"Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is…"

"The equations of conic sections involve at most the square of x and y, never the third or higher powers. In contrast,…"

"For about 1500 years, from the time of Diophantus to Newton, elliptic curves were known only as curves defined by cer…"

"This is as I have said in my Arithmetic:—The area of a circle is equal to the product of the circumference by one-fou…"

"Multiply the arc by the square of the arc, and take the result of repeating that [any number of times]. Divide [each …"

"The method represents a best approximation algorithm of minimal length that, owing to several minimization properties…"

"The process of reasoning called "Mathematical Induction" has had several independent origins. It has been traced back…"

"This method is supreme above all praise; it is certainly the finest thing accomplished in number theory before Lagrange."

"A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains fixed.The ax…"

"Having fixed a pole, on a level piece of ground, and having described a circle by a cord attached to the pole, one sh…"