The main purpose of this procedure is to allow a mobile device to connect to the mobile network, receive an IP address, and access external networks such as the Internet.
During this process, different network elements communicate with each other using specific protocols and messages. Each element has a particular responsibility, such as user authentication, IP address allocation, and data transmission.
This topic is important for Computer Science and Computer Engineering students because it helps them understand how mobile networks work, how network elements communicate, and how protocols are used in real-world communication systems.
The following explanation focuses on the interactions between network elements rather than the detailed technical implementation.
Note: In this explanation, the terms UE and user are sometimes used interchangeably to make the text easier to read. However, they have different meanings in technical standards. Also, the word subscriber refers to the mobile network customer and their SIM card information.
First, the user’s device sends an RRC (Radio Resource Control) message to the base station, called eNodeB.
The purpose of this message is to establish an initial radio connection and request the radio resources needed for communication.
In the second step, the eNodeB sends an Initial UE Message to the MME through the S1 interface, using the S1-AP protocol.
This message contains the initial request received from the user’s device in the previous step. It also carries a NAS request message.
The MME receives this message and starts the process of connecting the user to the network.
Now, the MME needs to communicate with the HSS (Home Subscriber Server) to authenticate the user.
The HSS may be located in a different city or geographical area.
The MME sends an AIR (Authentication-Information-Request) message to the HSS using the Diameter protocol.
The HSS checks the subscriber’s identity and sends an AIA (Authentication-Information-Answer) message back to the MME.
This response contains authentication information called an Authentication Vector (Auth Vector). It includes the security parameters and information needed to authenticate the user and establish encryption.
In this step, the MME sends the required authentication information to the eNodeB.
The eNodeB then forwards this information to the user’s device through an RRC message.
The device receives the authentication challenge and uses the information provided to prove its identity to the network.
In simple terms, the network is checking whether the user is allowed to access the mobile network.
After the authentication process, the MME sends a ULR (Update-Location-Request) message to the HSS using the Diameter protocol.
This message informs the HSS that the subscriber has been authenticated and is now being served by this MME.
The HSS updates its database with the current MME information. This allows the network to find the subscriber when future services, such as calls or data connections, are needed.
After updating the information, the HSS sends a ULA (Update-Location-Answer) message back to the MME.
This response may contain subscriber-related information and network service parameters, such as Quality of Service (QoS) settings and bearer configuration information.
At this stage, the user’s device needs an IP address to communicate with external networks, such as the Internet.
Therefore, the MME starts the session creation process by communicating with the S-GW (Serving Gateway) and the P-GW (PDN Gateway).
This communication uses the GTPv2-C protocol.
The MME selects an appropriate P-GW and requests the creation of a data session.
The P-GW is responsible for assigning an IP address to the user, creating the required bearer, and applying the necessary charging and network policies.
After the session is created, the response is sent back through the gateways.
In this step, the P-GW sends a response containing the user’s IP address and the related bearer information to the S-GW.
This information is necessary to continue setting up the user’s data connection.
Now, the S-GW forwards the received information to the MME using the GTPv2-C protocol.
The information includes the user’s IP address and the bearer identification information.
The MME uses these details to continue the connection setup process.
In this step, the MME sends the required connection information to the eNodeB through the S1-AP protocol.
This information includes the user’s IP address, QoS parameters, and bearer identification.
The eNodeB uses these parameters to prepare the radio bearer and allocate the necessary radio resources for communication with the user’s device.
The eNodeB now sends an RRC Connection Reconfiguration message to the user’s device.
This message contains the configuration information required to complete the radio connection.
The device receives the necessary parameters and prepares itself for data communication with the mobile network.
After receiving the configuration information, the user’s device applies the required settings, including the network configuration.
Then, it sends an RRC response message to the eNodeB to confirm that the configuration has been completed.
The eNodeB forwards the related confirmation to the MME through the S1-AP protocol.
This step informs the network that the radio connection setup has been successfully completed.
Now that the radio connection is ready, the MME sends a message to the S-GW.
The S-GW then communicates with the P-GW using the GTPv2-C protocol.
The purpose of this step is to update and activate the bearer so that the user’s device can exchange data with external networks.
In other words, the network completes the remaining configuration needed for data transmission.
Finally, the S-GW sends a Modified Bearer Response message to the MME using the GTPv2-C protocol.
This message confirms that the bearer modification process has been completed successfully.
At this point, the LTE connection setup is complete, and the user’s device can communicate with external networks such as the Internet.
