Voltaire Quotes

Our knowledge can only be finite, while our ignorance must necessarily be infinite.

Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

No one shall expel us from the paradise that Cantor has created for us.

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

I remember, at MIT, we had to write an essay about something mathematical that you do in your extra time. I basically wrote about how dance, to me, was geometry: it was all shapes.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualize a three-dimensional space!

There are all sorts of things embodied in the Lego brick - geometry and mathematics and truth and proportion and shape and colour... It is a faintly spiritual activity that everybody connects with.

Some of us are sixty feet long with a brain the size of a walnut.

I’m so tired... I was up all night trying to round off infinity.

Some infinities are bigger than other infinities.

A googolplex is precisely as far from infinity as is the number 1... no matter what number you have in mind, infinity is larger still.

Any model we make does not describe the universe it describes what our brains are capable of saying at this time.

...Science and mathematics Run parallel to reality, they symbolize it, they squint at it, They never touch it: consider what an explosion Would rock the bones of men into little white fragments and unsky the world If any mind for a moment touch truth.

I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me.

As long as our brain is a mystery, the universe, the reflection of the structure of the brain will also be a mystery.

The Ludolphian number is fixed in eternity— not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s diameter into its circumference.

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.

To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.

A pool game mixes ritual with geometry.