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Mathematics is the only instructional material that can be

presented in an entirely undogmatic way.

Mathematics is the only instructional material that can be

presented in an entirely undogmatic way.

It is the merest truism, evident at once to unsophisticated

observation, that mathematics is a human invention.

It is the merest truism, evident at once to unsophisticated

observation, that mathematics is a human invention.

The mathematical sciences particularly exhibit order, symmetry,

and limitation; and these are the greatest forms of the

beautiful.

The mathematical sciences particularly exhibit order, symmetry,

and limitation; and these are the greatest forms of the

beautiful.

As far as the laws of mathematics refer to reality, they are not

certain, and as far as they read more

As far as the laws of mathematics refer to reality, they are not

certain, and as far as they are certain, they do not refer to

reality.

As for everything else, so for a mathematical theory: beauty can

be perceived but not explained.

As for everything else, so for a mathematical theory: beauty can

be perceived but not explained.

Revolutions never occur in mathematics.

Revolutions never occur in mathematics.

Mathematics is written for mathematicians.

Mathematics is written for mathematicians.

The highest form of pure thought is in mathematics

The highest form of pure thought is in mathematics

How can it be that mathematics, being after all a product of

human thought independent of experience, is so read more

How can it be that mathematics, being after all a product of

human thought independent of experience, is so admirably adapted

to the objects of reality?