Even without electronic help, proofs
often get incomprehensible, so mathematicians frequently reduce them to essentials.
The following lemma says that, under conditions that will arise in the proofs
of the main theorems, we can always find two triangles that share a edge, or two tetrahedra that share a face.
Bailey and Borwein point out that mathematical proofs
can run to hundreds of pages and require such specialized knowledge that only a few people are capable of reading and judging them.
For instance, a large customer might have a proofer at its location, and the converter can set up a system where proofs
can be directly printed at the customer's location.
can be numbered, but often they are not.
Augustine sought to prove God's existence in a number of ways, including the proof
from the external world.
The combination of the two technologies will enable customers to quickly and accurately produce and verify spot colors to deliver top quality proofs
on an inkjet printer.
These results are still preliminary in the sense that they have not been refereed and have not even been submitted for publication," he noted, "but the proofs
are--to the best of my knowledge--correct and complete.
Using Otter, McCune and his coworkers have in recent years solved a wide variety of mathematical problems, generating original proofs
of theorems in logic, algebraic geometry, group theory, and other areas of mathematics.
-it-ONLINE's no-software application allows creative professionals to post proofs
for approval and enables their customers to mark up and review proofs
online - within minutes.
Blum has applied the concept of interactive proofs
to what he terms "result checking" or "program checking.
Standard posts 1,500 proofs
per month for review and at the end of each review, Standard's advertisers receive a reward offer with the opportunity to advertise on Standard Publishing's website for $200.