mathematics, the science of patterns

midory

Mathematics, the Science of Patterns

A common misperception is that mathematicians' work consists entirely of calculations. If that were true,computers would have replaced mathematicians long ago. What mathematiciansactually do is to discover and investigate patterns---patterns that arise innumbers, in abstract shapes, in transformations between different mathematicalobjects, and so on. Studying such patterns requires subtle and sophisticatedtools, and, until now, a computer was either too blunt an instrument, orinsufficiently powerful, to be of much use in mathematics. But at the sametime, the field of mathematics grew and deepened so much that today somequestions appear to require additional capabilities beyond the
human brain.

"There is a growing consensus that human minds are fundamentally notvery good at mathematics, and must be trained," says Bailey. "Giventhis fact, the computer can be seen as a perfect complement to humans---we canintuit but not reliably calculate or manipulate; computers are not yet verygood at intuition, but are great at calculations and manipulations."

Although mathematics is said to be a "deductive science",mathematicians have always used exploration, whether through calculations orpictures, to test ideas and gain intuition, in much the same way thatresearchers in inductive sciences carry out experiments. Today, this inductiveaspect of mathematics has grown through the use of computers, which have vastlyincreased the amount and type of exploration that can be done. Computers are ofcourse used to ease the burden of lengthy calculations, but they are also usedfor visualizing mathematical objects, discovering new relationships betweensuch objects, and testing (and especially falsifying) conjectures. Amathematician might also use a computer to explore a result to see whether itis worthwhile to attempt a proof. If it is, then sometimes the computer cangive hints about how the proof might proceed. Bailey and Borwein use the term"experimental mathematics" to describe these kinds of uses of thecomputer in mathematics.

- matematik bukan hanya mengenai pengiraan saje, malah matematik boleh diaplikasikan dalam pelbagai sudut. komputer pulak adalah salah satu complement atau pelengkap dalam matematik bagi pengiraan yang panjang untuk lebih efektif. walaubagaimanapon, otak manusia jauh lebih baik berbanding komputer kerana komputer hebat dalam pengiraan sahaja berbanding dengan manusia yang mempunya gerak hati (intuition) dan sebagainya.