Journey to the Edge of Reason: The Life of Kurt Gödel
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- Author：Stephen Budiansky
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Summary
Nearly a hundred years after its publication， Kurt Gödel’s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics， philosophy， and computer science。 Yet unlike Einstein， with whom he formed a warm and abiding friendship， Gödel has long escaped all but the most casual scrutiny of his life。
Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships， his moving relationship with his mother， his troubled yet devoted marriage， and the debilitating bouts of paranoia that ultimately took his life。 It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna， a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War， and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton， NJ， where Gödel and Einstein both worked。
Eloquent and insightful， Journey to the Edge of Reason is a fully realized portrait of the odd， brilliant， and tormented man who has been called the greatest logician since Aristotle， and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy， mathematics， artificial intelligence， and man’s place in the cosmos。
Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships， his moving relationship with his mother， his troubled yet devoted marriage， and the debilitating bouts of paranoia that ultimately took his life。 It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna， a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War， and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton， NJ， where Gödel and Einstein both worked。
Eloquent and insightful， Journey to the Edge of Reason is a fully realized portrait of the odd， brilliant， and tormented man who has been called the greatest logician since Aristotle， and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy， mathematics， artificial intelligence， and man’s place in the cosmos。
Reviews
U。
，
“Die Religionen sind zum größten Teil schlecht， aber nicht die Religion。”
Keith Maestas
，
History advanced mathematics and logic。 The story of the greatest logician since Aristotle。
Book O Latte
，
Einstein menggelarinya "logikawan terhebat sejak Aristoteles"， matematikawan legendaris John von Neumann menyebutnya "matematikawan yang benar-benar tak tergantikan"， filsuf Herbert Feigl menyatakan ia seorang "jenius kelas tertinggi"。Namun begitu， tidak banyak yang mengenal nama Kurt Gödel selain kalangan ilmuwan bidang tertentu。 Tidak sebagaimana orang awam mengenal nama Einstein， sahabatnya selama di Princeton。 Padahal karya utama Gödel yaitu Teorema Ketidaklengkapan， yang ia formulasikan di Einstein menggelarinya "logikawan terhebat sejak Aristoteles"， matematikawan legendaris John von Neumann menyebutnya "matematikawan yang benar-benar tak tergantikan"， filsuf Herbert Feigl menyatakan ia seorang "jenius kelas tertinggi"。Namun begitu， tidak banyak yang mengenal nama Kurt Gödel selain kalangan ilmuwan bidang tertentu。 Tidak sebagaimana orang awam mengenal nama Einstein， sahabatnya selama di Princeton。 Padahal karya utama Gödel yaitu Teorema Ketidaklengkapan， yang ia formulasikan di usia 24 tahun， adalah prinsip penting yang sangat fundamental dalam dunia ilmu pengetahuan。 Harvard University menyebutnya "penemuan kebenaran matematika terbesar abad ini"。Teorema tersebut menyatakan bahwa setiap sistem matematika yang konsisten dan mengandung aritmetika maka pasti tidak lengkap， dan konsistensinya tidak bisa dibuktikan di dalam sistemnya sendiri。Selain karena hanya sedikit yang mengerti keistimewaan karya dan pemikirannya， ia menjadi 'misterius' juga karena terbilang 'nyentrik'， 'nggak gaul'， serius dan tertutup， sehingga hanya sedikit yang mengenal sisi kehidupan pribadinya。Salah satu yang menyulitkan dalam usaha menuliskan kehidupan Gödel adalah karena ia menggunakan stenografi Gabelsberger dalam mencatat berbagai pemikiran pribadinya。 Upaya pendataan dan penerjemahan catatan-catatannya berlangsung bertahun-tahun oleh prof。 John Dawson dan istrinya Cheryl mulai awal tahun 1980an （yang menghasilkan buku "Logical Dilemma: The Life and Work of Kurt Gödel"， Dawson， 1997）。Dalam buku Journey ini， Stephen Budiansky， seorang penulis berlatar belakang sains & matematika yang memfokuskan diri di topik sejarah militer dan biografi， berhasil menampilkan Kurt Gödel secara lebih utuh。Ia membangun image Gödel melalui data arsip Institute of Advanced Study Princeton， berbagai sumber sejarah serta korespondensi yang tersisa dari keluarga， sahabat dan kolega-koleganya （surat-surat dari ibu dan kakak Gödel kepadanya dihancurkan oleh istrinya， Adele， setelah Gödel meninggal）。Buku ini dibuka dengan penggambaran situasi dan kondisi Austria yang membentuk Vienna awal abad 20 menjadi pusat ilmu pengetahuan yang dinamis， tempat Gödel tumbuh di tengah stimulasi intelektual berkualitas tinggi。Kepiawaian Budiansky mengisahkan sejarah membuat pembaca dapat ikut merasakan ketegangan Eropa di masa kebangkitan dan kejayaan partai Nazi， bagaimana perubahan suasana di kalangan intelektual universitas sehinggal banyak ilmuwan Yahudi yang dipersekusi atau pergi meninggalkan Eropa menuju Amerika。Ilmuwan-ilmuwan yang bukan dari ras Yahudi seperti Kurt Gödel pun tidak luput dari ancaman， karena ide-ide liberal （bahkan dalam sains dan matematika） dianggap sebagai "pengaruh Yahudi" yang menyalahi prinsip-prinsip Nazi。 Sungguh masa itu sangat kelam bagi dunia intelektual Eropa daratan。Sehubungan dengan ke'nyentrik'an Gödel dalam menjalani kehidupan sehari-hari， buku ini berargumen bahwa obsesi terhadap kesempurnaan yang ekstrimlah yang memunculkannya。 Digambarkan bagaimana Gödel punya gaya berpakaian tersendiri （harus rapi necis lengkap dengan mantel bahkan di tengah musim panas）， kesulitan mengambil keputusan karena selalu mempertimbangkan berbagai sisi， kecenderungan paranoid terhadap dokter dan kondisi kesehatannya， kepolosannya terhadap hal keseharian， dll。 Membacanya saya langsung teringat karakter unik Adrian Monk dalam film seri detektif obsesif-kompulsif "Monk"。Buku ini sangat bagus dan informatif bagi yang ingin tahu lebih jauh tentang kehidupan dan pemikiran Kurt Gödel dari mulai masa kecilnya di Austria hingga akhir hayatnya di Princeton。-dydy- 。。。more
Zarathustra Goertzel
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Really nice summary of Kurt Gödel's life， how many in the mathematical foundations community supported his ongoing existence in 'paradise at Princeton'， and some insights into how he viewed his work。Maybe I shall re-evaluate my stance on the Axiom of Choice for the study of pure mathematical objects！ 😜 Really nice summary of Kurt Gödel's life， how many in the mathematical foundations community supported his ongoing existence in 'paradise at Princeton'， and some insights into how he viewed his work。Maybe I shall re-evaluate my stance on the Axiom of Choice for the study of pure mathematical objects！ 😜 。。。more
