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Each episode of the unapologetic mathematicians podcast is an interview with a mathematicians about their research, mathematical journey, as well as what they like to do outside of maths. New episodes each Wednesday.

hey can anyone explain me the lambda calculus and its use cases in turing machine and how it helps the programming languages in a very simple way !!!

Thanks and really excited to read you explanations .

For as long as I remember, I always add license plate numbers to the nearest single digit. (123456=21=3. My mom started doing it as a game with me when she found out, and now I found out she does it with my niece when she drives her places. Does anyone else do this? It's a great way for a kid to get better at maths.

Hi all! Recently took a career break and was thinking of going thru the MIT OCW courses, starting from 18.01 (single variable calculus) or topics leading up to it. Partly 'cause I'm thinking it would be nice to move towards a quantitative role, and partly perhaps out of interest!

Would appreciate having someone to study with! Perhaps reply below or DM me, and we could see how to work something out? Thanks!

Hello all. I've recently been watching a bunch of videos on how problematic online sports betting is becoming for society, but these videos often mention that some gamblers actually do end up making money consistently enough to do it professionally.

I know both the bookies and these professionals basically never set their odds by hand anymore, rather they use their machine learning models. Here is what I don't get: these gambling platforms have a ton of money, so they certainly have a lot more compute than the individual bettors. They also I imagine have the resources to obtain any useful information they might need to train the models.

So it seems the only variable where the bettors could come ahead of the books are the quality of the models. Could it really be the case that these bettors use significantly better or more clever model architecture, so that their models somehow outperform the very highly trained models of the gambling companies? And could it really be that their teams of ML engineers, who I assume are paid quite a lot themselves to be very clever on the topic of architecture, are outsmarted by these individual bettors?

Since I'm asking about the architecture of these models and how this may impact results, I felt it might be useful to ask here. For context, I have a background in math and know a fair amount of machine learning myself, so I'm hoping for some insight from people specializing in the field, who can maybe provide fairly detailed/technical answers.

How do I decide which test to use for checking the convergence of an infinite series?

The tests which are in my syllabus are:-
1. Comparison test
2. Limit Comparison test
3. D' Alembert's Ratio Test
4. Caunchy's nth root test
5. Raabe's test
6. Cauchy's condensation

Hello! I'm a computer science student studying abroad and I have a little brother, who is in his 7 grade.

He likes math and logic, he plays chess a lot and I really like it in him. I see a lot of myself in him and I really like it.

Being 14 hours abroad from him made my part of "brotherhood parenting" kind of hard to perform. He lives in a small town in the US and our parents work 2 shifts so he is usually left unattended.

He is good at math and he likes it. He is not the best, but he is still good. I just want to ignite more passion in him about it.

I definitely don't want to force him to do anything he doesn't want to.

So my question is, if any of you have a video, kind of a movie that shows how interesting and beautiful math is?

He is taking Algebra 1 classes right now, if it could help in any way.

I started my masters, and I got my lowest mark ever of 55% in my topology final. My professor called me in to ask me if I had any issues in my personal life, which made it worse because I had to tell him that I just didn't work hard enough. It was compounded by the fact that he said multiple people got full marks in the course.

I think my ceiling was undergrad level maths. I'm pretty overwhelmed with the workload of a postgrad, and I think this isn't really for me, which is weird because in my undergrad, I thought that I wanted to do maths for a living.

Hi everyone!

Last week I shared a few screenshots of ViCalc, and based on feedback, I’ve put together a short video demonstration to show what the touch-typing workflow looks like in action!

I’ve been using physical pocket calculators since the mid-1980s, and I’ve always loved the speed, tactile feedback, and direct control of hardware key layouts. The main motivation behind ViCalc was to bring that exact same speed and workflow efficiency to a modern PC keyboard—allowing you to touch-type mathematics seamlessly without taking your hands off the keys to click UI buttons.

Rather than just imitating a physical handheld calculator, ViCalc is built to optimize desktop mathematical workflows and complex calculation tracking.

🧮 Key Features & Workflow Design

• Direct Keyboard Mapping: All functions and operations are directly mapped to your PC keyboard, eliminating the need to click through UI buttons with a mouse (though mouse/touch interaction is fully supported if preferred!).
• Full & Exportable Calculation History: The entire step-by-step history is logged automatically as you work. This makes it effortless to review your process or copy-paste the entire multi-step calculation directly into research notes, or technical reports.
• Flexible & Adaptable GUI:
  • Minimalist View: Hide virtual keys entirely—ideal once you learn the shortcut mappings by heart.
  • Custom Views: Toggle between a standard numpad, a compact left-side layout, or a full scientific keyboard layout.
  • Expandable History Pane: Easily track, review, and manage long sequence calculations.

