As he got deeper into it he began to run into a lot of mathematics, which he had to work out with a pencil and paper—you couldn’t do magical equations with computers, they just spat out inconsistent answers before hanging completely. Magical math had to be thought through with a brain.

We have written the equations of water flow. From experiment, we find a set of concepts and approximations to use to discuss the solution — vortex streets, turbulent wakes, boundary layers. When we have similar equations in a less familiar situation, and one for which we cannot yet experiment, we try to solve the equations in a primitive, halting, and confused way to try to determine what new qualitatitive features may come out, or what new qualitative forms are a consequence of the equations. Our equations for the sun, for example, as a ball of hydrogen gas, describe a sun without sunspots, without the rice-grain structure of the surface, without prominences, without coronas. Yet, all of these are really in the equations; we just haven't found the way to get them out.

...The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colourful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets — those eight or ten balls, each agglomerated from the same dust clouds and each obeying exactly the same laws of physics.

The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrodinger's equation contains frogs, musical composers, or morality — or whether it does not. We cannot say whether something beyond it like God is needed, or not. And so we can all hold strong opinions either way.

Can we use programs instead of equations to make models of the world? ...[I]n the beginning of the 1980s ...I did a bunch of computer experiments. ...It took me a few years to really say, "Wow, there's a big important phenomenon here that lets... complex things arise from very simple programs." ...[A] bunch of other years go by [and] I start of doing ...more systematic computer experiments ...and find ...that ...this phenomenon ...is actually something incredibly general... [T]hat led me to this... principle of computational equivalence... [A]s part of that process I said, "OK... simple programs can make models of complicated things. What about the whole universe?" ...and so I got to thinking, "Could we use these ideas to study fundamental physics?" ...I happened to know a lot about traditional fundamental physics. ...I had a bunch of ideas about how to do this in the early 1990s. I made... technical progress. ...I wrote about them back in 2002.

The equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result.

In our travels, we have come across many equations — math for understanding the universe, for making music, for mapping stars, and also for tipping, which is important. Here is our favorite equation: Us plus Them equals All of Us. It is very simple math. Try it sometime. You probably won’t even need a pencil.

I scarcely believe that in psychology data are present which can be mathematically evaluated. But one cannot know this with certainty, without having made the experiment. God alone is in possession of the mathematical bases of psychic phenomena.

Words are a pretty fuzzy substitute for mathematical equations.

Equations are the devil's sentences.

The laws of nature are but the mathematical thoughts of God.

What created by a human mind, can be solved by another human mind. From this point of view, unsolved problems do not exist and can not exist in any area of science.

Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, <math>E = mc^2</math>. I hope that this will not scare off half of my potential readers.

Scanning the past millennia of human achievement reveals just how much has been achieved during the last three hundred years since Newton set in motion the effective mathematization of Nature. We found that the world is curiously adapted to a simple mathematical description. It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within an enigma.

Many physicists these days sound like the Delphic oracle - with equations.

This is a mathematical universe. We are surrounded by equations and summations. Your life: the current state of your life and life itself is a direct summation of the equation you have created. Your life is a reflection of many choices you have made at the innumerable amount of choice-points you've crossed. Great endeavors are the summation of a great and deliberate equation.