Davewy
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history was interesting。。。。lost me on the math/logic
Porter
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Well-written book that keeps you interested along the way。 Nothing really exceptional about the book but the concepts are explained decently and Godel's life itself was amazing。 What a tragic and unnerving life to read about。 His life was so full of contradiction and oddities that it gives you sense of uneasiness as to its progression。 Overall worth the read from a historical point of view。 Well-written book that keeps you interested along the way。 Nothing really exceptional about the book but the concepts are explained decently and Godel's life itself was amazing。 What a tragic and unnerving life to read about。 His life was so full of contradiction and oddities that it gives you sense of uneasiness as to its progression。 Overall worth the read from a historical point of view。 。。。more
Dylan
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Didn't understand the math and logic， but was an interesting picture of Vienna pre-WWII。 Lot of it felt like it was less about Godel as much as it was about the times and places he inhabited。 Didn't understand the math and logic， but was an interesting picture of Vienna pre-WWII。 Lot of it felt like it was less about Godel as much as it was about the times and places he inhabited。 。。。more
Patrick Riley
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Godel's life was kind of ho-hum although the circumstances were interesting。 Vienna was a scholarly paradise until the Nazi's came。 Godel's mental illnesses were a big part of his mind along with his mathematical genius。 He is famous for his Incompleteness Theorem of which， of course， I understood nothing。 In fact， all of the math was beyond my comprehension。 Godel's life was kind of ho-hum although the circumstances were interesting。 Vienna was a scholarly paradise until the Nazi's came。 Godel's mental illnesses were a big part of his mind along with his mathematical genius。 He is famous for his Incompleteness Theorem of which， of course， I understood nothing。 In fact， all of the math was beyond my comprehension。 。。。more
Robert B
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A very readable biography of the Austrian logician / mathematician， Kurt Gödel， whose incompleteness theorems represent one of the great breakthroughs in 20th century thought。 More might have been done to explain the theorems themselves， but the book is good in providing the context in which they appeared and the world in which Gödel lived， including his years at Princeton's Institute for Advanced Study。 A very readable biography of the Austrian logician / mathematician， Kurt Gödel， whose incompleteness theorems represent one of the great breakthroughs in 20th century thought。 More might have been done to explain the theorems themselves， but the book is good in providing the context in which they appeared and the world in which Gödel lived， including his years at Princeton's Institute for Advanced Study。 。。。more
Bob Finch
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A well written， deeply researched biography of perhaps the most creative and original mathematical thinker in modern times。 One of Albert Einstein’s closest confidants late in his life， Gödel was also troubled by increasing bouts of mental illness。 One might be tempted to lump Gödel into the stereotype of the troubled genius， à la Van Gogh， despite innumerable counter-examples like Einstein or Picasso; though I’d hope not， as this diminishes Gödel’s unique personality and humanity。 The author do A well written， deeply researched biography of perhaps the most creative and original mathematical thinker in modern times。 One of Albert Einstein’s closest confidants late in his life， Gödel was also troubled by increasing bouts of mental illness。 One might be tempted to lump Gödel into the stereotype of the troubled genius， à la Van Gogh， despite innumerable counter-examples like Einstein or Picasso; though I’d hope not， as this diminishes Gödel’s unique personality and humanity。 The author does a great job of describing the societal upheavals （especially the rise of fascism） that Gödel—and his Vienna Circle—were experiencing and how those upheavals impacted Gödel’s life choices （cf。， Sigmund’s “Exact Thinking in Demented Times”）。The book also does a pretty good job of explaining Gödel’s famous Incompleteness Theorem， no mean feat （I heartily recommend “Gödel’s Proof” by Nagel & Newman for a more complete layman’s treatment）。 。。。more
Socraticgadfly
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Kurt Gödel ranks with the likes of Karl Friedrich Gauss and George Cantor as among the world’s greatest mathematicians。 And now， he has a full biography， that sets him within the late Austro-Hungarian Monarchy， as a Sudenten German who later moved to Austria， and as a man plagued ever more by various forms of mental illness as he aged。One of the funniest quotes is one that stands in stark contrast to the famous Douglas Hofstadter book， “Gödel， Escher， Bach。” That is: “Bach and Wagner make me ner Kurt Gödel ranks with the likes of Karl Friedrich Gauss and George Cantor as among the world’s greatest mathematicians。 And now， he has a full biography， that sets him within the late Austro-Hungarian Monarchy， as a Sudenten German who later moved to Austria， and as a man plagued ever more by various forms of mental illness as he aged。One of the funniest quotes is one that stands in stark contrast to the famous Douglas Hofstadter book， “Gödel， Escher， Bach。” That is: “Bach and Wagner make me nervous。”Not so funny is that， while Hofstadter had plenty of biographical elements about Bach， he had almost none about Escher and none on Gödel。 This book remedies that in spaces。Gödel is best known for his Incompleteness Theorem， but on the math and philosophy side， had more than that， and “informed” discussions of relativity and more in physics。Gödel had other oddities besides comment about Bach and Wagner。 He was a diehard mathematical Platonist， but others exist today。 That said， he seems to have been something like a diehard Platonist period。（view spoiler）[He rejected methodological naturalism， or as Budiansky calls is， scientific materialism。 