Many children don’t like mathematics. In fact, some of them are afraid of it. But rightfully, mathematics is called the queen of the sciences.
Mathematics is a very enjoyable subject if you understand the logic of its various concepts. In my personal opinion and experience, mathematics becomes painful when it is learnt in the opposite way – by blind remembering and rote learning. Thus mathematics is a double-edged sword. How we learn and use it is entirely up to us. The effect is not just on the individual or his family but on the whole society and the world.
As you can make a person entirely logical, inquisitive and responsible through right mathematical teaching and completely the opposite by wrong mathematical teaching. A logical person is a boon to the entire world and an illogical person is a bane. A logical person sees that selfishness is mere foolishness. Thus teaching mathematics the right way makes one happy, selfless and useful to the society.
The beauty of logic is its power. Through a well known fact in mathematics I would like to demonstrate the magic of logic. The power of logic is magical and amazing. You can attract your students or listeners through this power and make them addicted to logic and make them look for logic everywhere and in all their daily activities thus responsible citizens who are an asset rather than liability to the world. For this purposes, I use a field of mathematics called number theory. Number theory is recognized as the queen of mathematics.
Children are taught how to add two numbers first (1+2 as an example). And later how to add three numbers (1+2+3 as an example), later four numbers (1+2+3+4 as an example) etc. It becomes cumbersome as the number increases. How beautiful would it be if we can find a simple way to calculate the sum of first 100 such numbers or 1000 such numbers. In deed it is possible. And that is only possible through a clever idea and logic.
Suppose you want the sum of first 3 such numbers i.e. you want to find the sum of 1, 2 and 3. 1+2+3. It is 6 as you can calculate. You can also find the result in another way. The next number to 3 is 4. Multiply 3 and 4. It is 12. You divide it by 2. You get the answer 6.
Let us try the method for another sum. This time sum of the first 10 numbers. 1+2+3+4+5+6+7+8+9+10 which can be found to be 55 by simple addition. The next number to 10 is 11. Multiply 10 and 11 and you get 110. Divide it by 2 and you get the answer 55.
Now you get the pattern. This pattern is applicable to any number not just 3 and 10. The sum of the first 100 numbers is 5050. Which can be found by100 x 101 divided by 2.
Of course, finding that the pattern works for numbers 3, 10 and 100 is not a proof that the pattern works for any number because there are infinite numbers and if the number fails even for a single number, the pattern can not be used. Also, there are infinite such numbers and you can not check the pattern for all of them.
Logic not only gives this pattern or shows this pattern but it also proves that it works for any such number however big it is.
How amazing! I can not forget the beauty of the reasoning. Make mathematics surprising! Make it interesting! Students will love it and look forward to more mathematics! This love is eternal!
(The author is a former DRDO scientist and former Research Manager, AT&T Bell Labs Innovations)