Customer Rating: 
Summary: Forget the flaws. Enjoy it.
Comment: I just couldn't put this book down. I was so absorbed that I even missed my station and had to catch a train back. The biographies mixed with mathematical explanations and an outline of the significance of each work is brilliant. It gives one an insight into how context-dependent genius really is.
I knew that the book had flaws because I read these reviews a while ago. But so what! You wouldn't use this book for reference or as a text book. It's meant to be entertainment and entertaining it is. If you can understand the maths and the significance of the selected papers you can enjoy it without worrying too much about everything being crossed and dotted.
I knew the biographies of many, but not all, of these men. Of the ones I didn't know, my favorite is George Boole. The description of his unusual career and the amazingly clear and readable paper on symbolic logic are worth buying the book for. I almost choked up when I read how he died.
Anyway, in our age or irrationality and ignorance we need more books like this to show us that we can rise above it all.
Customer Rating:
Summary: Definitelly a great book but it serious editorial issues
Comment: I will be brief:
*** I miss a chapter on Euler. Wasn't he a great mathematician?
*** I need a magnifying glass to go with the book. The footnotes are very, very small
*** While I understand the editors that they did not want to bring the translated text up to today's standard I believe that a footnote or two to define the terms would have helped. Especially with the Riemann's seminal paper on Geometry
Customer Rating:
Summary: The Works and Biographical Details of Some of the World's Greatest Mathematicians
Comment: By way of introduction, the Egyptians and Babylonians did sophisticated math as early as 3500 BC. This book begins with the works of Pythagoras (his theorem), Archimedes (use of a pulley to do the work of 100 men; distinguishing gold from gold alloys), Diophantus (biographical word problem), etc. We then learn of such men as Descartes (on geometry), Riemann (on curved space), Laplace (on probability), Fourier (deciphering the Rosetta stone; propagation of heat), etc.
There is at least one inaccuracy in this book. Alan Mathison Turing is said to have cracked the Nazi Enigma Code. In actuality, the code was broken earlier by a team of Polish mathematicians headed by Marian Rejewski. The French and British mathematicians (including Turing) went on to build on Rejewski's breakthrough.
This book touches on the personal lives of many of the mathematical greats. Did you know, for instance, that Newton was personally hostile to Leibniz? Or that Cauchy had to flee Paris because of his royalist ties and consequent fear of being guillotined during the French Revolution? Or that Boole, at one time, compared the Trinity to the three dimensions of space? Or that Kurt Godel (Goedel), an eccentric fellow, had to be repeatedly hospitalized for severe depression?
Customer Rating:
Summary: Exactly what I wanted!
Comment: I read "Euclid's Window" last year, another mathematical history/overview book, and while I enjoyed it, it did seem to skim much and not get too deep into any one subject. I'm still glad I read it, because it's whetted my appetite for the subject, and this book is definitely the main course. It's a great companion to Roger Penrose' "Road to Reality", an overview of just about all we currently know about physics, which doesn't shy away from the math. Between these two books, my brain will likely explode (I'm a musician, but I love the subject), but they are full of depth for both thorough reading or just reference.
Customer Rating:
Summary: A great idea well executed (with a caveat).
Comment: Hawking here puts his name as editor to an outstanding collection of the writings, theorems and proofs of several of history's most influential mathematicians. He also contributes historical and biographical context commentaries. The choice of title, and implicit subtitle due to Leopold Kronecker, is itself interesting in its metamathematical posture, alluding to both the platonic (real but 'immaterial') mathematical Given, i.e., "God Created the Integers", and the concept of mathematics as human 'invention', i.e., "all the rest is the work of man". In his popular writings, Hawking has long identified with positivism, a philosophy claimed by relatively many in the natural sciences but by very few practitioners of mathematics (likely all the men profiled here would consider themselves Platonists, believing that mathematical truths are discovered as opposed to contrived/invented). I find it slightly fascinating that one can be so assertive in his scientific positivism while also frequently conceding a weak mathematical Platonism/realism.
While all of the 'chapters' are worthy of attention, I was particularly interested in Hawking's presentation of the life, work and thought of Kurt Gödel. I don't know that his perspective on Gödel's philosophical views or expectations, as regards this Incompleteness Theorems, or Gödel's relationship with the Vienna Circle, is portrayed accurately. Witnesses and other biographers have convincingly portrayed the story otherwise. Gödel's famous proofs may have surprised and disappointed the Positivists, but it seems they neither disappointed nor surprised [the Platonist] Gödel (although he calls his result "surprising," it seems he is speaking to how they must be received by Hilbert, Wittgenstein, and the positivists, rather than to his own view). There are several popular sources [books] on Gödel and his work that are available for the interested reader. A very nice exposition focused mainly on the philosophical import of Gödel's result is "Incompleteness: The Proof and Paradox of Kurt Godel" by Rebecca Goldstein (although, unlike Hawking's book, Goldstein presents only a good summary explanation of Gödel's famous paper, rather than the whole paper).