Philosophically， he had an ardent love affair with Leibniz， monads and all。 And， he was also a Leibnizian conspiracy theorist， claiming that up to his own time， certain concepts and findings of Leibniz were still being repressed， generally by an unidentified “them。”Related to that？ He claimed “religions were bad， but religion good，” as in， questioning individual religions but affirming the value of some deeper religion。 Indeed， in 1970， he claimed to have an ontological proof for the existence of God！His mental health？ Long before his suicide by starvation， he was a hypochondriac and probably had OCD。That said， the paranoia dramatically ramped up in the last half a dozen years of his life， leaving him an incredibly tragic person。 His paranoia eventually involved claims about Nazis resurgent in Austria and his own brother， before he eventually starved himself to death， including while in hospital the last couple of weeks of his life。 （hide spoiler）]That’s enough to give a good taste of this book， but without getting too deep into spoiler alert territory。 Even clicking open the spoiler alert won't give all away。That said， there are a couple of errata and issues in the book。One minor one is that Budiansky claims Wiener schnitzel is really nothing more than cotoletta alla Milanese imported from Italy in the 1850s， allegedly by Radetsky。 In 2007， a linguist totally debunked this。The larger issue is one of omission。 Many ideas that many people attribute to Gödel’s Incompleteness Theorem actually come from Tarski’s Undefinability Theorem。 Tarski’s theorem extends beyond mathematics into semantics in general。 That said， Budiansky isn’t alone。 Realistically， Hofstadter should have written “Tarski， Escher， Bach。” That said， in turn， Gödel did apparently discover this first， but never published， so the technical credit goes to Tarski。 It should be noted that Hofstadter references Turing MUCH more than Tarski， and Budiansky does just as much。 On the other hand， Budiansky does critique GEB， noting that Hofstadter “far outran Gödel’s proof，” while at the same time it “contained not a word about the man himself。” Budiansky gets this right， but it would have been a good place here to insert at least a small note about Tarski。Budiansky， besides remedying that， looks at Gödel’s actual reputation today in the worlds of science and philosophy。 He says that in math， most modern mathematicians have seen little reason to venture past his barrier and that philosophy （as seemingly， Gödel himself） have found his theorem limiting。 。。。more
Casey
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An engaging portrait of a tragic man and the times he lived in。 I enjoyed the general history and perspective on antisemitism in Austria， Europe， and the east coast US during， through， and after WWII。 The math concepts were well explained and accessible， I would recommend this to anyone with even a passing interest in math or history。
J。D。 Frailey
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Here’s what Brittanica says about Kurt Gödel: “Austrian-born mathematician， logician， and philosopher who obtained what may be the most important mathematical result of the 20th century: his famous incompleteness theorem， which states that within any axiomatic mathematical system there are propositions that cannot be proved or disproved on the basis of the axioms within that system; thus， such a system cannot be simultaneously complete and consistent。 This proof established Gödel as one of the g Here’s what Brittanica says about Kurt Gödel: “Austrian-born mathematician， logician， and philosopher who obtained what may be the most important mathematical result of the 20th century: his famous incompleteness theorem， which states that within any axiomatic mathematical system there are propositions that cannot be proved or disproved on the basis of the axioms within that system; thus， such a system cannot be simultaneously complete and consistent。 This proof established Gödel as one of the greatest logicians since Aristotle， and its repercussions continue to be felt and debated today。”I learned so much， even though pretty much all the math was WAY over my head， because the author made it kinda sorta accessible to me， at least as far as generalities。 More importantly for me was the clearly explained events leading to World Wars I and II primarily from the perspective of Austria and surrounding countries， starting in the 1850’s with the Hapsburg dynasty。 Once laws limiting the Jews academically， professionally， and artistically had been abolished， those pesky Semites had risen to dominate those fields like a cork in a bucket of milk （a shout out to Annie Proulx for that metaphor）。 Resentments were unleashed and restrictions were reestablished， ultimately contributing to the holocaust。 Gödel was able to make it to the US and eventually become a professor at Princeton and good friend of Einstein。 I also came out believing that genius is rarely only super high IQ， but often accompanied by eccentricities or even madness， as with Gödel。 In middle age and later he was consumed by hypochondria and paranoia， believing all kinds of self made conspiracies against him， wouldn’t eat anything unless his wife-who had cooked his food-tasted each bite before she fed it to him。 He weighed 65 pounds at the time is his death。 He also believed he could prove the US could be constitutionally turned into a dictatorship， an assertion still studies and debates today， fascinating， here’s the story as written in the New Yorker: “The story goes that Gödel， while preparing for a U。S。 citizenship test， in the nineteen-forties， imagined， in best Viennese form， that it would be a real test， not the pro forma examination it was。 He studied the local laws ferociously—trying to learn why， in New Jersey， a township is distinguished from a borough—and buried himself in the Constitution， which he studied as though it were the “Principia Mathematica。” And he emerged confident that he had found a logical contradiction in the Constitution that could reverse democratic government itself。 He shared this discovery with Einstein， and also with Oskar Morgenstern， the co-founder of game theory and a mutual friend; both men begged him not to make an issue of it during the test。 But， at the ceremony， the judge asked Gödel where he came from， and he explained that he was from Austria， which had once been a democracy but was now a dictatorship。 Isn’t it good that such a thing can’t happen here， the judge replied。 “But it can！” Gödel declared。 “I can prove it！””“Gödel’s loophole， as some have called it， remains a mystery。 