Another Crisis in mathematics

What does mathematics mean to me? There were a lot of ideas that were revealed to me. I think that there is a clue that I was going to be more of a philosopher than a mathematician. Mathematical ideas didn’t excite me so much as the philosophical ideas which were inspired by mathematics. 

1. I was trying to study physics for the first time. I don’t know how long it was before we studied static / dynamics / mechanics. But one day something struck me: we use mathematics a lot in physics because there is a similarity in structure between mathematics and the physical laws that govern our world today. In many ways, they were coherent / non-contradictory, consistent over time and space. The world is a predictable one because we can use mathematics to analyse things. People would say that this is obvious. But it’s not a trivial statement. What is the alternative, were this not to be true? Everything would be a mess. 

2. The idea that things resembled orthogonal dimensions: that we could treat different aspects of our wealth like they were on different spatial dimensions. Intelligence / wealth / other numbers that you could see in a dungeons and dragons profile. 

3. The idea that you could analyse and break down intuitive concepts into a series of mathematical tests. The delta and epsilon definitions of a continuous function. How do you relate a continuous curve to something else. 

4. The idea of a proof showing that a principle is scale free: the notion of continuity applies when you’re looking at a function at a bird’s eye view, and also at a worm’s eye view. 

5. The idea that knowledge is something that doesn’t really open up possibilities, but rather forecloses possibilities. Knowledge tells you that this and that possibility cannot be true, and in doing so, narrows the scope of what is worth taking into consideration. It clarifies by removing the clutter in your mind. A knowledgeable person actually has to think less than a novice because his head is not full of crap. A vector field dynamic system either has fixed points, or it tends to infinity, or it has loops or it has strange attractors. 

6. The idea of using mappings to reason: an algebra equation can map to curves of different shapes, which may cross this other line or axis, or it may not. 

And that’s the part of learning mathematics which is the most rewarding, that some of the lessons that you learn in mathematics will translate into how it teaches you to reason and argue in real life, even in domains that don’t obviously have to do with mathematics. 

The AI way of mathematics doesn’t really teach you that. 

One of my favourite classes in mathematics is nonlinear dynamics and chaos. 

I see it slightly differently. This is not a crisis for applied maths. It is a crisis for pure math.

Pure math does not seem to have real world applications for me. With only a few exceptions. Somebody solves an elliptical curves problem and a voice in my head says “who gives a fuck”. AI being able to prove theorems will make this voice louder.

I think there is a crisis in pure maths. There is no raison d'etre for pure maths, and that's why it's pure maths.

For applied maths, there will always be OR or machine learning or AI, so applied maths is in good health. In pure maths, because of the lack of applications, it's more like athletics. Pure maths is more like athletics than labour that produces economic value, and I feel that the AI developments have made this more apparent.

This is on top of the crisis in mathematics of the 20th century that I was taught in Snowy Hill. 

World War 3?

 First, I'd like to comment on the terms “World War 1” and “World War 2”. WW1 was not known as WW1 until after WW2. At the outbreak of WW2, it was known as the Great War. It was unprecedented in the scale of its destruction. But it was not unprecedented because when you study the history of Europe, it is a very war-like place. I went to the UK once on a trip and I recall there were castles everywhere. 

Castles are not dream houses, even though we like to think of them as being splendid. Castles are a monument to war. In a historical sense, we are reminded that some fucked up shit took place a long time ago. Typically, people living in temperate latitudes like beating the shit out of each other. Hence you have castles in Japan, China and Europe. 

WW1 and WW2 are unprecedented in some way, but they are an echo of the past in many other ways. There were times when Europe was constantly at war with itself. Europe from the Renaissance onwards has frequently resembled today's Middle East, with the vast wealth inequality and little kingdoms constantly at each other's throats. There were Reformation wars, 30 year wars, 100 year wars. That's why Gandhi made this snide remark that “western civilisation would probably be a good idea”. So that's the problem with calling those European wars WW1 and WW2: they were just 2 more European wars in a long history that had a lot of European wars. 

This is what made them different: they were “total wars”, in which case technology reached a certain level where it was possible to destroy everything within sight, and the entire citizenry were mobilised to fight. Either people were fighting on the front, or the people behind the frontline were running the factories that enabled the people on the front to fight. 

What followed WW2 was the Cold War, where the “Free World” and the “Soviet Bloc” had passive aggressive funky attitudes to each other, seldom truly fighting head on, and engaging in proxy wars and tit for tat in other parts of the world. But it was a surprisingly peaceful world order, with mainly Vietnam and Korea exploding into an orgy of violence. 

