Experimental mathematics is basically an approach in which number-based computation can be used for exploration of objects and recognize various patterns and properties. It is a branch of math dealing with coding and decoding procedures for transmission of insights within mathematical community with the use of experiments and investigation. It involves exploring the conjectures and analyzing the acquired data in a vigilant manner.
Mathematics is based on formulas and it doesn’t involve assumptions. There are proper procedures followed to prove a theorem and it doesn’t simply go with hypotheses. You can do trails and experimentation and there is no space for guesses. The facts need to be illustrated and you need to work out in a way to illustrate all the data with facts. You can think about being a laboratory technician who carries out every activity with experiments and relate mathematics to it to understand the concept of experimental mathematics.
History of Experimental Mathematics
Experimental mathematics has always been practiced by mathematicians at different levels. The earliest records suggest that Babylonian mathematics consisted of algebra concepts in detail, read more info on Babylonian mathematics at http://www.math.tamu.edu/~dallen/history/babylon/babylon.html. As the subject became vast, there were abstract and formal illustration of theorems made in the early 17th century. The numerical concepts used for creation of general theorem were forgotten at that time.
The idea behind experimental mathematics was entirely different and it emerged in 20th century. The innovation began with the introduction of computers having speed and precision more than other sources. Experimental mathematics was helpful in the discovery of formula for binary digits of pie (π) and termed as Bailey–Borwein–Plouffe formula. It was meant for making number-based searches on computer and came with a proof for creating formal reasoning procedures.
Uses of Experimental Mathematics
The main objective of experimental math is to help in understanding and confront conjectures. It can generate and confirm inferences for making mathematical concepts lively and tangible for professional researchers.
Major uses of experimental mathematics are:
- Getting insights and generating intuitions for computing projects
- Usage of graphics in displays for getting practical implementation of mathematical principles and concepts
- Discovery of new relationships and number-based patterns
- Testing conjectures and falsifying them
- Exploration of possible resultants to view if the formal proof is worthy
- Confirmation of analytical results derived with different concepts
- Replacement of hand written derivations with computerized derivations to save time and efforts
- Suggestion of approaches to give formal proof
- Exploration of feasible results to see if the formal proof is worth or not
This field of mathematics makes search for the ways to reach a particular proof or theorem. There are experimental results for every proof and these can be proved to reach the particular proofs. There are explorations done for significant conjectures for inspiring better equipped researches for investigation purposes. The main role of experimental mathematics is to formally discover formal proofs for number based statements. There are research journals covering the concepts of experimental mathematics and it has advanced for Computational Algebra studies.