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5 insanely great books about mathematics you should read.

Kelly J. Rose

I’ve been asked over and over for good books about mathematics for a layperson, someone who hasn’t taken advanced courses in university and is more simply interested in learning about what math is, and some of the more interesting historical figures and results from mathematics. Ironically, when you are a mathematics major at Waterloo, you get the opportunity in 4th year to take a course on the history of mathematics and you get introduced to a few really good books that start to explain the mindset and philosophy behind mathematics and not simply just the theorems and proofs.

Here are the 5 books about I most recommend to those who want to understand the mathematical mind and philosophy.

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Chapter 1. ATOMS

The sky was dark and gloomy and beautiful. Aurora borealis lit up the sky with multi colored strands of light. Stars could be seen through the weak orange glow of the dying sun. The stars never change their positions now. The earth has stopped rotating long since. The moon is just stuff of legend now.

The ROC hung like a miniature star high in the sky. Barely moving, barely stirring, it’s body glowing with its own bio luminescence as it looked about for it’s prey. It had been starving. The humans who lived on the ring of land around the equator now have moved underground. Nearer to the core, nearer to heat, away from the roc. Today, it spotted two tiny figures moving towards an underground entrance. There are many such entrances scattered all over the land. They provide access to the underground caverns and the roc knew that sooner or later people will come out to recieve or attack these two. The roc will feast then. It waited.

The smaller of the two looked up directly at the roc and said “That star just moved”

His companion gave a glance to the sky and quickened his pace.

“Judas, will you tell me what’s going on” the little man’s voice had become hysteric.

“That’s not a star” said Judas “that’s a roc. They use their body’s bio luminescence. From the ground they look like stars. Perfect camouflage. Don’t you think?”

“And what is a roc?”

“Wait a minute,Flint.” Judas said, a hint of suspicion entering his voice “You are a native of this place and you don’t know what a roc is?”

“Nobody tells me anything.”Flint complained “They say I am not old enough and if I hadn’t run away today I would…”

“…not have been attacked by the Kraith. eh!” Judas interrupted “You are not as old as you would like to believe,hmm.”

Something whistled out of the dark and missed Judas by an inch, Splattering the rock nearby with some green oozy fluid that started to dissolve the rock immediately.

“That must be Jonathon. And the hunt has begun.Normally HUNTS start only when hunger demands. But, this time it’s early.” Flint’s eyes got wider, “And he never misses..you must be lucky”

“Guess he didn’t want to hit me.”

“You don’t understand. Jonathon shoots to kill”

“For a kid who had been lost, you know a lot about them,eh”

“Naturally” Flint said with a hint of sarcasm,”They are my tribe and Jonathan is my father, Chieftain  of the l’hoh tribe.”

Two more arrows followed and both missed Judas, albeit closely and Flint’s eye grew wider.

“That isn’t possible” Flint muttered darkly “Jonathan must have become mad by now”

Three more arrows flew and they all missed. A sudden silence gathered around them.

“Who are you?” bellowed a man”What are you doing with my daughter.?”

More men emerged from behind innocent looking rocks and boulders.

“Father” Flint screamed, “This man saved my life, killed two kraiths with his bare hands. Show him some respect”

The silence deepened as all eyes turned towards Judas.

“You are a girl.?” Judas spluttered.

“A fanciful story,kid” Jonathan said,moving towards them “But, no man ain’t killed two kraiths, ever. Got that, kid..?”

“And as for you, sir” Jonathan continued, stopping mere two feet away, “the hunt doesn’t show any mercy.”

Jonathan lifted his heavy bow and pointed it directly towards Judas.

The silence became palpable, all eyes were fixed on Jonathan and the smiling Judas.

No one ever saw the stars in the sky move.

Flint was the first one to notice. She pointed and screamed, just as the first roc snatched a man and flew directly towards Judas, the man struggling in it’s talons.

Men burst into action as they aimed their chloro-pistols at the creature and Jonathan’s arrow made  a shattering sound as it flew through the air and struck the roc’s harder than diamond outer shell. The creature was fast, but Judas was faster and nearer. He jumped into the air as the roc flew directly overhead and threw something at it.

There was a huge burst of light as the roc disintegrated into glowing ash and the man fell to the ground, bruised but alive. All this took only seconds.

Stunned silence followed Judas as he landed gracefully in the midst of glowing ash falling from the sky and gave them a lopsided grin.

Jonathan’s face bore a look of incredulity and Flint’s, fierce pride.

“H..how did you do it. What was thing that you threw?” Jonathan whispered into the silence.

“Salt” Judas said, “It was just salt. Roc’s bodies are composed of 90% water, almost like a jelly fish. But, with a shell protecting it and the two pores at the end of the body.”

“From which they emit steam to fly.” Flint said, nodding.

