AN INTRODUCTION TO

MATHEMATICAL PHILOSOPHY

October 2057

As Alexa climbed out of bed after a night of wrestling with a million permutations of numbers, she felt it was forgivable to feel daunted by the scale of the challenge before her. But was she overwhelmed by it? Not at all; she had seldom felt so invigorated. Oh yes, at first it had seemed daunting—particularly because one of the conditions laid down by the tribunal was that her solution must be inscrutable to all but the most brilliant of mathematicians (of whom none officially remained). But when she realized that the answer lay in the familiar territory of Hilbert’s polynomials, everything fell into place. Triumph and relief made her giddy.

There was only one possible outlet for her euphoria. She made a cup of rooibos tea sweetened with honey, then picked up her Konektor.

Every call made on a Konektor was monitored, of course, and calls made to non-approved people could be audited and interrupted instantly, resulting in a reduction in Society Points. Alexa almost laughed out loud. She had no fears about the call she was compelled to make now, because it was the chair of the Agenda Implementation Tribunal that had personally told her that her one-time math teacher, “the now disgraced ex-professor Jordan McPhee,” did not exist. More than that, she’d been told, “If you choose to consult him on any of the matters we are going to discuss this morning, it should be evident to you that you have not consulted him—because he does not exist.”

“Konektor,” Alexa instructed, “connect me to Jordan McPhee.”

The red light came on, hesitated while the system ran the algorithm, then turned green.

“Alexa,” Jordan answered cautiously. “Have you cracked it?”

Despite the hesitancy in his voice, it seemed to her that, at this moment, his was the warmest and most comforting voice in the world. Who else could understand the enormity of the challenge she faced?

She told him about the solution she had discovered based on Hilbert’s polynomials.

“Excellent, excellent!” he enthused quietly. “That could well be a very elegant solution.”

Despite his obvious desire to maintain his distance, she took comfort in this open praise.

“I’ve been thinking about your other problem,” he continued, “and I just want to remind you that whenever something feels overwhelmingly complicated, the solution is invariably very simple. Remember the earliest principles you were taught about numbers. There’s a passage from Bertrand Russell’s Introduction to Mathematical Philosophy that I want to read to you. I have a copy of it right here. I think it might help you address your second problem. Russell says, ‘It is simpler logically to find out whether two collections have the same number of terms than it is to define what that number is. An illustration will make this clear. If there were no polygamy or polyandry anywhere in the world, it is clear that the number of husbands living at any moment would be exactly the same as the number of wives…’ Remember, this was written a hundred and fifty years ago, when ‘husbands and wives’ were common pairings. ‘We do not need a census to assure us of this, nor do we need to know what is the actual number of husbands and wives. We know the number must be the same in both collections, because each husband has one wife, and each wife has one husband. The relation of husband and wife is what is called One-One.’”

“Of course,” Alexa interrupted, “and a relation is said to be One-One when, if x has the relation to y, no other term x¹ has the relation to y, and x does not have the same relation to any term y¹ other than y.”

 “You were always an excellent student, Alexa,” he complimented her. “Now, tell me again exactly how they explained the nature of their second problem.”

Alexa took a deep breath. “The tribunal is alarmed that the United Nations compliance team is arriving shortly to audit our record regarding support for minorities. A minority is defined as any group that, either by gender or race, makes up less than five percent of the total population in any jurisdiction. With so many minorities choosing to self-identify because of the heavy incentives they receive through the Social Points system, what was once the majority, from which society needed to be protected, has suddenly become a minority, with no support systems in place for it.”

“You mean…?”

“Yes: white males now represent only 4.1 percent of the population, now that so many people choose to self-identify as minorities in order to gain Social Points. When the UN inspectors find out we don’t have a policy of positive discrimination for them, we will be fined billions of international credits. But you’ve just given me an idea. If a person has a portion of male gender X, and a portion of white ancestry Y, then regardless of their self-identification or the actual size of those portions, they can be classed in the category of ‘XY’—which is equivalent to Russell’s One-One.”

“Excellent, Alexa! And in this case, XY returns them to the majority. It solves the problem mathematically, but will they understand it?”

They agreed to meet at a later date when Alexa had decided how to deliver her solution to the tribunal, and he would peer-review her figures. (Of course, since he was deplatformed, his name would not be mentioned in her report.).