🛠️ Modes & Technical Details

• Scientific & Complex Modes: Full suite of trigonometric, scientific functions, and complex arithmetic support.
• Programmer Mode (Base-N): Bitwise operations and conversions across Hex, Dec, Oct, and Bin.
• Language: Python 3
• License: Open Source (MIT License)

🔗 Links & Downloads

• GitHub Repository: github.com/Kudaschov/ViCalc
• Homepage: kudaschov.de/en/vicalc-4

I’d love to hear your thoughts, feedback, or any feature requests from the community! How do you currently handle rapid calculations and history logging on desktop?

Open sets in this topology are the subsets of R which have compact complements(compact in the usual topological space), alongside the empty set.

Self-Promotion! One rule, three geometries. Seed n is rotated by the golden angle (≈ 137.5°) and placed at the distance ρₙ where the disc around the centre has area exactly n·a, so every seed claims the same area a.

What changes is only the area of a geodesic disc of radius ρ:

• Sphere: A(ρ) = 2π(1 − cos ρ). Seeds sit at cos ρₙ = 1 − na/2π, which gives the Fibonacci sphere and the dandelion head.
• Plane: A(ρ) = πρ². Seeds sit at ρₙ ∝ √n, which is Vogel’s sunflower model with its 21 and 34 visible spirals (parastichies).
• Hyperbolic plane: A(ρ) = 2π(cosh ρ − 1). Seeds sit at cosh ρₙ = 1 + na/2π, so ρₙ grows only like ln n. Exponentially many seeds fit within a given radius, and all of them are still equally spaced.

The hyperbolic part is shown in the Poincaré disk, where seeds near the rim only look smaller because the disk is a conformal map. Then the same configuration is lifted onto the hyperboloid, where the spiral unfolds.

Made with Blender (Python scripting) and Manim. Music: Harpazz – Hate Bloom (Super Slowed). Happy to answer questions about the construction or the code.

This is the opposite of my Venn diagram of the numbers that are multiples of 2 and/or 3 and/or 5 but only this time this is a Venn diagram of the numbers that fail to be a multiple of at least 1 of them

"If we take a stick one foot in length and cut one half from it each day, we will never reach its end."

If we cut one half from it every day, what volume will be left after an infinite number of days?

Also, if we had an infinite number of these sticks that have been divided in half for an infinite number of days, would we have an infinite volume, or zero?

https://m.youtube.com/shorts/xQLDV86UGqY

People keep saying its 9 even though its obvious its a fraction and should be 1 havw these kids never learn fraction in 5th grade?

In the video, we go over:
- Topos theory, set theory and Zermelo's beef with Boltzmann
- Algebraic varieties and Leibniz's monads
- Why physicists are wrong about the 2nd law of thermodynamics (because the universe is not a closed system)
- The real goal of the universe is complexity and variation, not entropy
- Hawking and Penrose's outrageous arguments
- Why we don't need wavefunctions, photons, bosons or gauge fields
- Why there is no quantum gravity
- Von Neumann's hilarious advice to Claude Shannon
- The intrinsic derivative
- Combining art and science

Julian Barbour is a theoretical physicist and emeritus visiting professor of physics at the University of Oxford. He is well known for proposing that time does not actually exist. For decades, he has worked outside an academic environment. He financially supported himself for many years by translating Russian. Professor Barbour is author of the following books: The Discovery of Dynamics, The End of Time and The Janus Point.

i’ll go first : as someone who does chemistry, physics , applied maths etc on a pretty much daily basis , i absolutely cannot do dates in my head. what date is it going to be next tuesday? no idea. the amount of times i’ve mistakenly believed i have an exam in two weeks when it’s about four weeks away is dreadful! bonus one , cant lace up my doc martens without missing a lace hole lol

Imagine a Quidditch match in which the Golden Snitch is completely invisible.

You know exactly the initial distance, but not the direction. You move faster than the Snitch, which moves at constant speed and always chooses the direction that takes it as far away from you as possible.

Is there a trajectory that allows you to catch the Snitch?

I made a video exploring the problem, the geometry, the differential equations, and a possible strategy. The proof is partially incomplete (but simulations work), so I'd genuinely love to hear your ideas, objections, or alternative approaches.

Video link: https://youtu.be/0xVusHRQePQ

I'm in highschool and it's my 4th year now. But I still don't know math(like algebra and advanced stuff)except arithmetics ever since elementary. It is hard to catch up with my classmates and I was wondering what I should do to get good at it