutoring in august of 1942 sasha was sent to auschwitz where he was assumingly executed and the camp closed down so groton deacon his mother ended up at the gulch camp near pooh with groton deak managing to escape he somehow made it to le chambon solino where he lived in a sheltered hidden boarding home despite the home being mostly safe groton deak would have to hide out in the woods every time authorities came looking for jews sometimes going days without food or water amongst all of this groton deak was still able to get an education while in champal groton deak attended college seven a secondary school founded in 1938 by anti-war activists it was here that he became truly fascinated with mathematics receiving his baccalaureate in 1945 and with world war ii now over groton deek and hanka moved to the village of maisog near montpolier where groton deak worked in the vineyards fortunately groton deak was able to get a small scholarship to the university of montpoli and began studying mathematics there while at the university of montpolier groton deak had issues with the way some of the mathematics was presented he already disliked the holes that his high school mathematics texts left vowing to fill the gaps when he had the chance and he found his professors at the university didn't help much in filling those gaps thus much of the work was done on his own one of his lectures monsieur sula had expressed that lubig had resolved the last outstanding problems in mathematics but it would be too difficult to teach alone amazingly this led grotin deak to rediscover the general form of the lebaig integral with almost nothing to go off of he ended up spending three years at the university of montp puglier and each year he grew more independent in his studies there per suggestion from sula groton deek went to go study mathematics in paris in 1948. from 1948 to 1949 grotindeg studied at the ecole normale superhere or ens with omri khal a 20th century mathematician who made large contributions to algebraic topology groton deak attended a seminar instructed by a call toll which covered algebraic topology and chief theory and he encountered many notable mathematicians of the time in the seminar including jean duduni a 20th century french mathematician notable for his research in algebraic geometry and being a part of the bohbaki group legends schwarz a 20th century french mathematician who pioneered the theory of distributions and andre vel a 20th century french mathematician notable for his foundational contributions to number theory and algebraic geometry grondik apparently commented that though he was able to eventually understand everything being lectured understanding didn't come to him as instantly as it seemed those around him at the ens with this slower understanding and general interest being in that of topological vector spaces calton and veg recommended groton deak move to the university of nancy to continue his studies groton deak moved to nancy in 1949 with his mother at the university of nancy who worked very hard to understand and solve problems in functional analysis having very little books at his disposal and basically reconstructing things on his own he also attended an active seminar that was held every saturday that was mostly attended by professors impressed by grotondig's abilities due doane and schwartz threw a series of unsolved problems at him as a means of helping construct a general theory of duality for convex vector spaces in less than a year of being thrown these problems groton d could solve them all going on to solve many more problems in functional analysis with the techniques he had developed on february 28 1953 groton deak advised by both the udon and schwartz presented his doctoral thesis topological tensor products and nuclear spaces leading applications in physics and computer science by this point he was now the leading figure on topological vector spaces with the udon comparing his impact to that of stefan banak a 20th century polish mathematician who is notable for being the founder of modern functional analysis after receiving his phd groton deak lectured and researched at the university of sao paulo in brazil from 1953 to 1955. around 1955 he began working on chief theory and homological algebra taking the theory of sheaves to a higher level of abstraction in 1956 he moved to the university of kansas leaving a year later to work at the suntre nationale du la rece or cnrs which he'd been funded by since 1950 and he also became one of the members of the baki group by 1957 groton deca completely shifted gears towards algebraic geometry and homological algebra his first discovery in algebraic geometry was a generalization of the hirzebrok riemann rock theorem which relates topological properties of complex algebraic curves to their algebraic structure he proved this algebraically and in doing so came up with techniques that started the study of algebraic k theory which is concerned with the structure theory of projective modules and of their automorphism groups and topological k theory which studies the topological properties of objects by associating them with rings he also produced the tohoku paper in 1957 published in the tohoku mathematical journal introducing abelian categories removing the need to distinguish the cases of modules over a ring and sheaves of abelian groups over topological space in 1959 groton deak began his golden age after being offered a research position at the institute sontifique or ihes where he would spend the next 11 years of his life during his golden age groton deak established several unifying themes in algebraic geometry number theory topology category theory and complex analysis to put it bluntly it was an insanely prolific eleven years that groton deak had at the ihes at this point groton deak stopped publishing mathematics through the conventional route of journals as the seminars were intense and productive enough that he attracted a wide enough audience to get his research exposed to just list a bit of his remarkable contributions during this time he introduced the theory of schemes allowing for vale's conjectures to be solvable the theory of topoi a category theoretic generalization of point set topology greatly influencing set theory mathematical logic and the algebraic definition of a fundamental group of a curve his influence is also attributed with category theory becoming a separate mathematical discipline though this was unintentional [Music] it would probably take an entire video or two to go more in depth with his contributions but let's at least discuss schemes within his research groton deak began adopting the use of non-closed generic points leading him to the theory of schemes a scheme being a mathematical structure that expands the notion of an algebraic variety in many ways such as taking into account multiplicities and allowing for varieties defined over any commutative ring to note an