“Which is a biological impossibility” Judas continued, “I mean, no living creatures should possibly be able to emulate a two way steam engine to fly. And look at them, with their size, how could they get the lift to fly so high. This doesn’t make sense…”

“..Many things don’t make sense since the Ska invasion, boy” Jonathan rumbled, “but, you were saying something about salt. Pray, continue”

“Right,” Judas conceded, ” What I did was that I threw the salt into one of the holes as it flew overhead and as the salt entered it’s system each crystal absorbed the water around it causing microscopic ruptures in the structure of the skin  when the water particles left their usual place to gather around the salt particles..”

“..eventually causing the skin to completely disintegrate.” Flint interrupted, nodding.

“Time for talk is over, boy” Jonathan bellowed, pointing up. “Prepare to fight”

Every eye moved upward and widened in shock. Hundreds of rocs were descending in a play of light and colors that dwarfed the majesty of aurora borealis themselves. Streamers of light, of unimaginable colors,unimaginably beautiful, were bellowing towards the awestruck humans.

Judas looked around him and found every one looking at the certain death above them, except Jonathan, who was staring at him, bow and arrow ready. Judas slightly shook his head. The old man looked at him steadily for a moment before nodding.

“Men, retreat” Jonathan barked, “We are too few to fight them. And Judas, you can come with us”

The cavern was huge. Bright sodium lamps hung from the ceilings. Smell of earth mixed with that of cooking and thousand other scents. A reassuring hum of human voices filed the cavern.

A shrill cry broke Judas’ reverie. It came from a old woman who was rushing towards them.

“O the lucky one is come. Man from the past. You are our last hope”

Judas stopped in his tracks.

“Don’t worry.” Flint said, “she is just a PEV”

“What is a PEV” Judas asked.

“They are all psychos. They claim that they are connected to their own versions in parallel worlds. That way they can view each timeline from any viewpoint possible. Or so they say. Whoever heard of parallel worlds. Eh” Flint laughed.

Presently they found themselves inside a big cave. Sans Jonathan’s men.

“These are our lab and our living quarters” Flint explained, “you can have the room at the back. But first I must analyze this piece of roc I found.”

“They are sentient and psychic, you know.” Jonathan muttered under his breath.

” Sentient may be,  but psychic, again  that’s biologically impossible their brains are not of right size” Judas said, his face twisted in thought, ” Someone’s messing with them.”

“Oh Gods in heavens. How is this possible. The atoms are alive, and they.. they are singing .”

Judas turned to see Flint standing slack-jawed in mid stride wearing her micro visor as she faltered.

Jonathan was there in a heart beat. Reaching out and steadying her.

Flint only said “See this for yourselves.” A smug expression on her face.

Judas took the visor from her face and switched on it’s projector. A magnified vision revealed itself on the opposite wall.

Thousands and millions of spherical things. Changing colors at random. Moving around, clashing with each other, swapping colors. Fusing, combining, breaking. Growing absorbing, dying. It was a whole world there.

“What are those?” Jonathan asked, awestruck.

“They are atoms”Judas whispered, “And they are alive”

“They are not from earth, or from that matter, the universe.” Flint said, “I have checked”.

Very very tiny voices  seemed to sing in Judas’ ear. He looked around and saw his expression mirrored on other’s faces.

They all could hear it. The changing colors on the wall have become less random now. Judas was still holding the visor. On a whim he directed a thought ‘STOP’ towards it. And the movement on the wall stopped.

For the blink of an eye,  the colors on the wall shimmered and froze. The singing reached a crescendo and fell silent. For that endless second, time slowed. A breeze came out of nowhere and ruffled Judas’ hair.

Blue, black,green, violet, a thousand colors passed his thoughts and the  atoms responded to them all. Sorrow, happiness, anger, pride, a thousand emotions crossed his thoughts and the atoms responded to them all. Judas’ vision blurred and he felt himself stagger. Then blackness took him.

“What did he say? Flint, what did Judas say, right at the end?”

Flint looked up from the unconscious form of Judas and into the eyes of every single person present in the med-camp.

He said…”The answer is in the atoms.”