He never defined it， and no trace of his discovery seems to linger in his papers。 But he was far too exact a reader， and far too exacting a logician， not to have spotted something。 Indeed， the question of Gödel’s loophole has inspired a remarkably large speculative literature， in serious scholarly journals as well as among scholars in this magazine， and recently among academics writing online。 What was it？ Probably not a loophole by which a Vice-President can simply refuse to recognize a slate of electors， during the Electoral College vote tally， and substitute one of his own choosing， thereby keeping his boss in power。 That， presumably， was a bridge too far even for a logician。 Dartmouth’s Dan Rockmore suggests that it might conceivably involve the contradictions of gerrymandering， which is constitutional but democracy-defeating， or the minority-empowering Electoral College。 Another Gödel biographer， Jim Holt， turns to Harvard Law School’s distinguished professor emeritus， Laurence Tribe， suggesting that what Gödel had in mind was Article V of the Constitution， “since it sets no limits on how the Constitution can be amended。” Holt goes on，‘The U。S。 could be turned into a Constitutional dictatorship by a series of amendments。 But it’s more interesting than that。 Article 5 makes the document self-referential: it refers to “this Constitution。” It says， in effect， “I can be amended by such-and-such procedures。” And it seems to leave open the possibility that Article 5 itself is subject to amendment。 This would permit a very direct route to dictatorship: amend it so that any diktat of the President is automatically an amendment。“And that would， of course， be a neatly Gödelian recursive arrangement， of a sinister turn。“But， when you think it through， there’s an overabundance of possible loopholes in the Constitution。 The President is the Commander-in-Chief of the armed forces， with no named constraints; his power to act in that sphere is largely undefined and has altered significantly through the years， restrained sometimes by acts of Congress but mostly by assumptions that are not enumerated in the text， possibly because no one imagined that they would need to be。 The President also possesses， under Article II， virtually unlimited pardon power for federal crimes， so he could， logically， have henchmen arrest or even kill elected federal officials who oppose him， and then pardon those same accomplices。 Or， to take an instance in the opposite direction: the power of impeachment resides in the Congress， with the assumption that it is reserved for cases clearly involving a strong violation of law—a high crime or misdemeanor—so extreme that it alarms all sides。 This has long been the case， and all three modern Presidential impeachments were treated as trials， with arguments， evidence， etc。 But， given that high crimes and misdemeanors are not defined in the Constitution， and are effectively what a sufficient number of legislators decide they are， there is nothing to prevent impeachment from simply being an ejection seat: at any point when one party has a majority in the House and a two-thirds majority in the Senate， it can summarily expel the President by pure fiat。” 。。。more
D。 Rogers
，
"Journey to the Edge of Reason" is a unique work on Kurt Gödel as it integrates the geographical， political， and social factors which shaped his world with the psychological factors which shaped his mind。This book will not give you deep insight into Gödel's intellectual triumphs （nor is it intended to do so）， but you will walk away with an understanding of their significance。 "Journey to the Edge of Reason" is a unique work on Kurt Gödel as it integrates the geographical， political， and social factors which shaped his world with the psychological factors which shaped his mind。This book will not give you deep insight into Gödel's intellectual triumphs （nor is it intended to do so）， but you will walk away with an understanding of their significance。 。。。more
Frank O'connor
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This is a book about Austria， America and the life of Kurt Godel。 It is interesting in how it places Godel within the context of Hapsburg Austria and its obsession with order， then parallel's Godel's collapse with the Austrian one。 Godel himself comes across as a typical charming and eccentric intellectual， if troubled in his later years。 The book goes a little into the complexity of his work and achievements， giving a flavour of this without becoming overburdened by mathematical complexity。 This is a book about Austria， America and the life of Kurt Godel。 It is interesting in how it places Godel within the context of Hapsburg Austria and its obsession with order， then parallel's Godel's collapse with the Austrian one。 Godel himself comes across as a typical charming and eccentric intellectual， if troubled in his later years。 The book goes a little into the complexity of his work and achievements， giving a flavour of this without becoming overburdened by mathematical complexity。 。。。more
Jeff Gabriel
，
While ultimately a good read offering insights into KG， the author seemed to be more interested in the history of pre-war Austria。 It seems likely that primary sources were light （meaning availability， not due to author's diligence） and so it was hard to draw a very full picture of the person。 I also like a bit more depth in the technical analysis of scientific bios。 Overall， good but not great。 While ultimately a good read offering insights into KG， the author seemed to be more interested in the history of pre-war Austria。 It seems likely that primary sources were light （meaning availability， not due to author's diligence） and so it was hard to draw a very full picture of the person。 I also like a bit more depth in the technical analysis of scientific bios。 Overall， good but not great。 。。。more
Timoer Frelink
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I hesitated: 3 or 4 stars and gave it the benefit of the doubt。 The book’s subtitle: “The life of Kurt Gödel” is misleading。 There is relatively little about the man himself and plenty on the history of Vienna and the people around him。 Maybe due to the lack of good sources， but dissapointing nonetheless。 It reads easily and part of the histories are very interesting。 3。5 stars would have been my choice。
Stephen Durrant
，