algebraic variety is a set of solutions of a system of polynomial equations this theory provided a new more flexible and general foundation to algebraic geometry that is used to this day and this theory was developed in detail between 1960 and 1967 by grotin deke and deuteronomy collected into the work el emonde de journal or ega the ega introduced a tal and ellatic co-homology theory which were used to prove the veil conjectures produced in 1949 but unsolvable until the ega the conjectures essentially observed there was a connection between topological characteristics of a variety and diophantine equations vale realized a new co-homology theory was needed to prove this but alas there were no experts capable of producing this theory until groton deak pierre a belgian mathematician who is one of groton deak's ph.d students completed the proofs for these conjectures in 1973. in 1966 groton deak received the fields medal for his contributions to algebraic geometry homological algebra and k theory but he did not collect the metal himself instead having the director of the ihes leon motchain collected for him the international congress of mathematics was held in moscow russia in august of 1966 and groten deak refused to travel there as political protest he had strong pacifist views which led to him campaigning against military buildup in the 60s thus russia was on his anti-travelist crotan deak made no public statement about the reasons for not going but declared himself a citizen of the world and requested u.s citizenship in december of 1967 groton deak visited north vietnam which was being bombed by the u.s he started off as lectures at hanoi university but the bombing became too intense so groton deak and the members of the university went to a secret location to finish them groten deak described it as a remote forest hideout in a desperately poor country that was being bombed into the stone age on may 25th 1970 groton deak put in his letter of resignation to the ihes after finding out the year prior that the university had been accepting military funding groton teak rallied up most of the faculty to convince moat chain to stop accepting this funding which they actually succeeded in doing but when funds got tight mo chain went back to accepting said funding grotnik tried getting faculty to resign in protest after this fact was revealed but he ended up being alone in this venture military funding was the primary reason for leaving but groton deak had also been experiencing a so-called spiritual stagnation which he had started to develop a few years before though he was still doing mathematics he had abandoned it as his main focus turning to political protest as mentioned earlier despite how powerful his mathematical influences were he ultimately had very little impact with his political campaigns after leaving the ihes groton deak over the next few years would distance himself more and more from the mathematical community still producing mathematics for the rest of his life but ending his standard career there nothing was ever stable for him 1970 onwards from 1970 to 1972 he held a post at the college du france from 1972 to 1973 he held an appointment at the universite pa sacre from 1973 to 1984 groton digg worked for the university of montpellier and from 1984 to 1988 he worked for the cnrs but still had an association with the university of montpoli in 1988 groton deak formally retired and was also offered the crawford prize by the royal academy which he declined expressing that established mathematicians had no need for additional financial support he went on to criticize the declining ethics of the scientific community as well as expressing belief that there would be an unprecedented collapse of civilization before the end of the century lastly he expressed that he regretted the inconvenience cause of the royal academy that his declining the prize may have caused in 1991 groton deak ultimately disappeared with virtually no contact with friends family or anyone in his previous academic circle for the remainder of his life he spent his time writing an extremely large work on physics and wrote a few philosophical meditations on subjects such as free choice and the existence of evil considering groton deak's early beginnings it goes without saying he had a rather unconventional life groten deak as we know became a refugee in france in 1939 records of his nationality were destroyed in the fall of germany in 1945 so he essentially became stateless refusing to apply for french citizenship after world war ii ended he traveled on a nonsense passport or stateless person's passport for the majority of his life his reasoning for not applying for french citizenship was that he did not want to be enlisted in the military he eventually applied for citizenship in the early 80s well past the exempt age for military service as mentioned while at the iags grotnik became more passionate about his political activism shortly after putting in his resignation at the ihes grotin deak made a political group called silver later renamed to silvive at vivir with two other mathematicians clued chevelle a 20th century french mathematician who made important contributions to algebraic geometry and was one of the founders of the baki group and pierre samuel a 20th century french mathematician notable for his work in community of algebra and his applications to algebraic geometry the group was dedicated to anti-war and ecological issues criticizing what they felt to be the indiscriminate use of science and technology the group was first formed in montreal but groton d headed the paris branch being the main editor of their newsletter for three years grundy felt that the best form of organization for the paris group would be a commune which he opened in chatunai malabri in 1972. the initial intention was for the warmth of a family environment and a meeting center but the commune was actually complete chaos with groton deak even having doubts about whether or commune life made sense despite the chaos any talks that groton d gave attracted the attention of sometimes 100 plus people one day after coming home to find people in the commune using some of his mathematical manuscripts as kindling for a bonfire he decided it was time to move on in less than a year of living on the commune grotnik moved a vehicle in 1973 staying there for the next six years in vehicle his house was open to everyone and he was remarked as looking cheerful and being extremely generous the home he chose was the smallest darkest and most unpractical house he could have picked being filled with fleas having no garden or terrace and looking more like a hideout than anything else he had no electricity working by the light of a petroleum lamp and apparently he unlatched his front door and slept on that when it came to food he lived on produce from local communes or individual alternative farmers with a typical diet being that of goat's milk