On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Godel used mathematics to underscore the weird paradoxical nature of reality ... took logic where Hilbert and Frege feared to tread. Math's answer to Escher. If you can deal with some heavy-duty equations and logic, this is very trippy fun reading that demolishes the old cathedrals and in their place erects a large question mark. Fast shipping and the price was good, only cost me a couple dollars.

Logically it made sense for me to purchase this book

This is not a simple read for non-mathematicians, but it is outstanding due to the extended explanatory introduction for others with backgrounds in natural sciences, logical, or philosophical matters.

I had to read it a few times but I thought it was worth reading.

THE proof as Goedel wrote it (plus typos). I have seen modern proofs of this theorem which are much easier to follow (as an example, a Mir book on mathematical logic by a Russian mathematician whose name I cannot recall), but this one is the REAL thing. Modern proofs can be much clearer, but the original always has an added value. The writing style is not the best, but by reading this version you get a clearer idea of how Goedel came up with his theorem and the many difficulties he faced. Remember, by the time most of us read or heard about this for the first time, mathematical logic had advanced quite a few decades.

Every mathematician or computer scientist must have this book. FULL STOP.

This book is quite short, but it is also very deep. Kurt Gödel was a mathematician back in the 1930s that had an idea. He grew up during a time where it was thought that everything could be explained through mathematics and that mathematics itself would be "complete." However, Kurt Gödel comes up one fine day in 1931 or so and publishes this little paper explaining that there are ideas that can't be expressed in the language of mathematics. Using the language developed by Bertrand Russell and Alfred North Whitehead, Kurt Gödel establishes basic math and then proceeds to tear it down. A tour de force of logic.

I wish I had been exposed years ago to the philosophy of mathematics and the inseparableness of mathematics and logic. Seems obvious now. I could blame the education I received and the focus it placed on how instead of why. But perhaps that’s too easy an excuse and the why was always there and I was too immature to see it. Either way, it’s a good read...

La argumentación de Gödel en su famoso teorema de incompletitud es sencilla —al igual que en la prueba de la imposibilidad de demostrar la consistencia al interior de cualquier sistema formal que contenga a la aritmética—, lo verdaderamente escabroso de este artículo, es la parte sobre funciones y relaciones recursivas: el lector debe revisar concienzudamente todas las definiciones que presenta el autor ¡aun antes de llegar al teorema de incompletitud citado! Sin embargo, leer la fuente primaria siempre es más gratificante para cualquier estudiante de matemáticas o ciencias de la computación: aprenderán como nunca.

This is a copy bought from amazon.in. The Indian copy printing is slanted, it cuts off the title itself on the cover page. And then inside, it cuts off number indices for referenced equations. When I tried to return it on Amazon, it offered me only a replacement copy. I have no reason to believe that the replacement copy is going to be better printed than the one I got, so I'm choosing to leave this review instead. This book is a classic and I was intending to keep the copy for perpetuity but the shoddy quality of it does a great injustice to what the book represents to me.

Excellent Product - Good Value

Testo molto compatto, chiede forti conoscenze già acquisite e grande concentrazione nella lettura. Ma possibile che nessuno lo traduca in italiano? Consigliato

El texto que cimbró las matemáticas para siempre. Es complicado para los que no estudiamos una licenciatura en matemáticas pero con algunos conocimientos se puede entender. Gran genialidad de Gödel