While it would take a more mathematically sophisticated reader than yours truly to unpack the critical pages of this book that concern Gödel’s “Incompleteness Theorem，” the philosophical implication that he drew from his work is clear and wide-ranging: there are truths that are unprovable， that will always escape the grasp of mathematical rules。 Quite beyond these issues， however， this book is a fascinating account of the remarkable group of mathematicians and other scientists， mostly Jewish， wh While it would take a more mathematically sophisticated reader than yours truly to unpack the critical pages of this book that concern Gödel’s “Incompleteness Theorem，” the philosophical implication that he drew from his work is clear and wide-ranging: there are truths that are unprovable， that will always escape the grasp of mathematical rules。 Quite beyond these issues， however， this book is a fascinating account of the remarkable group of mathematicians and other scientists， mostly Jewish， who gathered in Vienna during the 1920s and 30s。 We all know what was soon to happen， and the author traces the consequences， which he calls the largest brain drain in world history， as so many of these scholars fled Austria and settled in the West， particularly America。 Gödel was one of the more important members of the Vienna circle and later became a good friend of Albert Einstein， who held him in the highest esteem， at the Princeton Institute for Advanced Study。 Just as one has a hard time imagining Thomas Mann and Arnold Schönberg living out their lives in Los Angeles， it is sometimes hard to imagine Gödel， depressive and increasingly paranoid， and other Austrian and German refugees finding refuge in what was at that time a very conservative New Jersey town。 At any rate， this is an enjoyable and informative read on many levels， even if one doesn’t always get the math！ 。。。more
Angela Sorby
，
This is a fascinating wide-angle bio， situating the world that Goedel reflected/made in the context（s） of interwar Europe; the intersection/divergence of math and analytic philosophy; the politics of the war itself （which he seemed incapable of grasping）; and the war's existentialist aftermath。 It's also an even-handed portrait of his sustaining marriage， his friendship with Einstein， and his mental sensitivity/illness。 As a non-STEM person I found the technical bits well-summarized; even when I This is a fascinating wide-angle bio， situating the world that Goedel reflected/made in the context（s） of interwar Europe; the intersection/divergence of math and analytic philosophy; the politics of the war itself （which he seemed incapable of grasping）; and the war's existentialist aftermath。 It's also an even-handed portrait of his sustaining marriage， his friendship with Einstein， and his mental sensitivity/illness。 As a non-STEM person I found the technical bits well-summarized; even when I didn't follow Goedel's math the author managed to convey the *effects* of said math。 Side note: as an interwar Europe geek I also found this book a fun complement to other books like _The House of Wittgenstein_， _The Ink Blots_ （about Rorschach）， _Pushing Time Away_（about Peter Singer's sex-positive Viennese grandparents！！）， _Gropius_ （about the Bauhaus）， and the _Hare with Amber Eyes_。 。。。more
BlackOxford
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The Word Made Flesh in ViennaIt was Alan Turing who discovered an important implication of Kurt Gōdel’s Incompleteness Proof。 One of the consequences of the impossibility of finding a justification for the logic of arithmetic is that some mathematical propositions， although true， cannot be shown to be so。 The logical steps required to prove their veracity are infinite。 In technical terms， this makes them undecidable。 That is， both the proposition and its negation are possible without contradicti The Word Made Flesh in ViennaIt was Alan Turing who discovered an important implication of Kurt Gōdel’s Incompleteness Proof。 One of the consequences of the impossibility of finding a justification for the logic of arithmetic is that some mathematical propositions， although true， cannot be shown to be so。 The logical steps required to prove their veracity are infinite。 In technical terms， this makes them undecidable。 That is， both the proposition and its negation are possible without contradiction - a mathematical incongruity that stops reason dead in its tracks。 It strikes me that the central irony of Gödel’s life as described by Budiansky is precisely this kind of undecidability applied to himself。 Gödel had incredible insight and ability in logical reasoning。 But for him reason was a syntactical process， that is， a purely symbolic exercise。 It had nothing to do with the world outside mathematics。 Its semantics， that is the connection of abstract logic to the world outside of mathematics， was something Gödel had no interest in， and very little ability。Gödel was not unaware of his handicap。 In notes to himself quoted by Budiansky， he makes it clear that he is often simply incapable of what Immanuel Kant called Practical Reason， the logic of right action: “… [I]t takes me five to ten times as long to reach a decision than other people。” Budiansky reports that he filled page after page with procedures to employ in making decisions。 But his self-diagnoses transformed routinely into self-fulfilling prophecies。 It is as if his inner demon of abstraction and procedural inference had been given the task of correcting itself。 The result was predictably not very encouraging。 Yet he obsessively continued the practice of self-analysis and self-correction throughout his life， trying， it seems， to prove the reflexive paradox of his own Proof wrong。His decisiveness and fluency in mathematics were entirely absent from his personal and social life。 Taking action frequently made him ill with uncertainty。 For example， leaving Vienna to take up a position at The Institute of Advanced Studies in Princeton， he became so distressed he had to return to Vienna。 After his year long stay in America， he hospitalised himself almost immediately upon arrival home with concern about the prudence of his return。 Then venturing again the following year to Princeton for his second stint at the Institute， he resigned almost immediately claiming stress and ill health。 He had decided to return to an increasingly violent Austria in which university life had all but been destroyed！ Subsequently when it was clear that Austrian fascism had annihilated the intellectual life of the country and the Anschluss by Hitler was only days away， Gödel was offered an appointment at the University of Notre Dame。 Yet he dithered interminably and finally inexplicably rejected the offer。 Neither sensible judgement nor fortitude were Gödel’s forté。