goat cheese fresh vegetables fruit and rice many people frequented his house in the first few years mostly those in vehicle but occasionally friends family and colleagues as well since he was working at the university of montpulli he did own a car to be able to get there though it's claimed he was an incredibly bad driver with no one feeling safe getting in the car with him it took him nine tries to get his license [Music] in july of 1979 groton deak moved from velikov to la gacht the home being a lonely retreat which he kept top secret living there a year in almost complete isolation with no electricity nor running water in the home eventually he received many visits including from his two eldest children from there groton deak moved to lesometh in the second half of 1980 again a secluded home but this time had modern amenities he lived there until ultimately taking off in 1991 for an even more isolated life in total groton deak had five children spread amongst three different women the first child was with his landlady nancy alind lique a woman much older than he they had a passive affair leading to the birth of a sergey grotin deak largely being raised by lean for the first 13 years of his life the second woman whom groton deak had children with was mia dufour and the pair had three children together joanna alexander and matthew merce was a few years older than groton deak and originally came from normandy having received secretarial training and working occasionally as an accountant she was noted as being a strong and determined woman michael spoke fluent spanish and apparently had contact with spanish anarchist networks which is ultimately how she met grotin deak through these circles grotnick's mother whom growton deegan been living with a nancy since 1949 died of tuberculosis in 1957 an ailment she'd contracted while in one of the internment camps on her deathbed she had grotonique promised that he'd break off his relationship with aline and marry merce so grotnik did just that and it's important to note that their marriage was not happy conventionally grotnik ended up having many other lovers even bringing them back to the family apartment in 1972 milhei couldn't bear to live in their home anymore and moved out to the suburbs of paris the pair officially divorcing in 1981. she only took their two sons leaving joanna with groten deke joanna lived with groton deak on the chatunay commune eventually having a four-year affair with a boy she'd met there despite all the problems they had mihrae moved close to veliko just before he moved again as she felt that their son should be near their father moving again when groton deak moved to la gacht the third and final woman grotende had a child with was justine scalba whom he'd met when traveling to the united states after receiving an invitation to work with suny buffalo in new york state there for just a couple of months he ended up giving a lecture at rutgers university where justine was a phd candidate at the get-together after groton dig spoke with her about his plans to give up mathematics and move to the countryside justine was intoxicated by this idea and gave up her studies to follow groton deak to europe justine lived on the chateaunee commune with groton deak where she was ultimately impregnated by him giving birth to their son john on october 28 1973. she lived with groton deak for a few months in vehicle but the conditions were too unsavory for justine to raise a newborn there also commenting that groton deak would have rather scary breakdowns on occasion one of which resulted in him screaming in german even though she did not understand german justine went back to live in paris for a bit before moving back to the united states with jon during the 1980s though he wasn't publishing grotnik wrote thousands of pages of both mathematical and non-mathematical content between 1980 and 1981 he wrote the long march through galwa theory which was a hundred page handwritten manuscript that eventually led to sketch of a program written in 1984 it described new ideas for studying modulized spaces of complex curves and was a proposal to the cnrs for long-term research the cnrs turned down the proposal but still offered him a special position which allowed him to stop teaching at the university of montpellier though the cnrs turned the proposal down the ideas introduced had a profound effect on research today introducing the son don phone theory where the sondhofen is a type of graph embedding to study riemann surfaces and provides combinatorial and variants for the action of the absolute galwa group of the rational numbers and anabelian geometry which describes the way a fundamental group g of an algebraic variety v determines how v can be mapped into another object w under the assumption that g is strongly non-commutative he never published his work himself but it ended up being published in the two volume work geometric galwa actions in 1997 written by leila schnepps an american mathematician and fiction writer at the cnrs her focus being in number theory and pierre locheck a french mathematician working at the university of paris and is notable for his work on teich mueller theory in 1986 groton deak wrote a one thousand page autobiographical manuscript titled cult etzemai in which he described his approach to mathematics and his experiences within the mathematical community his view is that he was initially accepted with open arms but progressively perceived academia to be governed by competition and status he felt like his work was buried along with feeling betrayed by former students and colleagues after leaving the community after 1991 grotnik basically refused every human contact with the exception of the brief correspondence he had with schneps and locheck who somehow found his location and became the last members of the mathematical establishment to come in contact with him groton deak died on november 13th 2014 at the age of 86 dying in a hospital in sol jiron achieve from there it was revealed that he had been living alone in a house in la sage and that while he was alive he was sustained food wise by local villagers after they saw his attempt at living on a diet of dandelion soup well there you have it a glimpse into the life of the extraordinary alexander groton deak i'll end this on groton deak's obituary written by algebraic geometers david mumford and john tate although mathematics became more and more abstract and general throughout the 20th century it was alexander grotendik who was the greatest master of this trend his unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most abstract level revealed themselves and then like a magician show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed thank you for watching and i'll catch you next time you

Channel: moderndaymath

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Id: fFKhM4mEB4w

Length: 26min 53sec (1613 seconds)

Published: Mon Nov 30 2020