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A Cube of Sugar

There was a huge block of sugar on the table, before it was a deep pool of water and before it a patch covered with nails. To get to the sugar, I must overcome all this obstacles.
I broke into a run.
Jumping over the nails was not possible so I walked over them, I did not feel any pain.
I reached the pool of water and the shimmering reflection of the sugar was, well, yum.
The pool was very deep, I looked into it, and a face with two antennas looked back. It was red. Yep, that’s me. I wriggled my antennas.
The pool was too deep to cross and I couldn’t swim.
Presently another one of my fellow cadet came along; he decided that the sugar was worth the risk. He jumped and tried to swim, failed, drowned and floated up to the surface exactly 30seconds later.
I was contemplating this colossal act of stupidity when another fellow cadet came along. He took in the dead bloated body and raised an antenna towards me. I told him everything. With a wriggling of antennae that symbolised humour in our language, he proceeded to do the same thing and jumped. Not until he reached the body of the dead soldier and climbed upon it that I realised that he intended to use the body as some sort of boat. I had just started to admire his intelligence when his makeshift boat shook, unable to support his weight and another 30sec later a second bloated body had joined the first.
I was thoroughly nauseated by now. Two dead bodies, both staring up into the sky, and the still, drooping antennas was more than I could take. I was thinking of turning back when yet another cadet came along.
With some difficulty I made him aware of the situation. For quite some time, he stared at astonishment at, perhaps the colossal stupidity of the other two, and then he laughed, which to you is just twitching of antennae. With the same gesture he told me of his plan. He proposed to tie the body of the other two together and fashion a sort of boat. Since there was no rope and our body not being suitable for such dexterous works like tying, he asked me to hold together the dead bodies while he stood on my back and in this manner, me holding the bodies together and he standing on my back we crossed the pool.
Just as we left, I saw my friend becoming agitated and when we reached the other side, he won’t meet my antennas.
I thought nothing of that further and turned towards the block of sugar. I intended to divide the sugar block into two equal parts. However my friend didn’t think so. I turned just in time to see a flurry of movement and block the attack.
This had been a particularly hungry year. We had no food collection and cannibalism had become more common. So apparently, blinded by hunger and overcome by greed, my friend wanted the whole block. I tried to reason it out with him; I even agreed to give three-fourth of the block. He did not listen. I too was hungry and if my friend won’t listen to logic then fine. The fighting started in earnest.

…………………………………….

Kamal was only five years old. As all boys of his age, his foremost thought was cricket. He was just getting ready when it began to rain. Thunderclap shook the house, wind rattled the panes of his window and he understood that today he wasn’t going to take any wicket.
He became grumpy and went to sit near the window, so that in case the clouds came near he could scold them or better still, write their parents a letter for making so much noise. Sitting there and seeing no cloud come near his window, he began to wail loudly “Rain, Rain Go to Spain”.
He was thus engaged when his gaze fell upon a sugar cube that was lying on the floor near a puddle of rainwater. He saw some ants scurrying nearby, trying to get near the sugar cube. With his fingers he drew a circle of water around the sugar to protect it.
To him now this was a fort and the ants his enemy. The sugar likewise, was no ordinary cube of sugar; it was an enchanted food that grants, to those who eat it, the power to control rain.
Only the most worthy ant will get it. So to make the task hard he bought his pencil shavings and strewed them around the sugar cube.
Then he sat back to watch and judge.
Ants came and went, neither could cross the puddle.
Then an ant came, wriggled it’s antennae at the water and went away. However it did not go far, it remained there as if keeping watch. Two other ants came and promptly jumped to their deaths. The first ant remained still. Then another ant came.
Kamal was fascinated as both of them touched antennas. He wanted to see what happened. But, just then his mother came home and called out to him. She had brought some candy for him. After promptly gulping down the candy he ran back to his window seat. By now the ants had crossed the puddle. He mulled over it for quite some time but couldn’t think of anything, nonetheless he was duly impressed and decided to save some candy for these two. Since he was not paying attention to the scene unfolding before him, he was startled when one of the ants attacked another. The battle waged on, viciously and questions raged on in Kamal’s mind, “were these two not friends?”,”surely, they crossed the puddle together, the sugar belonged to both”. Then as suddenly as it had started, the fighting ended. The victorious ant stood still as the defeated one struggled in its death throes.
Kamal seethed with anger, his young mind recoiled at the injustice of it. One of the ant had just killed it’s what-?? brother\sister\mother\father\neighbour\friend…???
His young mind could visualise the concept of killing for greed. He never was this greedy. His teachers taught him to share. Did not the ants have teachers? His mother said killing is very bad. One should never harm others. Though his friends killed frogs, birds, ants he never did so. He didn’t like it nor could understand the sadistic pleasure his friends got out of doing these stupid acts. Moreover, they will go to “narak”, his mother said so. God will punish them. He waited.
…………………………………….

I won the fight. The traitor is dead now. I couldn’t help it. It was kill or die. I am exhausted and hungry. I started to move towards the sugar,
…………………………………….

Kamal saw the ant reach the sugar block. No one punished it. It began to feed. His mother had lied; no one punishes those who kill. Look at this ant, it killed its friend and is now eating the sugar. This ant deserved punishment. He lifted his finger.
…………………………………….

I tasted the sugar. It was nice, fulfilling. Hunger took over me. I started to eat in frenzy. A shadow fell across me and everything became dark…
…………………………………….
Kamal lifted his finger and brought it down, effectively crushing away the ant. When Kamal took his hand away, the ant was still. Everything was still.
The rain had stopped, the cloud cover had broken, and sunlight flooded the room. He realised that his friends were calling him.
He went out to play.