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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 31/08/2026

I've been greatly enjoying reading colleagues' posts in the "Proofs and Prompts" blog, so it's my pleasure to share my own post that just appeared! Hope you enjoy it too. Invest in Human Mathematicians! proofsandprompts.com/2026/08/31/i...

A room full of mathematicians listen to a video lecture by Dick Gross.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 03/08/2025

A sketch of the graph of a hyperbolic paraboloid 🤩 (z = x^2 - y^2)

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 11/07/2025

I met @clontz.org and got to hear him speak about the very cool project pi-Base! topology.pi-base.org

Steven Clontz speaks about pi-Base at ICERM.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 02/03/2025

Completely forget about central series!!! Look at the theorem here... The definition of nilpotent should be that it's a direct product of Sylow groups! That's so clearly important! The image is a screenshot of this paper by Daniels and Rouse: arxiv.org/abs/2409.00881

A screenshot of a paper that explains the usual definition of nilpotent group and then states a theorem that shows nilpotent iff the group is direct product of its Sylow subgroups

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 02/03/2025

My bougainvillea thinks it's spring in the US Northeast ... Bless you heart.

A photo of a bougainvillea in flower (pink flowers), indoors.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 26/02/2025

This is probably my favorite insult I've gotten on a TikTok 😅😂

An still from one of my TikToks and a comment that says "I love ur American girl doll teeth"

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 09/01/2025

And here is the same graph of P(x) and HL(x), but up to x=100000.

A graph of P(x) and HL(x) up to x=100000. The two are starting to look very similar.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 09/01/2025

Let P(x) be the number of n in [1,x] such that n and n+2 are both primes. And let HL(x) be the integral function such that, conjecturally, lim_{x->infty} P(x)/HL(x) = 1 Here is a graph of P(x) in blue, and HL(x) in red, up to x=1000.

A graph of the twin-prime counting function and the conjectural asymptotic function of Hardy-Littlewood/Bateman-Horn.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 08/01/2025

And here is a graph comparison of P(x) (blue dots) and HL(x) (in red) up to x=100000.

Comparison of P(x) and HL(x) up to x=100000. They are really darned close.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 08/01/2025

Here is a graph comparison of P(x) (blue dots) and HL(x) (in red) up to x=100.

Comparison of data for the number of prime values of x^2+1 (blue) and the conjectural asymptotical formula by Hardy-Littlewood/Bateman-Horn (red).

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 03/01/2025

Today I was interviewed by NBC Boston about the different number expressions of 2025! Hopefully it airs at 4pm Eastern.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 02/01/2025

If you ever wanted to know how to solve the problem in the image (the "fruits diophantine equation"), here is a video for you :D youtu.be/BG2vSPnDYJ0

A math problem with fruits instead of variables

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 25/12/2024

The Empire Strikes Back is a Xmas movie.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 23/12/2024

In other news, I lifted over 10M pounds this year.

A chart with some lifting stats: 243 workouts, 10,886,261 pounds lifted.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 10/12/2024

I was grading and I wrote two questions marks next to some math I didn't understand, then thought about it some more, and then underlined my question marks because I was still really confused... ... And now I see a "confused bunny" and I can't unsee it. I'm keeping it and using it again.

Two question marks are underlined (twice) and now the symbols look like a confused bunny.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 29/11/2024

I'm thankful for my kids (who made these awesome cupcakes from scratch!)

Homemade cupcakes that resemble little cartoon turkeys

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 22/11/2024

I'll go first: Silverman's "The arithmetic of elliptic curves." It's so nicely written it's a case study on how to write textbooks. It's the canonical reference to first learn about elliptic curves at the grad level. And at a personal level, it's the book that got me SO interested in this topic!

The cover of Joe Silverman's "The arithmetic of elliptic curves"

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 22/11/2024

The elliptic curve with LMFDB label 49.a2 hopes you have a nice Friday and a great weekend.

The LMFDB.org page for the elliptic curve 49.a2

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 16/11/2024

It doesn't get any more Zen than this for me. This is one of my bonsai that brings me so much joy and peace to look at!

Picture of a juniper bonsai on a wooden bench.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 20/10/2024

@xl772.bsky.social 's call to action to develop undergrad courses on quantum algorithms.

Screenshot of a slide during a talk with a "call to action" to develop undergrad courses on quantum algorithms

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 18/06/2024

Here is a group photo from the CTNT conference. The talks were amazing!

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 10/05/2024

Registration for the CTNT 2024 Conference (in Number Theory) is still open, until May 15. Please join us! And share with others! Thanks.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 30/03/2024

Can you solve this Connections puzzle that only has numbers in it? Find four groups of four numbers, where each group is connected by a well defined mathematical pattern. Enjoy.

A "Connections" puzzle but it's numbers instead of words. There are four rows of numbers: 2,3,4,5, then -1,257,21,-8, then 13,17,27,16, then 8,64,34,55

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 20/10/2023

You know those super obnoxious, super loud commercials that you are prisoner of at the gas pump, right? Do you know you can MUTE the screen?? You can thank me later.

The screen at a gas station pump. The second button on the right from the top is marked "mute" with a sharpie marker.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 23/09/2023

Finally got my hands on some Einstein monotiles! Made by Cherry Arbor Design.

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 23/09/2023

The building for UConn's Dept of Math is, like many other across the country, not the prettiest buildings on campus, but its location, next to Mirror Lake, is pretty amazing! 🤩

UConn's campus with the Department of Mathematics and a lake in view

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 19/08/2023

Take time to make sure you don't have any spelling mistakes before you print your clothing.

A picture of a hoodie at a store. The back has writing on it and it says "Take time to discover it's charms"

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 16/08/2023

Anyone knows what's the LaTeX package to make shower curtains!?

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Álvaro Lozano-Robledo @mathandcobb.bsky.social · 31/07/2023

@littmath.bsky.social Scientific American has edited their article about ABC!

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