It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth.

— Jean Piaget

## Viral Mathematical Logic quotations

### We are all concerned about the future of American education.

But as I tell my students, you do not enter the future - you create the future. The future is created through hard work.

Young man, in mathematics you don't understand things. You just get used to them.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

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.

Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

### The mathematical sciences particularly exhibit order symmetry and limitations;

and these are the greatest forms of the beautiful.

Logic and mathematics are nothing but specialised linguistic structures.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.

### Pure mathematics is, in its way, the poetry of logical ideas.

The general mental qualification necessary for scientific advancement is that which is usually denominated "common sense," though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.

### The only way to learn mathematics is to do mathematics.

That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.

### Obvious is the most dangerous word in mathematics.

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

There are three kinds of people: those who can count, and those who cannot.

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

What humans do with the language of mathematics is to describe patterns.

Since the mathematicians have invaded the theory of relativity I do not understand it myself any more.

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science.

Mathematics consists in proving the most obvious thing in the least obvious way.

### Science attempts to find logic and simplicity in nature.

Mathematics attempts to establish order and simplicity in human thought.

### The world is more than the sum of its suffering.

### A fist is more than the sum of its fingers.

The mathematician's patterns, like the painter's or the poet's, must be beautiful.

### Pure mathematics is, in its way, the poetry of logical ideas.

... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

Much of what I make is geometric, and has a kind of almost mathematical logic to the form.

The pursuit of mathematics is a divine madness of the human spirit.

But 'the physical level of rigor' is higher on certainty than the logical one, since reproducible experiments are more reliable than anybody's, be it Hilbert's, Einstein's or Gödel's intuition.

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.