One

The mathematician sat at his desk – bearded, unkempt, exhausted and exhilarated. His eyes were focused on the proof he had just scribbled. They betrayed excitement. His fingers trembled as he went over each line of his proof again. They betrayed fear.  He put out his lamp in an uncharacteristic swift motion, drowning himself in absolute darkness.

“Do you see what you are about to do? Actually, the question is ‘Do you see what you are about to undo?’ ” He chuckled at his own joke. “And they thought I was wasting my time. This will change everything. It must. I am closer to the Truth now. We have suffered in the darkness long enough. We have been soiled by rote -”

His monologue was interrupted by a call for dinner.  It was time to interact with his family or as he called them, people who will love him, but not his thoughts. Oft times he had pondered on this question. How do you love someone without understanding his beliefs? When his body would be no more, will they be indifferent to him. If they did not understand his ideas while he was alive, they wouldn’t after his death. He had solved this dilemma by believing his family did not love him. They loved the image of him  they have in their heads. It didn’t matter to them if he wrote 2 + 2 = 5 and called himself a mathematician. They were still going to love him. That was the ultimate truth about love. It existed only inside the heads of people like characters from fairy tales or numbers. You wouldn’t have these god- forsaken numbers if you did not have a human mind to make them up.

But, what would he be if not for these imaginary devices? He wouldn’t question them if he did not know they existed and had not studied them for years together. And today, he was going to disprove the validity of those very numbers. Wouldn’t it have saved a lot of time if he had not been introduced to them years ago? After all, he was simply going to prove to the world that the foundation of mathematics was on very flimsy grounds. He did not have an alternative to give to the world. Merely, a proof of how everything was wrong if you cared to look very closely. May be the best thing he could do now was save someone else’s time. May be that someone else will provide the world with a solution. His peers would obviously be the first to gauge the repercussions of his work. But they were already biased. His work won’t be accepted without resistance. In fact, it would be offensive to him if it was. He needed an untainted mind, a tabula rasa. His grandson. He didn’t need to know that mathematics behind the truth of the shaky foundations of mathematics. All he needed to know was that the foundation was flimsy. Surely, as he grew up this inception would accelerate him closer to the Truth. He had to begin somewhere. He resolved to begin at the beginning. He decided to teach his grandson about one.

The two equations he needed to teach his grandson were:

0 = {}

1 = {0} = {{}}

He rose from his seat and dashed to his grandson, who was drawing in his notebook.

“What is one?” he demanded of the boy.

The almost three-year old lifted up his index finger and shouted out “one.”

“Why did normal people have to borrow one  from mathematicians? Or was it the other way round? They do have the word a.  That is one finger or a finger,” he kept blabbering as he lifted him up into his lap. “There is only one you and one me. But what is one? What does one mean?”

The boy simply stared blankly at him.

The mathematician showed him two fingers this time and asks him to describe what he saw again.

“Two,” said the boy.

“Great! You already know one plus one is equal to two like the rest of the world but you don’t know what one is? Rote learning will drive more people away from true mathematics than anything else. And they won’t even know what they are missing out on. Doesn’t it matter to you what one is? Listen carefully to what one is. What do you have in your right hand?”

“Nothing.”

“Make a fist of your right hand and put it in your left hand. Now make a fist of your left hand. What do you have in your left hand?”

“A hand with nothing”

“Wait! Did you just say ‘a’? You mean one. That was easier than I thought. It is strange how easily you interchange a and one. That is one right there. Beautif-”

“But a hand, that has a hand, that has nothing, has nothing,” blurted out the boy.

The mathematician was stunned. He placed his grandson at arm’s length. He looked at him with utmost suspicion.

“Damn it! You are going to be a realist! You will not care for what I am going to do. In fact, you are going to mock me. And I thought we could be co-conspirators. Not likely.”

He doodled a dragon eating its own tail in his grandson’s sketchbook before leaving.

Ouroboros

 

Irked by the lack of mathematics above? Read more:
Foundational Crisis of Mathematics
Set-theoretic_definition_of_natural_numbers
Russell’s_paradox
Hilbert’s_problems
Godel’s_incompleteness_theorems

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