Mathematician of the Month – Somerville

Mary Somerville, a Scottish science writer and polymath, was nominated to jointly be the first female member of the Royal Astronomical Society at the same time as Caroline Herschel (the great German British astronomer). And coming at a time when women’s participation in science and math was discouraged, this accomplishment was highly praiseworthy on her part.

The young girl whose favorite pastime once used to be looking after the family chickens and hunting for starfish and crabs on the beach once unexpectedly encountered an algebraic puzzle with X’s and Y’s in a magazine. Our budding mathematician was very intrigued and eager to learn more on the subject. But unfortunately, her parents were of the belief that a woman’s constitution could not handle much intellectual effort without causing damage to her physical and mental health and so discontinued her studies.

But our enterprising lady would not accept defeat. She began by sneaking in on her brother’s math tutorials to learn more about algebra. She also creeped into her father’s study every now and then and read his books on navigation. She taught herself the Latin language so that she could learn more about Euclid and his geometry. Her parents eventually came to know that she was spending her evenings studying and so they confiscated her candles. But Mary found another way around this roadblock – she started memorizing mathematical problems and then solved them in her head in the dark!

An outstanding mathematician, astronomer, geographer as well as scientist of the Victorian period, Mary Somerville has not only the Somerville College in Oxford University named after her, but also an Arctic island by her last name. On her demise, she was rightfully dubbed ‘The Queen of Nineteenth Century Science’ by a newspaper.

Mathematician of the Month – Ramanujan

The fact that Srinivasa Ramanujan Iyengar has a feature film on his life called The Man Who Knew Infinity: A Life of the Genius Ramanujan speaks volumes about the greatness of this Indian-born mathematician. The downside to his great intellect? He was so far ahead of his time and his work was so unorthodox, that even the most celebrated scholars of his times couldn’t really understand him! It is only now, more than 80 years after he passed away that we are beginning to comprehend his work and apply it to computing and complicated physics.

Thanks to the English mathematician G H Hardy, Ramanujan came to England. But he was known for certain quirks. For instance, he refused point blank to wear shoes or socks. People started referring to him as a nutcase as he was in the habit of lying face down in a cot while working on mathematical problems, and that too on a slate with chalk rather than using pen and paper. The most infuriating habit of all – especially to his fellow mathematicians – was that Ramanujan would rub out all his complicated workings with his elbow once he solved a mathematical problem and just leave behind the solutions on his slate! As a result of which mathematicians, even today, are still in the process of figuring out how exactly this mastermind worked them all out so correctly.

The most popular story about Ramanujan comes from a visit G H Hardy made to him when he was on his deathbed. Hardy didn’t know what to say to cheer him up, so he commented on the boring number of his taxi – 1729. Our genius, even in that ill state, was instantly inspired and sat up: “1729 is a fascinating number! It is the smallest number that can be expressed as the sum of two cubes in two different ways!”

In his short yet extremely fruitful life, this mathematical prodigy rediscovered previously known theorems, produced new theorems of his own accord, independently compiled nearly 4000 results of identities and equations and made remarkable contributions to the fields of mathematical analysis, number theory, infinite series and continued fractions.

G H Hardy summed it up perfectly when he said: “Here was a man who could work out modular equations and theorems to orders unheard of, and whose mastery of continued fraction was beyond that of any mathematician in the world.” Undoubtedly, he was one of a kind, the only one in his league.

Mathematician of the Month – Archimedes

Archimedes of Syracuse – a mathematician, a physicist, an engineer, an astronomer, an inventor, a scientist – there was absolutely nothing that this brilliant man couldn’t do! No wonder he is considered to be the greatest mathematician of classical times and one of the greatest till date.

Archimedes’ first tryst with fame came when the ruler of those times, King Hieron, built a ship which was too heavy to go into the sea (Why did he build ‘a ship’ anyways if it couldn’t sail? Archimedes must have had a good laugh at the majesty!). Our budding genius was the savior – he came up with a slick contraption made up of pulleys, levers and cog wheels, which allowed a single individual to launch the massive ship into the waters, all the while sitting back in a chair and relaxing with a cool drink in his hands! And hence the famous Archimedes quote: “Give me a place to stand and I will move the earth!”

