During the remainder of the journey the licentiate held forth to them on the excellences of the sword, with such conclusive arguments, and such figures and

mathematical proofs, that all were convinced of the value of the science, and Corchuelo cured of his dogmatism.

There are hundreds of other ideas here worth reading like how modern science has shown that a butterfly's wing can stir up an Atlantic storm and the

mathematical proof of the existence of life in other galaxies.

Furthermore, it is so far from the kind of understanding we normally think a

mathematical proof should offer that some experts don't consider these computer-assisted strategies

mathematical proofs at all.

So here is

mathematical proof that rich fraudsters are engaged in more than three times the fraud of those improperly claiming benefits.

A Bitcoin wallet provides

mathematical proof that transactions came from a wallet's owner.

"It took us over a year to complete the

mathematical proof that makes it all possible." The pair figured out how to shape the magnetic field so energy could be beamed to smartphones placed or in use within a foot of a Pi.

Mathematical proof for the formation of an ellipse inside an ellipse

For 86 of these I can offer

mathematical proof of their atomic numbers by assigning alphabetical values to the letters of the element.

The show's treatment of this theorem--and its associated formal proof--can be used to facilitate a discussion about what constitutes a

mathematical proof. The episode proper includes a lightning-fast montage of how, precisely, each character was returned to their original form, and a freeze-frame analysis should confirm that the episode isn't cheating.

These are people in academia who provide

mathematical proof that our products are the most efficient way to achieve retirement success.

A Fields Medal winner, Villani recalls the peaks and valleys of his discovery of an important

mathematical proof.