The entire process can be divided into five main stages:
| Stage | Steps | Main purpose |
|---|---|---|
| Radio connection | 1–2 | Establish initial communication with the base station |
| Authentication | 3–4 | Verify the user’s identity |
| Subscriber registration | 5 | Update the subscriber’s location information |
| IP and session creation | 6–8 | Create a data session and assign an IP address |
| Connection completion | 9–13 | Configure radio resources and activate the data bearer |
Understanding the LTE Attach Procedure is useful for Computer Science and Computer Engineering students for several reasons:
The most important idea is that connecting a mobile phone to a 4G network is not a single action. It is a sequence of communication steps between different network elements, each responsible for a specific part of the process.
The original explanation is useful as a simplified overview. However, the following points should be considered when using it in an academic report or presentation:
Is X right or is Y right? Should I reply to this person or not? Should I study medicine or not? Someone did something wrong. Should I stay in this relationship or leave?
These questions remind me of a time when my own mind had the same simple challenges. But that time is long gone.
That was version one of my mind. I have already moved beyond versions two and three.
The difficult part of moving forward is that everything becomes too clear.
When the logical answer to every question is obvious, you can no longer hide behind anything. You know when you are doing something wrong. And you know it at the exact moment you are doing it.
Excuses no longer work. You cannot explain everything away.
It feels as if your whole self is inside a glass room. Everything about the way you think and act is now visible.
The same mind that once struggled to make decisions now seems to have only one job: to judge and blame you.
So, appreciate version one of your mind.
One day, you may even miss the days when you were unsure.
Imagine you are in the middle of a desert, looking out of a car window. The world outside is moving fast, and everything looks beautiful, like a picture on Instagram.
But what if the car suddenly breaks down? What if there is nobody around to help you? Now you have to spend the cold night in the darkness, surrounded by an endless desert.
Suddenly, the same place that looked beautiful becomes terrifying.
When you feel good, it means you are seeing the beauty of the road because your car has not broken down yet.
But a better state of mind is one that can see both the beauty and the fear.
If you want to feel better, you have to be willing to face problems. But you don’t want to. Because you are afraid of being afraid.
Having a breakdown means losing the things your mind was depending on. Things you thought you knew. Things you thought you understood.
Sometimes, the only way to see the road clearly is to let your car break down.
]]>This is not a complete roadmap, and I am not saying that everyone should follow the same order. It is simply a look at the path I have taken so far.
I think the Bitcoin Backbone paper is a good place to start if you want to understand how blockchain protocols can be studied and how their security can be proved.
The Bitcoin Backbone Protocol: Analysis and Applications (EUROCRYPT 2015)
This paper studies the security of Bitcoin-like systems. It introduces some important ideas that are useful for understanding how blockchains work and what makes them secure.
When reading it, try to understand the main security goals and the assumptions behind the protocol. You do not need to understand every proof on your first try.
The Bitcoin Backbone Protocol with Chains of Variable Difficulty (CRYPTO 2017)
This paper builds on the Bitcoin Backbone model and studies what happens when the difficulty of the chain can change.
Reading it after the original paper can help you understand how researchers change an existing model and study its security under new conditions.
Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol (CRYPTO 2017)
Ouroboros is about building a secure blockchain using Proof of Stake instead of Proof of Work.
While reading it, try to compare its main ideas with the Bitcoin Backbone paper. What changes when the system uses stake instead of computational work? What assumptions does the protocol need?
Proof-of-Stake Protocols for Privacy-Aware Blockchains (EUROCRYPT 2019)
This paper looks at privacy in Proof-of-Stake blockchains. It is a useful direction if you want to learn more about the connection between blockchain protocols and privacy.
Can a Public Blockchain Keep a Secret? (TCC 2020)
The title asks an interesting question: can a public blockchain keep information secret? While reading this paper, focus on the exact problem it tries to solve and the conditions under which its solution works.
Privacy-preserving auditable token payments in a permissioned blockchain system
This paper studies how a blockchain payment system can protect privacy while still allowing payments to be checked when needed.
It is a useful example of how researchers try to balance different goals when designing a system.
Reading research papers takes time. Sometimes you understand the general idea but cannot follow the proofs. Sometimes a single definition can take hours to understand.
I think this is a normal part of the process. You do not have to understand everything on your first try.
It also helps to keep notes. I write down useful definitions, questions, and papers that I may need to read later. These notes make it easier to return to a topic after some time.
