Video: Is mathematics discovered or invented?

If there’s a number of trees in a forest, and there’s no one there to count them, does that number exist? This is the same question as the existence of mathematics. Is mathematics discovered or invented? If human beings do not exist, would mathematics still exist?

Watch the video from TED as Jeff Dekofsky traces the history of this famous classic question and how mathematicians throughout history think about it.

What’s your take? Write your comments below.

Who is the greatest mathematician?

For you who is the greatest mathematician? This was a question asked to me by a kin, a freshman who is currently studying a  mathematics related course. This question is probably asked by many others who are just starting studying mathematics or those who are just simply curious.

Asking who the greatest mathematician is like asking who the greatest singer is. Singers have different genre that it is nearly impossible to tell. Pop lovers would probably suggest that it was Michael Jackson, but classical singers would probably disagree and would suggest some names like Luciano Pavarotti.

I think, determining the greatest mathematician is even more complicated than determining the greatest singer. Mathematicians lived in different times and the maturity of mathematics at different times is enormously different. For example, during the time of Euclid, it takes a high-caliber mathematician to prove that the inscribed triangle in a circle containing its diameter is right, while they can be easily proved by eighth graders of the present time. Of course, we cannot claim that our eighth graders are better than or even at the same level as Euclid because mathematics has changed so much.  Those who are only read by mathematicians during the time of Euclid are now taught in the elementary and high school levels.  In addition, mathematicians study different fields and it is impossible to compare the level of difficulty or even to quantify the effect of their contributions. Continue reading

8 Amazing Mechanical Calculators Before Modern Computers

Before there are graphing calculators, spreadsheets and computer algebra systems, mathematicians and inventors searched for solutions to ease the burden of calculation. Today we celebrate human achievement in creating these calculators. Below are the 8 mechanical calculators before modern computers were invented.

1. Abacus (ca. 2700 BC)

Although abacus is not mechanical, it was one of the most widely used calculating device for many years.  The abacus is one of the earliest counting machines used for arithmetic calculations. It made up of beads and frame. It was particularly used Japan, India and China. Although they are popular in Asia, the abacus has a long history which originated 2700 years ago in Sumeria. It was also used in Egypt, Persia (Iran), and Greece.  The reason why the abacus is popular was probably because it’s very easy to use. Until now, there are still people who use this ancient tool. Continue reading

Calculating The Value of Pi

We have met the number 3.1416 or the approximation of pi (written as \pi) in our good old elementary school days. In fact, we have used it a countless number of times in mathematical computations. Most of us have used it when calculating the area of a circle or volume of a sphere, but only a few probably know that it appears in numerous branches of mathematics and even in other sciences.

pi

The number \pi is the ratio of the circumference of a circle to its diameter. What does that mean? It means that if we measure the circumference of a circle and its diameter and divide them, the quotient is “three point something.”  Now that three point something is \pi. What is amazing is that this is always true even if the circle is a big as a planet or as small as an atom. Continue reading

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