What’s more, this prodigy also had a hand in fighting with the Romans. Legend has it that he helped the army build huge wacky catapults that hurled boulders through oncoming ships and mirrors that reflected the sunlight onto ships, which resulted in them erupting into flames, even before they got close to the land! The best story of all is that of a gigantic crane he constructed that had the capability to reach over the wall, lift entire ships up, shake them around till they rattled and then drop them back into the seas – upside down! Must have been a sight to behold!

To put it in a nutshell, here is a man who invented the water screw, made war machines, made a heat ray, created a miniature planetarium, worked with pulleys and levers, invented calculus (to the woes of many like me, no doubt), invented the odometer and is more famous for his inventions in life than just math alone!

His last words supposedly were: “Don’t disturb my circles!” as a Roman soldier walked across his drawings in the sand for his latest mathematical theorem. The soldier was so incensed, that he stabbed the mathematician. Thus came to an end the extraordinary life of the greatest ‘Eureka’ genius in Greek history.

Mathematician of the Month – Newton

‘There is no great genius without a touch of madness,’ so they say. And Isaac Newton, supposedly the greatest mathematician (and physicist and scientist and natural philosopher) Britain has ever produced, was no exception.

In a way, it is his uncle who is to be credited for giving the world one of the most brilliant scientists of all time. Newton’s uncle noticed that Isaac was very poor at farming – his traditional family occupation – and hence persuaded his mother to send him to college for higher studies. Not many know that one of the greatest ambitions of Newton’s life (which was unfortunately left unfulfilled) was to get his hands on the philosopher’s stone (yes, the same Harry Potter one) which contained the secret to turn common metals into gold.

He is credited with numerous contributions. He is credited for laying down the foundations of classical mechanics, through his book ‘Mathematical Principles of Natural Philosophy’. It was he who came up with the laws of motion (planetary and otherwise), universal gravitation, calculus and the rules of color and light. And he did so much more, things which cannot be enumerated here due to lack of space (and effort, since the list seems endless).

And remember there was a tree under which he was sitting, when an apple fell on his head? Well, apparently, that tree is real. A piece of the same old iconic apple tree was even loaned by the Royal Society to NASA who took it into space. This is the sort of real-life stuff fairytales are made of!

Mathematician of the Month – Napier

Well, what is this ‘log-in-a-rhythm’ up to? And what does this have to do with our celebrated Scottish mathematician of the month – John Napier? A lot, actually. It is this Mr. John Napier who is credited with making an incredible contribution to the field of mathematics, in the form of the invention of the mathematical concept of ‘logarithm’.

A logarithm can be defined thus: It is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Didn’t get it? Well, in simpler terms, it is a method by which relatively complicated mathematical calculations involving multiplication and division can be replaced by the simpler mathematical processes of addition and subtraction to arrive at the required result. This process of simplification of large calculations paved the way ahead for many scientists of yesteryears (and is even helping them now!), leading to significant advancements in the fields of science and technology.

As with a majority of the other eminent scientists and mathematicians, Mr. Napier also led a crazy smart life of sorts. He was seen as a virtual recluse – roaming around in his nightclothes according to his whims and fancies, muttering all the while to himself. For some reason unknown to the world, he always carried around a black spider in a small box kept in his pocket.

Legend has it that once upon a time Napier suspected that one of his servants had started stealing from the estate. In order to nab the culprit, he devised a clever plan – a black rooster (that, on a brainwave from Napier, was brushed with black soot), which allegedly was blessed with the power of divination, was kept inside a shed. Each of the servants was asked to go inside and touch the rooster in question, which would eventually come up with the name of the thief. The servants did so; and as expected, one of the fellows that went in came out clean-handed and was rightly proclaimed the thief!

It is said that Napier considered the subject of mathematics more like a hobby; he enjoyed it immensely (It fails me how anyone can enjoy maths and my kids take after me – I have to put in a huge amount of effort just to get them to do their math worksheets… Phew!). . The first time he set foot in a school was at the age of 13 years. But soon he dropped out and not much of his life is known till at the age of 21 years, he bought his own castle in Scotland (aaah, if only wishes were horses, beggars – like me – would ride!). Today, it is a part of the prestigious Edinburgh Napier University.

Theorems in spherical trigonometry (maths that deals with the relations of the sides and angles of triangles), Napier’s bones (a multiplication tool using a set of numbered rods) and extensive books on logarithms are just some of his contributions to astronomy and dynamics, in addition to other areas of physics. Hats off, Mr. Napier!