Another useful thing is to compare papers. When two papers study similar problems, try to understand what is different between them and why the newer paper was needed.
Most importantly, do not treat reading papers as a race. Reading ten papers without understanding them is not necessarily better than understanding one paper well.
This is the path I have taken so far, and I still have a lot to learn. I will update this list as I read more papers and explore new topics.
I hope it helps someone who is following a similar path.
]]>“Everyone is the other, and no one is himself.”
— Heidegger in Being and Time
There is a kind of courage that has nothing to do with hormones.
The usual kind of courage is doing something scary, like jumping from a high place, fighting someone who might beat you, or standing in front of a crowd and saying what you think. This kind of courage is partly connected to our biology. Some people are naturally more willing to take risks than others.
But there is another kind of courage. It is not about facing danger. It is about the way we see life.
I would call it the courage to exist.
Once, a meditation teacher was trying to teach me how to meditate, but he wasn’t getting very far. He told me that he often said this to his students:
“The highest level of control is being able to stay calm even if you are buried alive in a coffin. You should be able to face death peacefully, not like someone who has lost all hope.”
I told him I thought he was looking at it the wrong way.
I said, “You should tell them this instead: You are not really in control of yourself. Your body still reacts in ways you have learned over time. The goal is not to learn how to stay calm when you are buried alive. The goal is to become the owner of yourself. And if you really are in control of yourself, one sign might be that you can even stay calm in a situation like that.”
He thanked me and said he would use my explanation from then on.
But I didn’t tell him the rest of my thoughts.
I knew his students might turn this idea into another exercise. They would treat self-control like going to the gym. They would see it as another skill to practice to improve their lives.
But the truth is, you cannot really understand yourself if you don’t change the way you see life.
We are taught to see ourselves like machines made for special purposes.
Imagine that you see yourself as an off-road vehicle. You believe you are good at driving over rocks, mud, and rough roads. You accept that you may not be the fastest car on a racing track.
Now imagine that you see yourself as a racing car. You believe you are made to go fast and win races. You accept that even a small hole in the road might stop you.
We do the same thing with our personalities.
Someone might say, “I’m just not the kind of person who can be alone.”
Another person might say, “I’m not good at dealing with emotions,” or “I need to be around people all the time.”
These statements may sound like self-knowledge, but they can also become limits.
We create an image of who we are, and then we try to live inside that image. We begin to believe that some experiences are right for us, while others are not.
We start to see life as a huge place, but we believe that only a small part of it belongs to us.
The courage to exist means seeing things differently. It means understanding that life is much bigger than the small picture we have created of ourselves.
It means being open to different experiences, even when they are difficult or unfamiliar.
Heidegger’s ideas also invite us to think about time and the future.
We often spend our days worrying about what might happen.
What if we fail? What if someone leaves us? What if we lose everything we have worked for?
We want to know that we will be okay before we take the next step.
But life never gives us complete certainty.
There will always be things we cannot control, people we cannot keep forever, and experiences we cannot fully prepare for.
The courage to exist does not mean believing that nothing can hurt us.
It means understanding that we do not have to know everything about tomorrow before we allow ourselves to live today.
We can love without knowing how long the relationship will last. We can try without knowing whether we will succeed. We can begin again without knowing exactly where the road will take us.
We do not need to become perfect before we deserve to live.
And we do not need to remove every fear before we can move forward.
Perhaps becoming the owner of ourselves means learning to live without demanding that everything happen according to our plans.
It means accepting that life is uncertain, that we are changing, and that we will never have complete control over everything that happens to us.
The courage to exist is the courage to live without needing life to be perfect first.
And perhaps, in the end, that is what it means to become more fully ourselves: not to control every feeling, not to escape every difficulty, and not to become someone who can never be hurt, but to remain open to life even when it surprises us.
We are here for a limited time.
We may never understand everything. We may never become exactly who we imagined we would be.
But we can still choose how we meet the life we have been given.
And that choice begins now.
Dedicated with respect and appreciation to Ali Barfar and Dr. Shiri, whose names I wish to place beside this reflection on being, self-understanding, and the courage to live.
]]>Differences in opinions and tastes, everyday friction, bad moods, and stubbornness keep you focused on learning about your father. You build a collection of things you know about him, then grow to hate that collection, and then use that hatred as proof that you’re different from him.
As Philip Larkin puts it in This Be The Verse:
They fuck you up, your mum and dad.
They may not mean to, but they do.
