Based on quotes from http://en.wikiquote.org/wiki/John_von_Neumann

“I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics.”, Me: truly beautiful explanation of how mathematics is built; this is why we need to iteratively revise the foundations; this is why we need to allow more people in and bring in some experiment; the mathematics of the future will be for everyone, also for the robots

“Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.”, Me: true randomness cannot come from a deterministic process, we can use all (an infinite number of) primes to achieve the idea of “deterministic random”, which attracts my mind, as opposed to the explanation that there is no determinism (dr. Arkani-Hamed, on amplituhedron); just because we cannot see it from the inside of the box does not mean it does exist when a take a peek outside of it

“A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.”, Me: this happens, because we model things from imagination, which then sometimes turn out to be applicable to certain fields from the outside of mathematics; also, all things, which relate to numbers, are also related to any science, even though the relation may be disguised

“The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.”, Me: as stated earlier, any mathematics that we know is inspired by experiment, no matter how tough to see that is

“It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.”, Me: objects, which we use in mathematics, may not come from our direct experience, and, nevertheless, we feel compelled up to use them; everything is low level in mathematics (mathematics is lowest level physics) and thus our ability to experiment with them is limited; thus, the limitation in question becomes severe; indeed, mathematics is an experimental science; even if we make a proposition of a feature like a complex number (from complex numbers), we either feel it describes well our experience (because we want to have it as a feature)

“When we talk mathematics, we may be discussing a *secondary* language built on the *primary* language of the nervous system.”, Me: we want to have it like that, for it is mathematics a low-level part of physics; we need to remember that our model selection in mathematics (numbers, operations) very strongly defines our science- a beautiful example here would be the connection of lim and exponentiation over the integers resulting in e; how could we know in first place that it was limited?

“You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.”, Me: the dissipation of state is for a reason and is not a feature, which the universe itself knows

“Young man, in mathematics you don’t understand things. You just get used to them.”, Me: took me years to understand it; true; we have a set of experimental features to investigate; mathematics is going to become more like a sculpture, where a sculpturer iteratively improves his vision, based on experiment; mathematics has a big help now – we can see nanostructures better now, we learn to talk to quants

“You don’t have to be responsible for the world that you’re in.” (von Neumann to Feynman) , Me: you don’t, because you are part of it, and hence cannot embrace it, i.e. you are not the owner; but, for the life to be beautiful, i want to feel responsible and therefore believe that we all have a part of the infinity that goes beyond the observable in the world (is from outside of it)

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”, Me: agreed; in addition, features such as the infinitesimal, seem now to represent a straight-forward (naive) approach

“If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.”, Me: boils down to gaining a deeper understanding of things

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”, Me: nothing to add, agreed