This profound indecisiveness was apparently accompanied by an equally profound fear of being observed， that is of being seen as a person apart from his mathematical accomplishments。 He did give occasional lectures in front of colleagues and otherwise sympathetic audiences。 But at his courses at Princeton， Gödel stood speaking with his back to the students facing the blackboard but never writing on it。 Clearly he wanted his students attention solely on the ‘mask’ of his symbolic reasoning and not directed to his physical person。 Yet his stance suggests not shyness or even a sense of threat but almost shame for betraying the guilty secret of mathematics as well as his own judgment in devoting his life to a ‘defective’ pursuit of truth。 So as an example of someone who identifies him or herself as their work， Gödel is hard to better。 What seems especially significant though is that his quasi-paranoia was directed at himself rather than at those he perceived as observing him。 This doesn’t appear to have been a form of autism - Gödel did frequently， and annoyingly， ignore events he found distracting but he could be charming and had a droll sense of humour。 He was apparently a devoted and sensitive friend。 It was his own physicality that Gödel did not trust， perhaps originating in his recognition that he was unable to make reliable decisions outside of mathematics， particularly about his own life。 That he had discovered the black hole in mathematical reasoning could well have been as much as a psychic tragedy as much as a professional triumph。This is obviously a terrible psychological burden to bear。 It is a commonplace that mathematicians do their best work in their youth。 Gödel berated himself in his mature years for his lack of work of the same quality that had made his reputation。 No assurances from friends， colleagues or university administrators that he was still regarded as an important mathematician could convince him to mitigate his own self-reflective judgement。 He simply could not be consoled。 And as his German-speaking colleagues， especially Einstein， either died or left Princeton， Gödel showed full-blown signs of breakdown。 Another implication of Gödel’s Proof was developed by his friend Alfred Tarski。 It turns out that not only are some propositions undecidable but also that even the notion of what constitutes truth is undefinable in arithmetic。 Could this be the subconscious origin of Gödel’s indecisiveness and defensiveness？ Certainly many others have lived out their neuroses in useful ways。Perhaps Gödel’s life， therefore， was not only an example of total devotion to mathematics but also a physical manifestation of his primitive insight about it。 He fought passionately against metaphysics using patently metaphysical arguments， arguing for example that his Proof showed both the Platonic reality of numbers and that this reality was permanently beyond human comprehension。 As he matured is it possible the basic incongruity in his Self of abstract reason simply took its course to disintegration？ That he became more himself in other words。 I’m not being trite when I suggest that Gödel had a bug in his organic operating system， a genetic quirk that led him gradually into extreme self-alienation。So for me the question this biography raises is something both personal to Gödel and yet general to the science of mind。 Is it better， that is to say more accurate， more productive and in some ways more fair， to describe Gödel as a psychologically aberrant personality， or as someone who just lived out his fate as best he could？ In more poetic terms Gödel seems very much the incarnation of his own mathematical word， a person of total although tragic integrity。 Might it be that each of us has some similarly in-built genetic logic that will have its way in whatever circumstances we might find ourselves， in fact motivating us to create those circumstances as well as respond to them？ 。。。more
Camille
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Interesting look at a genius and the ideas he surrounded himself with。 I thought that there was too much talk of other colleagues and although his prowess with mathematics was carefully considered， I felt that too much time was spent on his health and mental states。
Nirmal
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This book is a fascinating （and later disturbing） insight into the mind of Gödel。 His work in mathematics and logic is of course superlative （which I do not understand fully）， but it was somewhat surprising to know he was a "conspiracy theorist" believing nothing ever happens without a reason。 He also believed that Leibniz kept his philosophical and logical work to himself and a conspiracy was afoot to suppress this work。 Paul Erdős amongst others were dismayed that Gödel was squandering his gen This book is a fascinating （and later disturbing） insight into the mind of Gödel。 His work in mathematics and logic is of course superlative （which I do not understand fully）， but it was somewhat surprising to know he was a "conspiracy theorist" believing nothing ever happens without a reason。 He also believed that Leibniz kept his philosophical and logical work to himself and a conspiracy was afoot to suppress this work。 Paul Erdős amongst others were dismayed that Gödel was squandering his geniuses on such things。Another interesting aspect was learning about social life in Vienna before he moved to the USA， and found that life in Princeton too conservative。 。。。more
John
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Cross posted from my blog Analyze the Data not the Drivel。If you’re faced with undeniable evidence that Shakespeare was a racist， would you change your opinion about the play Othello？ I’m in the habit of asking myself such hypotheticals; it helps me clothe my opinions in reason。 Here's another one。 If you learn that one of the greatest mathematicians in history was prone to conspiracy theories， as idiotic as the most moronic twaddle slushing around the Internet today， would you change your opini Cross posted from my blog Analyze the Data not the Drivel。If you’re faced with undeniable evidence that Shakespeare was a racist， would you change your opinion about the play Othello？ I’m in the habit of asking myself such hypotheticals; it helps me clothe my opinions in reason。 Here's another one。 If you learn that one of the greatest mathematicians in history was prone to conspiracy theories， as idiotic as the most moronic twaddle slushing around the Internet today， would you change your opinion about this mathematician's work？My answer to both of these questions is a resounding no！