They fill you with the faults they had
And add some extra, just for you.But they were fucked up in their turn
By fools in old-style hats and coats,
Who half the time were soppy-stern
And half at one another’s throats.Man hands on misery to man.
It deepens like a coastal shelf.
Get out as early as you can,
And don’t have any kids yourself.
Because everyone’s default assumption is: I’m not the thing I hate.
But that doesn’t prove you’re different.
To learn more about yourself, you have to bump into things. When you cut your hand on something sharp, you learn how easily skin can be cut, how much pain a small cut can cause, and how quickly it can heal. You didn’t know any of that before you got cut.
You have to collide with other people to find out what kind of person you are.
You have to be provoked, humiliated, condemned, encouraged, angered, excited, hurt, disappointed, energized, numbed. You have to be envied. You have to have people resent what you have. Sometimes you have to go unnoticed, and other times you have to be noticed too much.
All of this happens when you come into contact with other people. Each of them has their own way of hurting you. One rubs you raw. Another leaves a bruise. Another gives you blisters. Another cuts you. Another burns you.
Only after you’ve been wounded by all kinds of people do the pieces of information you’ve collected about yourself begin to fit together, like a puzzle.
Only then do you start to see where people can fool you. What can make you cry. What can make you act against your own interests just because you want to react. What can turn you against the people you love. And what can make you abandon yourself in front of other people.
You learn where you shut down, and where you can’t keep anything to yourself. What turns you into a child, and what makes you unwilling to show even a child any mercy. What keeps you awake at night, and what makes you reach for a sleeping pill instead.
Once you’ve gathered all this information, you can finally start figuring out who you’re like, and how far you really are from the person you thought you were nothing like.
Most people who go through this process and realize they aren’t all that different from their fathers complete the puzzle at an age when it’s already a little too late to do much about it.
So whatever age you are, start gathering information about yourself. Don’t put it off until tomorrow.
]]>You’re going to spend several years locked in solitary confinement, in a cell with no lamps or artificial lighting. The cell is 150 square meters. That’s the size of an apartment that would rank among the most expensive in the world, anywhere you happened to buy it.
But there are two kinds of cells, and you have to choose one.
The first has a concrete ceiling and windows in its walls, looking out onto something like a small garden. The second has a completely glass ceiling. You can see the clouds, but there are no windows in the walls.
Most people choose the one with the windows.
Why? Because the garden changes more visibly than the sky. And the rate at which things change affects how we perceive the passage of time.
Is that true? Yes and no.
People calculate which view offers more visual variation, but their calculations are biased. They make those calculations based on their experience of living freely, outside prison, in apartments with concrete ceilings and windows in the walls.
Without that bias, they might reach a different conclusion. They might even correctly realize that the cell with the glass ceiling receives several times more natural light than the other one. And nothing in solitary confinement reduces the suffering of being imprisoned quite like an abundance of natural light.
This is a kind of paradox: a person trying to escape their old cell chooses their next cell to be made of the same things as the last one.
In the previous cell, their brain had learned to switch off certain alarms after ignoring them for long enough.
If something tells you a hundred times that you’re in the wrong place, and you keep ignoring it—or have no way out—the hundred-and-first time, it stops telling you. Once the alarm goes silent, the steering wheel turns in exactly the opposite direction. You may even start adding certain features to the list of reasons why your situation is good.
Like when someone shows you an apartment whose builder has already installed metal bars on the windows, and you think, Great. I won’t have to install them myself.
The alarm that used to tell you, Windows with bars mean you’re the prisoner, not the thief, has been silent for a long time.
It went silent in your previous cell.
One of the most important questions anyone can ask themselves is this: Why do I like the things I like?
And the answer belongs to you. No one else can give it to you.
But whatever the answer is, it leads back to the cells you’ve been imprisoned in before. The things you learned to tolerate. The things you stopped questioning. The alarms you trained yourself not to hear.
That’s why leaving a cell doesn’t necessarily mean you’ve escaped it. You can walk out of one prison and carry its architecture inside your head. You can even mistake that architecture for your own taste, your own judgment, your own idea of a good life.
There is a passage from T. S. Eliot’s The Hollow Men that captures something of this condition:
We are the hollow men
We are the stuffed men
Leaning together
Headpiece filled with straw. Alas!
