Levels of Infinity: Selected Writings on Mathematics and Philosophy

by Hermann Weyl, Peter Pesic

This original anthology collects 10 of Weyl's less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl's mentor, David Hilbert. 2012 edition.

Genres: Mathematics, Philosophy

256 pages, Paperback

First published September 20, 2012

About the author

Hermann Klaus Hugo Weyl (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines including number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.

Weyl published technical and some general works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. While no mathematician of his generation aspired to the 'universalism' of Henri Poincaré or Hilbert, Weyl came as close as anyone. Michael Atiyah, in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him (The Mathematical Intelligencer (1984), vol.6 no.1).

Source: http://en.wikipedia.org/wiki/Hermann_...

Reviews

[Mosaad Al Thokair · Rating 5 out of 5]

الكتاب مجموعة مقالات لهرمان ويل تكلم فيها بشكل رئيسي عن الجبر، الطوبولوجيا، والمنطق من ناحية تطورهم تاريخيا، وآخر ماتوصلت له الرياضيات في وقته. شرحه جميل جدا. يعتبر "ويل" من الرياضيين القلائل اللي يهتمون بسلاسة التعبير.
الكتاب مو بس رياضيات، بل يشمل فلسفة الرياضيات وفيزياء، حتى أن آخر مقال كان عن النسبية، ولم تخلُ المقالات السابقة من ذكر النسبية وأفكار فيزيائية ثانية.
من المواضيع الفلسفية اللي تطرق لها هو مسألة الرياضيات هل الحقائق الرياضية لها جذور بواقعنا، ولا هي كونها الخاص (immanence vs. transcendence)

موضوع فلسفي ثاني كان الرياضيات "البناءة"(constructive) و"الرمزية"(axiomatic)
واللي تتلخص فيما يلي: هل نكتشف الرياضيات بشكل قريب للعقل، بعدين نثبته، ولا نلعب بالرموز ونعوض قيم وإذا وصلنا نتيجة نحسها مثيرة للاهتمام حاولنا نفهمها؟
هالطريقتين يسهل إيجادهم بالطوبولوجيا والجبر، بالترتيب، ووضح الكاتب طرق تكملتهم لبعض.

يحتاج خلفية رياضية في المنطق أو الجبر أو الطوبولوجيا عشان تستمتع فيه، وفيه مواضع متقدمة لكن تقدر الفكرة بدون ماتفهم كل التفاصيل.
=
5 نجوم لأنه من الكتب اللي تعيد حماسك للرياضيات.

[Hao Ca Vien · Rating 5 out of 5]

Levels of Infinity is an excellent survey and genealogy of the state of mathematics during Weyl's time. Levels of Infinity is very complete and in depth without being overly rigorous. Weyl is a good read for the train and cafe without conversation and will thoroughly entice the reader into the mathematical joys of its science.

[Kyle · Rating 5 out of 5]

This is bit of a different reading experience. These are essentially transcripts of lectures given by Weyl, but don't let that dissuade you from reading them as they are well-edited. They also go quite deep into the weeds of mathematical notation and thought at times, so unless you are well-versed in the areas Weyl covers, you are likely to either get lost or think hard (esp. because the notation and wording can be somewhat different than modern mathematics). But Weyl brings out interesting points and usually does a good job of explaining the main idea of what he is getting at. The obituaries for Hilbert and Noether are excellent for explaining the accomplishments of these amazing mathematicians. The last essay on why the world has 4 dimensions was also one of my favorites.

If you aren't willing to deal with more advanced mathematics, then this book won't be of interest. Also there are a couple of pieces with parts that repeat previous ones. This makes sense since they are lectures on similar topics sometimes, but it's something to be aware of even if it is not extremely common.