Theorems – Page 6

Can the difficulty of

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn’t make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All … Read more

Combinatorial analysis, in the

Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century. Richard Askey

A proven theorem of

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution. Richard Arnold Epstein

If we knew what

If we knew what it was we were doing, it would not be called research, would it? Albert Einstein

To insure the adoration

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well. Albert Camus

We are on the

We are on the verge: Today our program proved Fermat’s next-to-last theorem. Alan Perlis

It is a matter

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted … Read more

Geometry has two great

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.
Johannes Kepler