Our dried voices, when
We whisper together
Are quiet and meaningless
As wind in dry grass
Or rats’ feet over broken glass
In our dry cellarShape without form, shade without colour,
Paralysed force, gesture without motion;Those who have crossed
With direct eyes, to death’s other Kingdom
Remember us—if at all—not as lost
Violent souls, but only
As the hollow men
The stuffed men.
True escape, then, cannot happen without a kind of death.
Not physical death. The death of the person who lived in that cell. The person whose desires were shaped by its walls, whose fears adapted to its limits, and whose idea of comfort was built around what they had learned to endure.
To leave the cell for real, that person has to die, and someone else has to be born in their place.
And most people would rather remain prisoners than face the death of who they used to be.
]]>A relationship ends, but your mind keeps working on it. You go through old conversations, think about things you could have said differently, and try to understand what went wrong. You imagine different versions of the past, as if finding the right one could change the present.
And sometimes, the more you think about it, the worse you feel.
I think there is something strange about the way we deal with problems when we are emotionally attached to them. We can spend hours looking for complicated solutions to something that might have a very simple answer. We try to fix things, explain things, and find another way. We keep looking for a door even when the room has no exit.
Maybe we do this because accepting the simple answer hurts too much.
If a relationship is over, one possible answer is that it is over. It does not mean that everything was a lie, that the good moments were meaningless, or that the other person was a bad person. It only means that something that once worked no longer works, or that two people can no longer build the same life together.
But this answer is often not enough for us. We want a better explanation. We want to know exactly why it happened. We want to find the one mistake that, if we could go back and change it, would make everything right again.
We treat the past like a problem that has not been solved yet.
And maybe that is where some of the pain comes from. We are not only sad about losing someone. We are also fighting the fact that we cannot change what happened.
There is another thing I find difficult to accept: sometimes, we are willing to put up with a lot just to avoid being alone.
We are afraid of losing someone, so we accept things we would never advise a friend to accept. We make excuses. We lower our expectations. We tell ourselves that things will get better, that everyone has problems, or that maybe we are asking for too much.
Of course, no relationship is perfect. People make mistakes, misunderstand each other, and hurt each other without always meaning to. Love requires patience, and it would be unreasonable to expect everything to be easy.
But there must be a difference between being patient with another person and slowly giving up on yourself to keep them around.
The fact that losing someone hurts does not mean that keeping them is the right choice.
I think we sometimes forget that a relationship is a choice between two people, not a sentence that we have to serve until things get better. We should be able to leave when staying becomes wrong for us. We do not need to prove that things were terrible enough, or that the other person was bad enough, before we are allowed to walk away.
And we do not have to hate someone to accept that we cannot be together anymore.
This is probably one of the hardest parts for me. It is easier to leave when you are angry. It is easier when you can point to something terrible and tell yourself that the decision is obvious. But what do you do when you still care about someone? What do you do when there are good memories, when you miss them, and when a part of you still wants things to work?
I don’t know if there is a simple answer to that.
Maybe you just have to accept that two things can be true at the same time: you can miss someone and still know that the relationship is over. You can love what you had and still believe that it should not continue. You can wish things had gone differently without spending the rest of your life trying to change them.
I am not saying that this makes moving on easy. Knowing something and accepting it are two different things. Sometimes, your mind understands a situation long before your feelings catch up.
And I think that is okay.
There is no need to turn every painful experience into a lesson immediately. There is no need to pretend that you are grateful for what happened, or that everything was supposed to happen this way. Sometimes something ends, and it hurts. You can be sad about it without needing to find a greater meaning behind it.
But I don’t want to make my own life harder by treating every ending as a problem that must somehow be reversed.
I don’t want to spend all my time searching for another explanation, another possibility, or another version of the past in which things worked out differently. I don’t want to turn a painful situation into an even more painful one just because I cannot accept the simplest answer.
Maybe the answer is not to stop caring. Maybe it is to stop asking the past to become something else.
I still have to learn how to do that.
There is a passage from Alfred, Lord Tennyson’s Ulysses that I keep coming back to:
I am a part of all that I have met; Yet all experience is an arch wherethro’ Gleams that untravell’d world whose margin fades For ever and forever when I move.
How dull it is to pause, to make an end, To rust unburnish’d, not to shine in use! As tho’ to breathe were life! Life piled on life Were all too little, and of one to me Little remains: but every hour is saved From that eternal silence, something more, A bringer of new things; and vile it were For some three suns to store and hoard myself, And this gray spirit yearning in desire To follow knowledge like a sinking star, Beyond the utmost bound of human thought.
