One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels… — John D. Barrow Copy Share Image
“The ease with which collaboration occurs in mathematical research and the essential similarity of the fruits of such collaboration to that of… — John D. Barrow Copy Share Image
“Moreover, there is no known reason why the geometry of space and time should be described by the particular types of curved… — John D. Barrow Copy Share Image
“Grosseteste influenced Roger Bacon's ideas about mathematics and Nature. Bacon wrote hundreds of pages on the subject and, indeed, no historical figure… — John D. Barrow Copy Share Image
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and… — John D. Barrow Copy Share Image
“In the Middle Ages, this conflict between the Platonic and Aristotelian views of the relationship between mathematics and the world began to… — John D. Barrow Copy Share Image
“Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that… — John D. Barrow Copy Share Image
“Non-Euclidean' became a byword for non-absolute knowledge. It also served to illustrate most vividly the gap between mathematics and the natural world.… — John D. Barrow Copy Share Image
“The fact that simultaneous discovery occurs in mathematics, as well as the sciences, points toward some objective element within their subject matter… — John D. Barrow Copy Share Image
“We have seen that our numerical zero derives originally from the Hindu sunya, meaning void or emptiness, deriving from the Sanskrit name… — John D. Barrow Copy Share Image
“Topology is that branch of mathematics which is interested in the forms of things aside from their size and shape, Two things… — John D. Barrow Copy Share Image
“Aristotle draws a sharp dividing-line between the activities of the physicist and those of the mathematician. The mathematician limits his enquiry to… — John D. Barrow Copy Share Image
“But, as powerful mathematicians like Minkowski and Hilbert found striking harmony between their pure mathematical results and the workings of the physical… — John D. Barrow Copy Share Image
“One of Nature's deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries… — John D. Barrow Copy Share Image
“The effect of the 'time becomes space' proposal is that there is no definite moment or point of creation. In more conventional quantum mechanical… — John D. Barrow Copy Share Image
“Humans are distinguished further by the highly effective way in which they have pooled the individual intelligence of single individuals to produce a collective… — John D. Barrow Copy Share Image
We can predict the present without having to know everything about the past. — John D. Barrow Copy Share Image
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we… — John D. Barrow Copy Share Image
“If the deep logic of what determines the value of the fine-structure constant also played a significant role in our understanding of all the… — John D. Barrow Copy Share Image
“Each of us is a complicated assymetrical outcome of the laws of electromagnetism and gravity.” — John D. Barrow Copy Share Image
“Impressed by the success of high-level mathematics in the formulation of the general theory of relativity in 1915, we find that Einstein's life-long quest… — John D. Barrow Copy Share Image
“Jewish philosopher Martin Buber, who died in 1965, wrote of how the mere thought of the infinite led him to contemplate suicide: “A necessity… — John D. Barrow Copy Share Image
“As we look way back into the first instants of the Big Bang, we find the quantum world that we described in Chapter 3.… — John D. Barrow Copy Share Image
“The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to… — John D. Barrow Copy Share Image
