Tools and Techniques
Experimental mathematics makes use of numerical methods to calculate approximate values for integrals and infinite series. Arbitrary precision arithmetic is often used to establish these values to a high degree of precision – typically 100 significant figures or more. Integer relation algorithms are then used to search for relations between these values and mathematical constants. Working with high precision values reduces the possibility of mistaking a mathematical coincidence for a true relation. A formal proof of a conjectured relation will then be sought – it is often easier to find a formal proof once the form of a conjectured relation is known.
If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers.
Frequent use is made of general computer algebra systems such as Mathematica, although domain-specific software is also written for attacks on problems that require high efficiency. Experimental mathematics software usually includes error detection and correction mechanisms, integrity checks and redundant calculations designed to minimise the possibility of results being invalidated by a hardware or software error.
Read more about this topic: Experimental Mathematics
Famous quotes containing the words tools and/or techniques:
“Justice and truth are too such subtle points that our tools are too blunt to touch them accurately.”
—Blaise Pascal (1623–1662)
“It is easy to lose confidence in our natural ability to raise children. The true techniques for raising children are simple: Be with them, play with them, talk to them. You are not squandering their time no matter what the latest child development books say about “purposeful play” and “cognitive learning skills.””
—Neil Kurshan (20th century)