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I am a university student of mathematics and is also interested in philosophy, mainly spiritualism. Besides knowing that mathematics is, in general, also a study of how the world works, I do not know if there is any specific branch in mathematics where fundamental questions of life -- for example: why does the universe exists? -- are pondered and explored? More precisely, can mathematics contribute to attaining what Gautam Buddha calls 'enlightenment' or 'nirvana'. If yes, which field in mathematics does so?

Sorry if my question seems vague. I couldn't think of a better formulation.

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    "Mathematics is, in general, also a study of how the world works": I wouldn't say so. Mathematics strictly speaking has got nothing to do with the real world. Sure, it is very effective in describing real-world phenomena, but then you're doing physics. – Ben Jun 26 '13 at 22:17
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    What you are looking for is probably mathematical philosophy (mathematics doesn't deal with philosophy; however, mathematics can be used in philosophy, but then you're doing mathematical philosophy, not mathematics). There's a course on Coursera starting on July 1st in this subject. – Ben Jun 26 '13 at 22:18
  • @upaudel you might also be interested in this post although it is a little bit more computer science-y than the lay preconception of math. – Artem Kaznatcheev Jun 27 '13 at 16:27
  • I would recommend reading books by leading mathematicians (also physicists) who are/were also interested in Philosophy: e.g. Alain Connes, Henri Poincare (plus other nationalities :) – Drux Jun 28 '13 at 9:28
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I think you need to look much more broadly than mathematics if you want to ponder the difficult questions of life. Plato himself said that mathematics gives a glimpse of the eternal - in the sense its truths don't seem to vary; but he also said that as a discipline it is too narrow to ponder the larger, deeper & more difficult problems. Philosophy, theology or literature are probably better.

I'm not sure just how useful mathematical philosophy is. Plato in Timaeus which describes his mature cosmology also has a demiurge to create the world and suffuse it with soul, but he also merges in Pythagorean thought (which held that the world was mathematically formed) and Democritean atomism in that his atoms were platonic solids and made up from triangles.

Mathematics is there - but its certainly not the most important part of his conception.

People like Spinoza & Wittgenstein are clearly influenced by its formal axiomatic structure. Descarte by his cogito looked for an irrefutable beginning to start his excavation of epistemology. Liebniz tried to reduce everything to the principle of efficient cause & non-contradiction. But also quite clearly Spinoza & Liebniz were Christian philosophers - they clearly believed in God; whereas Descarte did his best to find that hypothesis redundant to understand the world. Wittgenstein in Badiou characterisation is an ascetic mystic; Wittgenstein himself stated that the philosophy is not best way to the 'truth' but for those of us who are not genuine mystics to whom 'truth' is revealed or the veil of mystery removed - it is perhaps the only way.

Kant, said the prestige of mathematics (within the right circles) led to fallacious attempts to prove Gods existence. They're metaphysical truths that do not admit such proofs.

Contemporary Anglo-American philosophy is, from my decidedly faint acquaintence, strongly influenced by the positivistic philosophy that emerged from Vienna, and the turn toward language by Wittgenstein and logic by Frege. So this may be a good place to start if you're looking for mathematically based philosophy in a broadly conceived way. Its detractors say that it is narrow, and treats questions of no real substance to life.

Continental philosophy is much more catholic in its influences - it permeates & is permeated by marxism, literature, anthropology, psychoanalysis & sociology. Its detractors say that its obscurantist and mystifying. Its much less marked by mathematics and formal logic; however Badiou, a contemporary french philosopher has tried to inaugurate a turn towards mathematics as an ontology based on ZFC - or as Hilbert put it Cantors Paradise, the place where he tamed the infinite by inaugurating the arithemtic of the transinfinite, and where von Neumann constructed his model of ZFC from 'nothing'. Its definitely based within the continental tradition. But quite how Badiou has overcome objections to the finitude of mathematical infinity (which was clear to Cantor but perhaps not to his impetuous followers) and the emerging sense that there is pluralism in Set Theory & Logic is not clear to me.

A recent trend is paraconsistent logic which attempts to formalise dialethism - that there are true contradictions. In the continental tradition, one can consider Hegel as a dialtheist, in Buddhism - Nagarjuna and also the classic poem - The Tao. Da Costa kick-started the modern revival of formal paraconsistent logic, and Graham Priest is an able practitioner.

If you're interest in Buddhism & connection with mathematics, there is a school of Buddhist logic & atomism which would be probably worth investigating. It isn't logic in the formal Freagean sense - consider for example Hegel who used the word Logic in a very different way. The Catuskoti is a logical mantra that is used by them, and in particular by Nagarjuna. The jains also have their own distinctive logic and phenomenology. Interestingly enough two of their truth values go like this: it exists and is indescribable; it does not exist and that is indescribable. I find this useful in pondering Kants noumena.

Finally for mathematical philosophy orientated towards the mathematics broadly concieved, probably Lakatos, Lautman & Zalamea are your best bet.

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