Maybe moving on is not about leaving the past behind completely. Maybe it is about understanding that the past has become part of us, while there is still a world ahead that we have not seen.
For now, I am trying to understand that not everything can be fixed, not every question has an answer that will make me feel better, and not everyone who leaves my life has to become a villain for me to let them go.
I am trying to understand that not everything can be fixed, not every question has an answer that will make me feel better, and not everyone who leaves my life has to become a villain for me to let them go.
Sometimes, a relationship ends. Sometimes, you don’t get the explanation you wanted. And sometimes, the only thing left to do is to let something be over, even when a part of you is not ready.
I think that is what I am trying to learn: how to let something end without letting it destroy everything that comes after it.
]]>People say that writing somewhere that offers no feedback is like talking to a wall in solitary confinement. Maybe that’s true for some people—for those who aren’t allowed to leave comments, perhaps they really are no different from a wall! As if you have to be able to talk back to someone in order not to be a wall yourself.
Others say that writing in a space where dialogue is no longer possible reveals the writer’s selfishness. Maybe that’s true of some people, too. Apparently, even if people voluntarily choose to listen to someone speaking one way, it is still the speaker who’s a dictator!
But there’s no need for everyone to set up a miniature democracy in every corner they occupy. If they don’t, we’re not going back to the days of Mao. Nor does freedom of expression have to be secured through instant chat. Some of the boldest criticisms exchanged among twentieth-century intellectuals took the form of essays: days could pass between the publication of an original text and a response, sometimes printed in another city altogether. Yet people followed those exchanges, and the back-and-forth itself became thought. We don’t even have that now.
Nor should we see progress as dependent on online arguments, as though every time a discussion is shut down somewhere, a stone is thrown into the gears of progress. Let’s not kid ourselves. From Facebook’s early days, when serious dialogue between opposing viewpoints began to take root, to the present day, what truly significant contribution have we made to the kind of progress we so often talk about? Those who were angry back then are still angry, and those who argued for fun are still doing it, still having fun. We should stop assigning an illusory value to the time we’ve all wasted—and continue to waste—on these arguments.
Has online interaction had effects on many of us that we ourselves consider positive? Of course it has. But we shouldn’t exaggerate its scale. Besides, a person’s private journey can be almost entirely disconnected from the course of society. Since 2019, I’ve personally rolled over and changed direction seventy times. How many times has society?
So even if a hundred more people like me leave these spaces, retreat into solitude, and so on, two things will not happen at once: the millions who use social media for entertainment won’t even notice we’re gone, and the slow train of idea-making won’t slow down—because it never even left the station.
So please, Don’t mourn the death of something that was never truly alive. There’s no reason to be disheartened by the fading of ideological conversations that resemble a nightclub on social media. What should dishearten us is the absence of thought and ideas. If there’s a little less noise in the desert, it hardly matters. It’s still a desert, and there’s still no water.
We have active minds, and we express opinions, talk, write, and react to keep them active. We also follow what other people are thinking so that, even if we don’t get ahead, at least we don’t fall behind. All of this is natural, and it will continue to be. That is especially true in the one-voiced, centralized, totalitarian environment of our country, where an opposing opinion stops being merely an opinion and becomes a banner of identity. We need plenty of those banners.
But activity is not the same as progress. Take technical debt in software development. We have spent decades discussing bad architecture, fragile code, and the long-term cost of postponing fixes. The problem is well understood, the warnings have been repeated countless times, and the solutions are hardly a secret. Yet when it comes to actually changing the way we work, we remain remarkably incapable of acting on what we already know. We can diagnose the problem endlessly; what we struggle to do is fix it.
Our minds are active, and we try to keep them that way. We follow the activity of other minds, too, in case we can’t get ahead, at least so we don’t fall behind. We shouldn’t attribute anything more than that to all this content—including my own writing.
]]>AI is getting better at solving problems. It can write code, help prove theorems, find patterns, and do many things that used to require a lot of human effort. I think it is reasonable to expect these systems to become much better in the coming years.
But there is one thing I think we should talk about more.
Math is hard. And making AI smarter does not necessarily make math easy.
Of course, AI might solve thousands or even millions of mathematical problems that humans have not been able to solve. It might solve problems that people have spent their whole lives working on. That would be amazing.
But does solving more problems mean that we will eventually run out of hard problems?
I don’t think so.
One reason is that mathematics is not just a collection of questions waiting for answers. Solving one problem can lead to new questions. Sometimes a result gives us a new way to think about something, and that leads to problems we could not even ask before.
