Story

Chapter 1: Preface
Requirement: Launch the game for the first time.

Transcript: English= You are a talented undergraduate student.

Your professors see a bright future ahead of you.

A professor you respect hands you a formula.

He asks you if it converges to a finite value.

It is an exponential recursive equation.

Not knowing how to solve it, you make a small program that calculates it for you.

Chapter 2: Change Of Strategy
Requirement: db ≥ 0.001.

Transcript: English= Your knowledge is growing!

You know how to perform changes of variables and it looks like the function value is still increasing. However, you don't know if it converges to a finite value yet.

There is one parameter that you did not see. You decide to change your strategy and increase the value of "b" with a Prestige.

Chapter 3: Scholarship
Requirement: Prestige for the first time.

Transcript: English= Proud of your work, your professor offers you an internship in his research lab. Having some funds left from previous projects, he provides some money to help you with your research.

It is not standard money though. He calls it a "Prestige" currency, named μ. You are a bit disappointed since you cannot pay your rent with it, but you accept anyway. Maybe you can find a way to use it in your project...

Chapter 4: Working On It
Requirement: Prestige for the second time.

Transcript: English= It's the second time you increase "b".

You reached a higher value, but still far from infinity. However, you do not have any other parameter left to play with.

The function value grows at an increasing pace. It starts to feel like an idle game. Your professor rewards your hard work by adding a new variable in your equation.

Hopefully, it will pay off...

Chapter 5: Serendipity
Requirement: b ≥ 1.

Transcript: English= A friend introduces you to the concept of serendipity. They say it's when you work on seemingly unrelated stuff, and then by chance you realise that it can be beneficial to your current research. Bob Ross would call it "Happy Accidents". Ideas start to pop when looking at the night sky...

Chapter 6: Some Hope
Requirement: d𝜓 ≥ 0.75 (f(t) ≈ $ee33.05)

Transcript: English= You have been working on this project for a while now. You started to think that it was an impossible task. However, you are starting to see the light at the end of the tunnel. You will soon graduate and be ready to start your master's thesis. Your colleagues are talking about a type of grant that provides "Supremacy" currency, named ψ. You cannot apply for it yet. You don't despair...

Chapter 7: Last Course
Requirement: d𝜓 ≥ 1.5

Transcript: English= You just passed the last exam.

You leave the university and wonder what you are going to do with your life.

You remember that your colleagues talked to you about a grant that would allow you to progress even further in your research. You decide to start a master's thesis and apply for the grant.

To do so, you need to Supremacy...

Chapter 8: Graduation
Requirement: Supremacy for the first time.

Transcript: English= You made it! You finally graduated and started your master's thesis. You applied for the new grant and got it. It is not much, but it is enough to provide a substantial boost for the progress of your project.

It requires you to start from scratch though... But don't worry, you'll get back on your feet quite quickly. Plus, the ideas you got before are still fresh in your mind, so you can reuse them right away. Good luck!

Chapter 9: Call Me Master
Requirement: Supremacy for the second time.

Transcript: English= You are gaining confidence.

Your master's thesis got accepted.

You are a master.

Sure, you progress. But can you stop being so arrogant? Your professor wants to teach you a lesson. He destroys all of your work again in exchange for a bigger grant for your doctoral thesis. This one will require hard work. You may even need to apply for more grants at some point.

Your motivation is higher than ever.

Chapter 10: The End
Requirement: Reach f(t) = $ee200.

Transcript: English= To see a World in a Grain of Sand

And a Heaven in a Wild Flower

Hold Infinity in the palm of your hand

And Eternity in an hour

- William Blake -

The End

Or...

Is it?

You decide to Supremacy one last time to make sure you didn't make a miscalculation.

Chapter 11: Doctoral Thesis
Requirement: Supremacy after reaching the first infinity (f(t) = $ee200).

Transcript: English= Well done! You just finished writing your doctoral thesis. Everything is written down and ready to submit to the examination committee. You are quite excited about the result. You should be proud of yourself, it is a remarkable milestone in your career. While the committee is at work, you revise your work, you double-check everything.

One last time…

Chapter 12: Honors
Requirement: Purchase upgrade "Unlock $$x_1$$"

Transcript: English= Congratulations! You finally did it.

You defended your thesis with success.

You got your Ph.D. with honors despite not having a definitive answer to your question.

But that's OK. Research is always an ongoing process, and your committee knows it.

You just discovered that you could modify the equation a little bit to accelerate the process. You decide to pursue a postdoc to go deeper into your project...