I agree with Flaubert， “The man is nothing， the work — all。” Othello remains a masterpiece even if we someday discover Shakespeare subsisted on a diet of roasted black babies。 Similarly， Gödel’s Incompleteness Theorem will stand forever as a landmark of mathematics even though its creator， as brilliantly told in the new biography Journey to the Edge of Reason The Life of Kurt Gödel， was prone to inane conspiracy theories。 My favorite was Gödel’s expressed belief that some unknown works of Leibniz， that supposedly anticipated many later discoveries， were being suppressed by nefarious agents of big philosophy。In this Gödel， somebody that had a much higher IQ than you， （no matter who the Hell you are）， and produced some of the greatest theorems ever， was a total nut job。 Nobody is suppressing Leibniz， nor is it likely that any of Gödel's doctors ever tried to poison him。 Gödel was simultaneously a giant of logic and the mayor of Crazy Town。 Even Shakespeare would have been impressed by the dichotomy。 Clearly， this brain thing we all have in our heads is capable of some deeply weird shit。Journey to the Edge of Reason is a fabulous and fascinating book。 I enjoyed every word， but a few days after putting it aside， a niggling little thought， an epiphany of sorts， percolated up from the bowels of my brain。 If a genius like Gödel could not lay off conspiracy theories what are the chances that your average Internet imbecile will？A snowball’s chance in Hell comes to mind。 。。。more
Robert Borter
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An interesting biography of one of the great logicians of the 20th century。 It details his childhood in Vienna， his escape from the Nazis， to his friendship with Albert Einstein at Princeton。 The author provides a good explanation of his incompleteness theorems which can be quite daunting to those without a good background in mathematics， logic or philosophy but these sections are to provide an understanding of the importance of his work。 The balance of the text is about the man， his life and th An interesting biography of one of the great logicians of the 20th century。 It details his childhood in Vienna， his escape from the Nazis， to his friendship with Albert Einstein at Princeton。 The author provides a good explanation of his incompleteness theorems which can be quite daunting to those without a good background in mathematics， logic or philosophy but these sections are to provide an understanding of the importance of his work。 The balance of the text is about the man， his life and the terrible events in Europe。 Some reviewers feel that there is too much detail in describing Vienna at the turn of the century but how events unfolded for those that were not murdered is frightful。 It is such a shock to see how the cultured society changed overnight into thieves and blood thirsty brownshirts。 I had a couple of friends who escaped from Vienna， ended up on a ship full of refugees that for months wandered from port to port and ended up in the far east before they were finally able to get passage to come to America。 To they dying day， they said they would never go back to Vienna they had only terrible memories。 The last section of the book also touches on why Godel would never go back and it resonates with the tales my friends told。 The book "The Escape Of Sigmund Freud" is another interesting account of how Freud escaped from Vienna and the Nazis。 The book is in the same genre as "A Beautiful Mind" and "The Man Who Knew Infinity"， if you liked these titles you will enjoy "Journey to the Edge of Reason"。 Sadly all of these geniuses were plagued with psychological problems of one kind or another yet were responsible for some of the most significant advances in math and logic in the first half of the 20th century。 。。。more
Jamie Greene
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Well written biography of one of the pre-eminent mathematicians of the 20th century。 It is also the story of someone who achieve fame at a young age， then struggles with that legacy later in life。 I was somewhat familiar with his life and work， but this book provided a lot of additional information。
Robert Pachella
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This is the third biography of Gödel。 The first two focused on his important work。 This one focused more on his mental illness and the eccentricities of his life， exactly what I was looking for。 Why read three biographies of the same person？ Because his work is that important Even though he is not as well known than other luminaries， his work belongs in the same framework as that of Newton and Einstein。 （BTW， I have also read three biographies of Newton and Einstein。）
Chris
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The title and cover photo lead one to expect one of those stories about a genius whose intensity and quest for truth pushed him over the edge， something like A Beautiful Mind。 That might have been the book Budiansky shopped to his publisher， but it isn't really this book。 The book really never gets close enough to its subject to develop a clear psychological profile。 I kept waiting to learn what it was about Gödel that made him such a favored friend of Einstein。 What did they talk about and what The title and cover photo lead one to expect one of those stories about a genius whose intensity and quest for truth pushed him over the edge， something like A Beautiful Mind。 That might have been the book Budiansky shopped to his publisher， but it isn't really this book。 The book really never gets close enough to its subject to develop a clear psychological profile。 I kept waiting to learn what it was about Gödel that made him such a favored friend of Einstein。 What did they talk about and what did Gödel sound like？ I kept waiting to learn more about the domestic life of Gödel and his wife， who apparently his friends did not like。 Where is his personality， his voice， the "real" Gödel that I picked up the book to learn about？ What were his values and how were they reflected in his lifestyle？ Many unanswered questions。 I would guess that there just wasn't enough material available to create that kind of a biography。 Gödel comes into and goes out of focus at different points along the way but never really emerges as a person you feel like you know。Nevertheless， it is a readable book and was often quite interesting。 The portrait of Vienna during Godel's time there， from roughly the final years of the Hapsburgs to the rising influence of Nazism there was interesting。 Gödel was certainly part of that portrait but the overall picture of the Vienna Circle and the other intellectuals who were also there was more interesting than anything we learn about him during that time。 