Mathematician of the Month – Babbage

To the humble PC that is displaying this text as I type it, Charles Babbage is its father. A British mathematician and engineer, Charles ‘Father of Computers’ Babbage was very picky about his Math. In fact, he even wrote to Lord Tennyson (apparently some sort of famous poet) and asked him to correct the lines of his poem ‘Every minute dies a man, Every minute one is born’ to ‘Every minute one and a sixth is born’. Of course, he was refused.

Having come into a lot of riches courtesy his dad, he spent all his money inventing rather exciting gadgets including the speedometer and the cowcatcher, which kept cows with wander lust off the railway track. Indubitably, his greatest invention was the calculator. The first one he ever invented was called the ‘Difference Engine’.

The British Government, sold on the idea of this Difference Engine, gave him £1 million so he could build it. After 11 years of trying and trying, Babbage gave it up for a better idea. Furious that their money was wasted, the government refused to give him any more. Not to be deterred, he continued on as before because, well, he was rich!

The Difference Engine version 2.0 was going to be bigger and better. It could do more than just add and subtract. It would be able to do multiplication, division and also printing. Babbage envisioned that the new machine would use similar technology to that of carpet making looms. Unfortunately, he died before the machine could be built.

In 1890, an American guy by the name of Herman used Babbage’s ideas to build a much simpler machine. If his name sounds familiar, it is because he went on to found International Business machines aka IBM. However, it wasn’t till 1944 that the machine of Babbage’s dream was built. The first calculate needed 10sqms to house it and it weighed 30 tons! The Science Museum in London built a model of the original Difference Engine in 1992. That one was only 2 meters high and over 3 meters long. Can you imagine what owing a computer those days would look like? Yikes!

Mathematician of the Month – Pythagoras

Mr. P was born in a Greek island called Samos and despite the great views; he was more interested in Philosophy and Mathematics. He was also an expert in Astronomy, Religion and Music and wanted nothing more than to share his brilliant ideas with the world. Unfortunately, most people didn’t understand what he was saying and didn’t humor his grand thoughts. Eventually he paid a young boy to listen to him and soon he had created enough interest to start a school and recruit 300 pupils.

He was the most entertaining teacher of the time. He would hide behind a curtain and wait for his class to settle down. He would then jump out and yell the problem at the class and then go back into hiding. After a few minutes, he would jump back out and announce the answer – much to the amusement and confusion of his students.

Pythagoras is known for two major theorems. One is about whole numbers and the other about right angled triangles. They say that he stole the theorem from someone else (even the Egyptians say they knew of the theory) but he was the first one to be able to prove it. To celebrate, he sacrificed 100 cows only to find out that his second theorem disproves the first one. He covered up his mistake but his student leaked the information and was murdered for it.

The secret brotherhood of the Pythogorean School was being viewed suspiciously by the people. It came across as a dodgy sect. When people learnt of the student’s murder, the public rioted and set fire to the school when the members and Mr. P were still locked inside. Despite the horrible way in which he had to go, Pythagoras’s theorem is still being taught at school 2500 odd years later!

Mathematician of the Month – Descartes

You know that quote “I think, therefore I am”? Yep, René Descartes said it – our beloved Mathematician of the month. The French philosopher had so many brilliant ideas, he had to stay in bed almost all day just to be able to wrap his mind around them (it might have to do with him being sickly, but we’ll ignore that for now)

His specialty is Geometry – you know, the math of beautiful shapes. One day while he was lying in bed, waiting for breakfast to be brought to him (philosophy seems a great career if you ask me), he observed a fly crawling around the ceiling. When his maid arrived with breakfast, he tried to tell her where the fly had been without pointing it out to her. This obsession led to him chancing upon his greatest idea – grids with axes.

While we give directions in relation to the most recognizable landmark, “along the corridor, second door to your left”, he created grids with numbers. So the fly started at 4,2 which means 4 along the grid and 2 up. The maid rolled her eyes and walked away slowly, refusing to acknowledge the importance of his discover. Within a few years, however, it started being used in Math, Physics and even Geography and is popularly called the Cartesian coordinates.

Personally, thinking causes me a lot of confusion and so for now, it’s on hold! To be continued …

Mathematician of the Month – Pascal

Blaise Pascal was an extremely gifted Frenchman who spent a majority of his life devoted to God and the Christian faith. However, he was a genius mathematician who as a young boy and was saved from becoming just another obscure mathematician due to his remarkable contributions and discoveries.

