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In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.

 

Hermann Weyl

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Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.

 

Doron Zeilberger

 

Benjamin Peirce deserves recognition, not only as a founding father of American mathematics, but also as a founding father of modern abstract algebra.

 

Benjamin Peirce

 

Topology provides the synergetic means of ascertaining the values of any system of experiences. Topology is the science of fundamental pattern and structural relationships of event constellations.

 

Buckminster Fuller

 

The authorities teach that next to the first emanation, which is the Son coming out of the Father, the angels are most like God. And it may well be true, for the soul at its highest is formed like God, but an angel gives a closer idea of Him. That is all an angel is: an idea of God. For this reason the angel was sent to the soul, so that the soul might be re-formed by it, to be the divine idea by which it was first conceived. Knowledge comes through likeness. And so because the soul may know everything, it is never at rest until it comes to the original idea, in which all things are one. And there it comes to rest in God.

 

Meister Eckhart

 

All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.

 

Benjamin Peirce