Similarly the description of Princeton in the 1930s and the Institute for Advanced Study's founding was more interesting to me than the portrait of Gödel at Princeton。 Budiansky is clearly a capable writer， so I suspect that there just isn't enough primary materials on Gödel to allow him to create a fuller portrait of Gödel in either his Vienna incarnation or later at Princeton。 What about the math？ I think more should have been done to make Gödel's work accessible and to provide more of his contributions than just the primary focus on the incompleteness theorem and its proof。 It is really abstruse stuff and I can't say I have a very clear sense of the math or why it is considered both important and beautiful。 As I understand his proof， Gödel showed that one can never prove that a mathematical system is complete in the sense that all true statements expressed within the system （theorems） can be shown to be true by the axiomatic statements that are the foundation of that system。 We would hope we could prove true statements are true by the axioms of the system and deductive reasoning， but Gödel's proof shows this is impossible。 Reading the description of the proof in the provided appendix was a challenge--it is sort of like reading a secret code， even though this was not the actual math but a description of it-- but it was really quite interesting to sort of peek over the shoulders of mathematicians。 Even if I was not able to follow the argument to the end， the journey was interesting， and I'd say that is true of this book as a whole。 The journey was interesting。 。。。more
Tiago Faleiro
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I've always been fascinated by Gödel's incompleteness theorems。 I knew very little about him despite being a hugely influential logician and his ontological proof of God， but after seeing that he had a well-rated biography， I figured I would learn more about his life。Gödel's intelligence is beyond absurd。 He master calculus and other high-level mathematics at 14 and read Kant at 16。 Russell described him as: "perhaps the most perfect example I have ever known of genius as traditionally conceived I've always been fascinated by Gödel's incompleteness theorems。 I knew very little about him despite being a hugely influential logician and his ontological proof of God， but after seeing that he had a well-rated biography， I figured I would learn more about his life。Gödel's intelligence is beyond absurd。 He master calculus and other high-level mathematics at 14 and read Kant at 16。 Russell described him as: "perhaps the most perfect example I have ever known of genius as traditionally conceived， passionate， profound， intense， and dominating"It is rather funny， at least to our modern sensibilities， that mathematics and logic are so associated with science and objectivity， and yet Gödel was far from a materialist， I had the impression that what drew him to mathematics was precisely it was entirely mystical for him。 And while he was well versed in philosophy and could casually talk about Hegel， he had confessed that he never pondered some metaphysical questions as much as he wanted。 The biography covers a lot of his personal life， which was enjoyable in itself。 He was certainly an odd character and in many ways the typical stereotype of a mathematic genius。 On top of that， he also struggled with mental health。 First with just general anxiety and depression， and progressively severe hypochondria。 He ended up dying after delusions of being poisoned through food。 It also covers a fair bit of his work。 Obviously including the Magnus opus of the incompleteness theorems。 It was super interesting， and I felt that I understood it better because of it。 Although as usual， I seem to quickly lose such understanding over time。 I found his views on his own theorem very odd and surprising。 Rather than a pessimistic piece of evidence about mathematical knowledge， he saw it as evidence that human reason can directly intuit mathematical reality， given the power it provides and yet there can't be any rational foundation for it。 He conceived of it as a kind of perception and he thought it was completely valid。 Other work was covered as well。 Sometimes going to sufficient depth to please any mathematical aficionado （not me）， but while certain parts were beyond my understanding， they were always short and didn't discourage me from continuing。 He published his incompleteness theorems rather young and what give him so much professional success was also something that haunted him。 He also felt that his best work was behind and that he never produced anything of value ever again， suffering from perfectionism， anxiety， poor self-esteem and impostor syndrome。 He had a serious， solitary personality， but he was always kind to others。 The context of Gödel's life is what makes the book shine。 It is deeply interconnected with everything else and thus what the biography covers is very vast。 He was one of the key figures of the Vienna Circle， which influence is massive for almost any intellectual field of the 20th century。 It also covered the Nazi Regime in Austria where he lived and his immigration to the United States。 Another aspect that made it very enjoyable was his social circle。 Because of his time period and his field， his life is full of fascinating figures。 Including Bertrand Russell， von Neumann， Whitehead， Wittgenstein， and most importantly， Albert Einstein。 Towards the end of Einstein's life， they were best friends and visit each other often， despite their personalities being so different。 Einstein's death， and later von Neumann， deeply affected him and likely contributed to his mental health deterioration。 It was a pleasure to read and I didn't expect to enjoy it as much as I did。 From his personality and life story to his work on the foundation of mathematics， Gödel's life is fascinating。 Although unfortunately， it has a very depressing end， as his life crumbles into bigger and bigger chaos until he ends his own life。 But his enormous legacy lives on。 。。。more
David Given Schwarm
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Interesting biography that mostly demystifies Gödel by placing his live in a deeper historical context and his work in a more specific context。 I read it because of the anorexia angle， but enjoyed the math part a lot more。 Overall， not a strong recommendation unless you are very into turn of the century math and logic， Princeton， or weird academic wives。
Peter
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