Staying with Hawking's presentation of Gödel, I also note that, in his introduction (xii), Hawking writes "Kurt Gödel proved a theorem troubling to many philosophers, as well as anyone else believing in absolute truth: that in any sufficiently complex logical system (such as arithmetic) there must exist statements that can neither be proven nor disproven." Dividing Hawking's statement into those segments defined by the sentence's punctuation, Gödel would quickly protest, "yes, no (!), and yes": True, Gödel's result troubled certain philosophers -- most especially Wittgenstein! (Wittgenstein is said to have, in frustration, resolved to "ignore" Gödel's result; Gödel, for his part, considered Wittgenstein to be not only a poor judge of mathematical thought, but also a poor philosopher generally.) What Gödel would categorically deny of Hawking's summation, is the idea that his result in any real way questioned the ontology of 'absolute truth.' In fact, he inferred exactly the opposite. His result addressed the decidability of propositions and not the existence of truths! Hawking obviously understands this, but has taken some license in assailing 'truth' anyway, perhaps subconsciously attempting a kind of Wittgensteinian proxy revenge; but Gödel's result addresses the limits of formal logic, NOT any constraint on 'truth' itself. (Sorry if this seems like a lengthy digression, but as Kurt Gödel isn't around to defend the philosophical meaning of his work from positivistic spin-doctoring, other mathematical Platonists must.)
One indicator of this volume's uniqueness is the fact that some of these texts had not previously been published in English. The book is a great idea well executed, and is definitely recommended to anyone with an interest in the history of mathematics or in familiarizing themselves with great (and often quirky) mathematicians. Read it front to back or in any manner you wish, although there is an obvious 'building' through the book, the segments on the life and work of each mathematician will be of interest in their own right.
Summary: Forget the flaws. Enjoy it.
Comment: I just couldn't put this book down. I was so absorbed that I even missed my station and had to catch a train back. The biographies mixed with mathematical explanations and an outline of the significance of each work is brilliant. It gives one an insight into how context-dependent genius really is.
I knew that the book had flaws because I read these reviews a while ago. But so what! You wouldn't use this book for reference or as a text book. It's meant to be entertainment and entertaining it is. If you can understand the maths and the significance of the selected papers you can enjoy it without worrying too much about everything being crossed and dotted.
I knew the biographies of many, but not all, of these men. Of the ones I didn't know, my favorite is George Boole. The description of his unusual career and the amazingly clear and readable paper on symbolic logic are worth buying the book for. I almost choked up when I read how he died.
Anyway, in our age or irrationality and ignorance we need more books like this to show us that we can rise above it all.
Customer Rating:
Summary: Definitelly a great book but it serious editorial issues
Comment: I will be brief:
*** I miss a chapter on Euler. Wasn't he a great mathematician?
*** I need a magnifying glass to go with the book. The footnotes are very, very small
*** While I understand the editors that they did not want to bring the translated text up to today's standard I believe that a footnote or two to define the terms would have helped. Especially with the Riemann's seminal paper on Geometry
Customer Rating:
Summary: The Works and Biographical Details of Some of the World's Greatest Mathematicians
Comment: By way of introduction, the Egyptians and Babylonians did sophisticated math as early as 3500 BC. This book begins with the works of Pythagoras (his theorem), Archimedes (use of a pulley to do the work of 100 men; distinguishing gold from gold alloys), Diophantus (biographical word problem), etc. We then learn of such men as Descartes (on geometry), Riemann (on curved space), Laplace (on probability), Fourier (deciphering the Rosetta stone; propagation of heat), etc.
There is at least one inaccuracy in this book. Alan Mathison Turing is said to have cracked the Nazi Enigma Code. In actuality, the code was broken earlier by a team of Polish mathematicians headed by Marian Rejewski. The French and British mathematicians (including Turing) went on to build on Rejewski's breakthrough.