So even if we solve a lot of the problems we know today, there is no good reason to believe that we will be close to the end of mathematics.
But I think there is another, more interesting point.
Some problems are hard not simply because we are not smart enough to solve them. They can be hard because solving them requires a huge amount of computation.
Computer science has a whole field dedicated to this question: computational complexity. It studies how the resources needed to solve a problem change when the problem gets bigger.
For some problems, making the input twice as big might not be a big deal. For others, it can make the problem much harder. In some cases, the amount of work grows so quickly that even a very powerful computer cannot solve problems of a realistic size.
This is one reason I find the P versus NP problem so interesting. We still don’t know whether every problem whose answer can be checked efficiently can also be solved efficiently.
I don’t want to make a big claim about what the answer will be. But the question itself shows how much we still don’t understand about computation.
And even if AI becomes much better at mathematics, it does not automatically mean that it can solve every problem we give it. Being very good at solving problems and being able to solve all problems are two different things.
Maybe future AI systems will be able to do things that we cannot even imagine today. Maybe they will be better than humans at almost every part of mathematical research. I’m not ruling that out.
Actually, I think we should take this possibility seriously instead of assuming that humans will always be better at something.
But then what happens to us?
If AI can solve problems better than we can, what is the point of doing mathematics ourselves?
I think the answer partly depends on how we decide to do mathematics in the future.
If we want to discover new mathematics, we should probably learn how to use the best tools available to us. If AI is good at searching for patterns, we should use it for that. If computers can check proofs much faster than humans, we should let them do it.
There is no reason to make our work harder just to prove that we can do it without machines.
At the same time, we should not assume that the way we do mathematics today is the only way to do it. New tools might change the kinds of questions we ask and the way we work on them. Maybe the role of mathematicians will change a lot. Maybe some parts of mathematical research will become almost completely automated.
I don’t know.
But I think there is a difference between saying that AI might do mathematics better than humans and saying that AI will eventually finish mathematics.
The first seems possible to me. The second is a much bigger claim.
We don’t even know how to describe all the mathematical questions that might be interesting in the future. And we certainly don’t know whether the resources available to us will ever be enough to solve all of them.
This is what makes me less worried about the future of mathematics.
I’m not saying that humans will always be necessary. Maybe one day we will build systems that can do almost everything a mathematician does, and do it better. Maybe we will not even understand some of the mathematics they discover.
But why should that mean there is nothing left to do?
I think we sometimes look at progress as if the goal is to solve every problem and eventually have nothing left to work on. But I don’t see why mathematics has to work that way.
Every new tool gives us new possibilities. Some problems become easier, some become possible to solve for the first time, and others become interesting because of what we have just discovered.
Maybe AI will change mathematics more than anything before it. Maybe it will completely change our idea of what doing mathematics means.
Still, I have a pretty strong feeling that we are very far from a future where there is no interesting mathematics left.
And if AI really does become better than us at mathematics, I think we will have much more important questions to think about than whether we are still the best at it.
I want to end with a quote I came across in a Telegram channel:
]]>“If there is only one job left for humanity, it will be some form of doing mathematics.”
That is one advantage of slow poisoning: your body has time to get used to something it should never have had to tolerate.
The same thing can happen with reality. You do not have to wake up one morning and find that everything has been taken away from you. It is enough for a little more of what once seemed unacceptable to become normal every day. Today, you ignore a lie. Tomorrow, you look away from an injustice. A few days later, you start treating humiliation as part of life. Eventually, when someone complains about it, you might even wonder what their problem is. Isn’t this how everyone lives?
That is when the damage has already been done, even if you have not noticed it.
People do not only get used to good conditions. They get used to bad ones, too, even when those conditions are destroying them. And once they get used to something, they no longer need a reason to tolerate it. The habit itself is enough.
Let me give you an example.
When I was a kid, my father used to mix cement to repair things around the house. There was always a little cement left at the bottom of the bucket. When he wanted to wash it away, I would tell him it was a waste. Then I would take the leftover cement and smear it over the entrance to an anthill.
Back then, it was probably just a game to me. Ants were tiny creatures whose path I could block, whose home I could destroy, and whose suffering I could watch for fun. I did not have to ask myself why I was doing it. I did not have to think about what happened to them. They were just ants, and I was just playing.
But this is exactly what worries me: people can keep the same impulse into adulthood, the impulse to hurt something weaker than themselves simply because they can.