Chapter 13: Publishing Papers
Requirement: Purchase upgrade "Unlock $$x_4$$"

Transcript: English= You now have a deeper understanding of infinity. You published your first paper in a renowned journal. You went to present it to a conference but you got a lot of criticism from your peers. They say that your numbers are not big enough to ensure that the limit is infinite. They say that those are rookie numbers and that you gotta pump those numbers up. You go back to the drawing board and rework the equation...

Chapter 14: A Successful Career
Requirement: Reach f(t) = $ee2000.

Transcript: English= A chapter of your life finally ended.

You gave all you got for this project.

You published many papers based on your results. For most people this is gibberish, but mathematicians know that it is a significant achievement in your domain. A successful career is ahead of you and you are now on your own.

You got a position as an assistant professor in a renowned university. You have a team of bright students that come up with clever ideas and you are very excited about what's next.

You can either graduate students now or continue your project alone until more students want to join the team.

Chapter 15: First Cohort
Requirement: Graduate new students once.

Transcript: English= You remember when you started this project. You were young and innocent. You thought this problem could be solved within a week. And yet, here you are: seeking the help from people younger and smarter than you. But don't feel bad. It's normal for older people like you to lose a bit of sharpness.

These new students will take up where you left off. Relax in your office, and let the younger ones do the hard work.

Chapter 16: More Monkeys
Requirement: Graduate new students twice.

Transcript: English= You never thought it would be so easy to be a professor.

You sit on your chair and when a student asks you a question, you just have to answer: "It's your job to figure this out."

You are thinking about the Infinite Monkey Theorem, hoping that one of them will end up achieving something great.

Maybe not today though...

Chapter 17: Synergy
Requirement: Unlock the "Recurrence Relations" theory, a.k.a. theory 1.

Transcript: English= A group of frustrated students comes to you. They ask: "What is the point of all this?"

You drop your coffee. You were not expecting students to challenge your authority.

You tell them to try something different if they think they can do better. Deep inside, you know that this will not lead anywhere.

They call it "synergy", you call it a loss of your precious time.

Chapter 18: Head of Department
Requirement: Graduate after unlocking the first theory.

Transcript: English= Theories ended up being quite fruitful. Among all professors in your department, you were the one who has published the most papers this year. You have been nominated to be the head of the department and you got the position. During your acceptance speech, you praise your students for their hard work and tell how you always believed in them and their ideas.

Why would you lie? It's the truth!

Chapter 19: Existential Crisis
Requirement: Unlock the "Polynomials" theory, a.k.a. theory 4.

Transcript: English= "Who is it that can tell me who I am?"

One equation.

Is it my life? Really?

If only there was an easier way to prove that this equation tends towards infinity...

You should explore more areas, more theories.

You invested so much time in it.

Why give up now?

Chapter 20: Butterfly Effect
Requirement: Unlock the "Chaos" theory, a.k.a. theory 8.

Transcript: English= An annoying colleague of yours comes to your office and starts talking about the weather and how unpredictable it is. You don't like small talk, so you just nod, hoping he will leave soon. He keeps talking. Maybe things would have been very different by now if you didn't smile at him the first day. While he's talking, you stir your coffee, observing that even if you stir exactly the same way, the patterns will be different every time.

Anyway... later that day, a student asks you if he can start a project on chaos theory. You have no idea what it means but it sounds cool, so you accept.

Chapter 21: Sabbatical
Requirement: Buy the Reseach upgrade #9 Transcript: English= You have to admit it. This is getting out of hand. Even after all your attempts, infinity seems to be very far away.

Maybe infinity is not a number.

Could it be just a concept?

If you cannot observe it,

how can you prove that it exists?

You decide to take a sabbatical year to think about your life and future projects. You take a notepad with you to continue working on theories.

Students will do their job during your leave.

Chapter 22: Eureka
Requirement: Unlock the "Convergence Test" theory, a.k.a. theory 9. Transcript: English= Of course!

Why didn't you think about it before?

Convergence tests can indeed be useful to test the convergence of your equation.

You have a feeling that this will finally solve your problem.

It's time to end your sabbatical and get back to work.

Chapter 23: Quod Erat Demonstrandum
Requirement: Complete the "Convergence Test" theory, a.k.a. theory 9. Transcript: English= What a journey it has been.

You feel that it's a good time to retire.

You start packing your stuff and say goodbye to your students.

It's their turn to be on their own.

You think about all the efforts that you have put in this project and all the things you learned.

Was it worth it?

Yes, it was.

Q.E.D.

The End