Then what followed the Cold War was the “unipolar moment”, where the USA for a relatively brief few decades was by far the most powerful country in the world. They were so assured of their military dominance that they felt they could squander it in foolish wars in Afghanistan and Iraq. 

I still remember an ominous line when reading about international relations in college: the Cold War was not a perfect internation order, but when it's gone, we'll miss it. We call it WW1 and WW2 for narcissistic reasons: because we only mainly know about the 20th century, we think that this is the only time that Europe has kicked the shit out of each other. We forget that colonialisation and slavery means that a lot of people around the world have been at the receiving end of angmoh violence. 

When I think about the future, I think that it will not resemble the worst or the best of the 20th century. The Ukraine War has been going on for years, but it's not as bloody and terrible as the Nazi-Soviet theatre of WW2. To the extent that WW3 is actually going on right now, it's not as warlike as WW1/WW2 total war. But it won't be as peaceful as the Cold War or the Unipolar Moment. 

Einstein said something like: “I don't know what WW3 will be like, but WW4 will be fought with sticks and stones”. His answer sounded quite profound but he's wrong. WW3 is not going to destroy civilisation. He only thinks that way because of what WW2 was like. Even with WW3 going on, we're still going to have the bare neccesities, because supply chains are robust. 

I think about Singapore being founded as a result of the Anglo Dutch treaty. Raffles was the colonial overlord of Java at that time. This was because the Netherlands had their asses kicked by Napoleon. Eventually, the Dutch and the British settled up. The Dutch took what is today Indonesia, and the British took what is today Malaysia and Singapore. 

We are maybe not talking about WW3 per se. We won’t be talking about total war, or anything as barbaric and savage as WW1 or WW2. If you see the movie poster of “North by Northwest”, there’s Cary Grant running away from an airplane who’s controlled by a shadowy force. This sense of terror anticipates what the frontline in the Ukrainian war is like: to be a Russian soldier hunted down by a Ukrainian drone. First, there were the incredibly violent children’s cartoons of the 1980s, that I grew up watching, MASK and Transformer cartoons. Full of gleeful and wanton violence, that would resemble video games. Then there was the 1990 Gulf war, where CNN brought live footage of the war to cable TV for the first time: people would experience the war the same way they experience a Nintendo game. That’s why that war was known as the video game war. The future of the war is video game wars. The war being fought by autonomous or remote drones further strengthens the resemblance to video games. 

We are in a period which is not unusually war-like like the total wars of WW1 and WW2. It won’t be as peaceful as the period between 1945 and 2025, when Europe was stupefied and lulled into this great sense of complacency and slumber. It is amazing that a continent that had been incredibly war-like since the Renaissance was on a holiday from either beating the shit out of each other or beating the shit out of their colonial subjects. This holiday was over when Russia invaded Ukraine but when the alarm clock was ringing, they had been hitting the snooze button quite a few times. 

It will be like the Anglo Dutch rivalry during the time of Raffles. Sometimes passing each other like ships in the night, sometimes confronting each other head-on. Trying to “friendshore”: ie do business with only your allies and friendly states. 

We will have China spying on the rest of the Asia Pacific countries, getting their grubby paws on Taiwan. We'll have Russia conducting hybrid warfare on Europe. It resembles the constant bickering between the imperial powers of Europe and the jockeying for influence. Except this time, it's a lot more messy. 

Let's see how things have played out in the Middle East recently. Israel has egged on Donald Trump to start a war with Iran that it turns out he can't win. It's impacted many Middle Eastern countries who rely on the Persian Gulf having access to the Indian Ocean. The UAE trusts the USA and Israel for security matters, but that hasn't prevented Iran from being able to attack them. The Saudis have this alliance with Turkey and Pakistan, but they are a NATO style alliance, if NATO stands for “no action talk only”. The UAE and the Saudis are frenemies. The UAE and Iran are frenemies. The UAE and Israel are frenemies. The USA is no longer a reliable ally. The world has become more complex. You could no longer count on peaceful relations. The notion that every trading platform is neural is gone. You could build a supply chain today, and a few years later there would be some stupid thing and your infrastructure investment would be gone. You can't plan for the future because you can't tell who's going to be friends with you in the future. 

Yet, a world like this would still have some semblance of normalcy. Unless you are living in a disaster zone, things will still work somehow, maybe with higher prices and more disruptions. The standard of living won't drop precipitiously like it did during the Japanese Occupation.