When he was a kid, he was amazing at geometry and not having known about some mathematical discoveries, he rediscovered many of Euclid’s findings. At the age of 18, he invented an adding machine that seemed way ahead of its time. His invention was so well received that there is a computer language that is named after him.

Pascal and another top mathematician called Fermat invented probability in a bid to help a friend who had a gambling problem and was losing a lot of money. It turned out to be one of the most widely used branches of mathematics and perhaps the most important.

While working on the theory of probability, he did what he was slowly starting to get recognized for = rediscovering. He rediscovered an ancient Chinese triangle that is now popularly known as Pascal’s Triangle. I could go on about this triangle but it would give me you a headache so I won’t go there.

At 23, Pascal unfortunately developed a condition called dyspepsia which along with his insomnia made his life extremely difficult. Descartes suggested he should stay in bed and live on a diet of beef tea. This didn’t help him. Shortly after, he had a freak accident where he dangled from a bridge and his horses drowned. He convinced himself that it was a sign from God, telling him to give up Math. Vowing to live a more spiritually oriented life, he lived with Math. 16 years later, he died from stomach cancer.

Apart from his mathematical contributions, he is known as the inventor of the one-wheel wheelbarrow, of hydraulics and of public transport. It is safe to say he lived a very full life – the effects of his great work are felt even to this day.

Learning Activities with Water Beads

Water beads are such a versatile yet hardly explored tool for learning that you’ll not realize its benefits unless you start playing with them. Add a handful of water beads to the child’s activity time (well monitored to ensure kids don’t swallow the beads) the next time she brings out her toys and see the difference. Learning will reach a different level altogether with the effective play tool.

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Learning Math with Water Beads

Have fun simply counting the tactile, colorful water beads with the kids. Line up a handful of water beads in a row and take out a couple from it. Ask kids to count how many remain. Add a few and ask them to recount. Play the symbol game where you write two digits on the left of an ‘equal’ sign and a resultant on the right. Ask the kids to guess the math symbol which will get the resultant and have them write the symbol with water beads. Though water beads don’t hold any topical significance in this activity, kids will be eager to play it out just to enjoy the tactility of the beads. If you are playing with a group younger than 6-7 year olds, here are a couple of more activity ideas.

• Have them put red beads in one spot and the yellow ones in another. Ask them to count both the groups individually as well as together.
• Have kindergarteners make shapes and patterns with the beads. You can choose to make the first shape and ask them to follow you.
• Ask them to count if they’ve got more blue water beads or white water beads? If they have mastered their math by now, ask them to count the difference in the number of beads of the two colors.

Learning Science with Water Beads

It’s time to explore the science behind water beads that swell up to look like the way they do. Start by handing over an unopened pack of water beads to the kids. Let them experience the fun of these tactile beads from the beginning. Have them play with these beads which have not been soaked in water yet. They’ll be coarse to touch, similar to M&M candies. Keep a notebook handy to document the experiences step by step. Read out the packet instructions to the kids and have them follow. The steps will mostly ask you to add a liter of water to a packet of beads. Find out if the kids are surprised at this stage at the proportion of water to the beads. Let the beads soak in the water and the kids marvel at the change of the beads’ appearance. To add more fun, divide the beads into three bowls and add a few drops of food color to the water in each to get colorful beads. Let kids squash, squeeze, squish, and smash the beads and understand why the beads swelled up. Encourage them to test out the properties of the swollen beads and compare these with the ones with which they started. Do they roll, bounce, go flat or back to their original shape? Explore the possibilities with the kids.

Learning English with Water Beads

Right at the beginning, we told you water beads are versatile. Well, here is an English activity too with the multipurpose water beads! Play this activity with the kids before the water beads go all dry and you have to throw them away. Fill up a bowl with squishy water beads and add a number of letters into the bowl. Instead of using tongs or another similar tool to pull out the alphabets, blindfold the kids and have them put their fists into the bowl and pull out any three random letters. Next, ask them to make a syllable or a word with them. If the letters cannot make up a word or a syllable, you can give them an imaginary vowel to complete the task. You’ll be surprised at how long this alphabet game can go on!

Explore the many learning possibilities of water beads with the kids as you play with them!