This book touches on the personal lives of many of the mathematical greats. Did you know, for instance, that Newton was personally hostile to Leibniz? Or that Cauchy had to flee Paris because of his royalist ties and consequent fear of being guillotined during the French Revolution? Or that Boole, at one time, compared the Trinity to the three dimensions of space? Or that Kurt Godel (Goedel), an eccentric fellow, had to be repeatedly hospitalized for severe depression?
Customer Rating:
Summary: Exactly what I wanted!
Comment: I read "Euclid's Window" last year, another mathematical history/overview book, and while I enjoyed it, it did seem to skim much and not get too deep into any one subject. I'm still glad I read it, because it's whetted my appetite for the subject, and this book is definitely the main course. It's a great companion to Roger Penrose' "Road to Reality", an overview of just about all we currently know about physics, which doesn't shy away from the math. Between these two books, my brain will likely explode (I'm a musician, but I love the subject), but they are full of depth for both thorough reading or just reference.
Customer Rating:
Summary: A great idea well executed (with a caveat).
Comment: Hawking here puts his name as editor to an outstanding collection of the writings, theorems and proofs of several of history's most influential mathematicians. He also contributes historical and biographical context commentaries. The choice of title, and implicit subtitle due to Leopold Kronecker, is itself interesting in its metamathematical posture, alluding to both the platonic (real but 'immaterial') mathematical Given, i.e., "God Created the Integers", and the concept of mathematics as human 'invention', i.e., "all the rest is the work of man". In his popular writings, Hawking has long identified with positivism, a philosophy claimed by relatively many in the natural sciences but by very few practitioners of mathematics (likely all the men profiled here would consider themselves Platonists, believing that mathematical truths are discovered as opposed to contrived/invented). I find it slightly fascinating that one can be so assertive in his scientific positivism while also frequently conceding a weak mathematical Platonism/realism.
While all of the 'chapters' are worthy of attention, I was particularly interested in Hawking's presentation of the life, work and thought of Kurt Gödel. I don't know that his perspective on Gödel's philosophical views or expectations, as regards this Incompleteness Theorems, or Gödel's relationship with the Vienna Circle, is portrayed accurately. Witnesses and other biographers have convincingly portrayed the story otherwise. Gödel's famous proofs may have surprised and disappointed the Positivists, but it seems they neither disappointed nor surprised [the Platonist] Gödel (although he calls his result "surprising," it seems he is speaking to how they must be received by Hilbert, Wittgenstein, and the positivists, rather than to his own view). There are several popular sources [books] on Gödel and his work that are available for the interested reader. A very nice exposition focused mainly on the philosophical import of Gödel's result is "Incompleteness: The Proof and Paradox of Kurt Godel" by Rebecca Goldstein (although, unlike Hawking's book, Goldstein presents only a good summary explanation of Gödel's famous paper, rather than the whole paper).
Staying with Hawking's presentation of Gödel, I also note that, in his introduction (xii), Hawking writes "Kurt Gödel proved a theorem troubling to many philosophers, as well as anyone else believing in absolute truth: that in any sufficiently complex logical system (such as arithmetic) there must exist statements that can neither be proven nor disproven." Dividing Hawking's statement into those segments defined by the sentence's punctuation, Gödel would quickly protest, "yes, no (!), and yes": True, Gödel's result troubled certain philosophers -- most especially Wittgenstein! (Wittgenstein is said to have, in frustration, resolved to "ignore" Gödel's result; Gödel, for his part, considered Wittgenstein to be not only a poor judge of mathematical thought, but also a poor philosopher generally.) What Gödel would categorically deny of Hawking's summation, is the idea that his result in any real way questioned the ontology of 'absolute truth.' In fact, he inferred exactly the opposite. His result addressed the decidability of propositions and not the existence of truths! Hawking obviously understands this, but has taken some license in assailing 'truth' anyway, perhaps subconsciously attempting a kind of Wittgensteinian proxy revenge; but Gödel's result addresses the limits of formal logic, NOT any constraint on 'truth' itself. (Sorry if this seems like a lengthy digression, but as Kurt Gödel isn't around to defend the philosophical meaning of his work from positivistic spin-doctoring, other mathematical Platonists must.)
One indicator of this volume's uniqueness is the fact that some of these texts had not previously been published in English. The book is a great idea well executed, and is definitely recommended to anyone with an interest in the history of mathematics or in familiarizing themselves with great (and often quirky) mathematicians. Read it front to back or in any manner you wish, although there is an obvious 'building' through the book, the segments on the life and work of each mathematician will be of interest in their own right.
God Created the Integers: The Mathematical Breakthroughs that Changed History Reviews: Page 2 of 5
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