Only the targets are no longer ants. They are people.
Getting older does not automatically make anyone kinder. Growing up does not necessarily mean growing morally. Sometimes, we only learn to carry out the same old cruelties with more sophisticated tools. We learn how to humiliate, intimidate, and threaten others, then come up with reasons why they deserved it.
Perhaps the most disturbing part is not that people can be cruel. It is that they can become so used to cruelty that they no longer recognize it as cruelty.
Of course, not everyone has equal access to reality. One person knows nothing about the job market, another knows little about the state of the country’s industries, another has no idea what happens in the courts, and another has never experienced what it means to live under unchecked power. A person can be well informed about one part of life while living inside a bubble that has almost nothing to do with the world outside.
The problem begins when people mistake their own bubble for the whole world.
If you have never experienced something, it is easy to deny that it exists. If you have never been humiliated, you might think other people are too sensitive. If you have never seen someone’s life turned upside down by a government decision, you might assume things cannot be that bad. When you are protected from the consequences of a situation, it is easy to mistake its normality for its acceptability.
And if you stay in that environment long enough, you may eventually stop noticing what you cannot see.
In an authoritarian system, humiliation is not just a way to punish people. It can also be a way to train them to accept the lower position assigned to them.
Humiliate people until they learn not to complain. Treat them badly until they start ranking different forms of mistreatment by how tolerable they are. Eventually, they stop asking why they should have to accept it. They start asking which kind of humiliation is easier to live with.
One person accepts it because they do not want to lose their job. Another needs the income. Another is thinking about their family. Someone else has simply concluded that there is no alternative.
This is how people can reach a point where they defend the very thing that is crushing them. Not necessarily because they like it, but because they can no longer imagine their lives without it.
When humiliation becomes part of everyday life, self-respect starts to look like a luxury, something only people who can afford the consequences can have. You learn to give up a little of your dignity to keep your job, your position, or simply some peace of mind.
Then you start making excuses so that you do not have to face what you are doing. This is how the world works. Everyone does it. You have to be realistic. You cannot fight everything.
Maybe you really cannot fight everything. But that is not the same as treating everything as normal.
People do not always change overnight. Sometimes, someone who once felt guilty about owing even a small amount of money gradually comes to believe that being ethical only puts them at a disadvantage.
In the past, if someone paid their fare because they did not have enough change, they might come back the next day, even in the rain, to return the money. They were afraid of dying and leaving the world in someone’s debt.
Then one day, that same person might say, “Fuck it, man. That’s the law of the jungle. I’ll do whatever it takes for my own kid. Everyone else does the same for theirs.”
It is not just the behavior that has changed. The standard for right and wrong has changed, too. The person no longer asks, “Is this the right thing to do?” They ask, “What do I get if I don’t do it?”
And to avoid thinking of themselves as a bad person, they have a ready-made explanation: everyone does it.
That sentence is one of the easiest ways to escape moral responsibility. If everyone is guilty, no one has to feel guilty.
Of course, people in difficult circumstances face hard choices, and we cannot judge every situation in the same way. But one thing remains true: the fact that a behavior has become common does not make it right. Having a reason for doing something does not automatically make it ethical. And the fact that other people cause harm does not relieve us of our own responsibility.
Perhaps this is what the whole thing comes down to: we think getting used to something means adapting to reality. But sometimes, getting used to something only means learning to tolerate what should never have become normal.
If we are humiliated a little more every day, we may eventually stop recognizing humiliation. If we hear a little more lying every day, the truth may start to sound stranger than the lies. If we witness other people being mistreated often enough, we may become less disturbed by the mistreatment and more annoyed by the person who keeps talking about it.
By then, the poison has done its job.
Not necessarily because it has destroyed us completely, but because it has taken away some of our ability to recognize that we are sick. We are no longer just suffering from the disease. We may have started defending it.
That is why the first step may not be finding a grand solution or pretending we can change everything. It may be something simpler, but also harder: refusing to treat something as acceptable merely because we have become used to it.
We can ask ourselves: if this were happening to someone we cared about, would we still call it normal? If we did not have to justify it to get through our own lives, would we still defend it? And if nobody else were doing the same thing, would we still believe it was right?
Maybe we cannot remove all the poison from our bodies at once. But at least we can stop adding the next dose to our own food and to everyone else’s.
The real danger is not just living in a sick society. It is getting so used to the sickness that we no longer remember what being healthy looks like.
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