Teenagers doing Mathematical Research

I’d like to ramble about another program that our group is running. We are searching for unusually promising high-school-age students and mentor each in a serious research project. We started doing this already before our REU program. However, I never advertised this program before, because I felt that we were still learning how to do such mentoring. We are still learning, but I now feel more comfortable talking about this.

A couple of recent students. Let’s start with a couple of examples. These are the two most recent young students we worked with.

Kiki Pichini is currently 16 years old. She lives in a small town in the middle of Washington State, far from any big city. A few years ago, she wanted to learn more advanced mathematics but did not wish to leave home at her age. So she enrolled to an online undergraduate program of Indiana University. She will complete her undergraduate degree this upcoming spring.

While working on her degree at 15, Kiki wanted to continue to even more advanced projects, so I started working with her on a research project. This was done purely by email and video chats. Kiki just submitted her paper to a combinatorics journal. It can also be found on arXiv here. Kiki improved the current best upper bound on the number of rectangulations a planar point set can have – a bound that remained unchanged since 2006.

Our second most recent student is Michael Manta. Michael is a high-school student in Xavier High School in New York City. He was studying more advanced mathematics through an NYC-based program called Math-M-Addicts. We met Michael in the summer after his sophomore high-school year. He worked under the mentorship of Frank de Zeeuw and proved a new result about triangle colorings of the plane. He submitted his paper to a combinatorics journal a few months ago and it is currently being refereed. The paper can also be found on arXiv.

Michael is currently applying for college. After finishing his research project, he wanted to do more math. So he is currently taking a couple of the more advanced courses our department has to offer.

We’re Hiring!

Come join us! This year our math department has two types of positions available. We have a standard tenure track position, which would hopefully continue our awesome sequence of recent hires. But this post is not about the standard position. Instead, I’d like to talk a bit about our other type of position – a Lecturer position.

The lecturer position is basically a teaching-based “tenure-track” position. This brief description gives the wrong impression about the position. So here is a bit more information:

• Lecturers must have a Ph.D. in math. They choose whether they wish to continue doing research – some do and others don’t. (This summer one of our lecturers had a paper accepted to the Annals of Mathematics!)
• Our lecturers are some of the most highly respected people in the department. All of our current lecturers are amazingly professional and productive. They run a large part of the department, work closely with the chair, and so on.
• After 5 years, a lecturer applies to receive a CCE status (Certificate of Continuous Employment), somewhat similar to tenure.

If you are a strong and enthusiastic teacher, and may be interested to join our team, apply on mathjobs.org. (Here is our standard tenure track position). I very much hope that we will hire someone who could be part of our REU program. But I’m only one person, and others have other priorities.

Since Baruch College is not the most well-known place in the mathematical world, I would like to also tell you a bit about us.

• Baruch College is highly focused affordability, diversity, and social mobility. It is consistently ranked #1 in Social Mobility Index, towards the top of Money magazine’s Best Colleges For Your Money, WSJ Biggest Bargains Among U.S. Colleges, Affordable elite ranking, and so on.
• We have a strong group of “junior” mathematicians. For example, Louis-Pierre Arguin‘s work was recently featured in the Bourbaki seminar (Louis-Pierre also holds an NSF career award). Other recent hires include strong people such as Yumeng Ou and Andrew Obus.
• Our department’s financial math team has several impressive achievements. The master’s program in Financial Engineering is consistently ranked as one of the top in the world (see here and here) and the financial math students keep winning trading competitions (see here).
• I believe that another advantage of our department is its unusually friendly and positive atmosphere. Somehow one does not see very bad politics here. For example, our last vote for the executive committee (handling hiring, tenure, etc.) was over extremely quickly and was almost unanimous.

Abstraction is Hard

A few weeks ago I read Malcolm Gladwell’s book The Tipping Point. The book doesn’t really deal with mathematics, but it does contain one math-related anecdote. This anecdote demonstrates an interesting principle of learning mathematics, so I wanted to share it.

Problem 1. We have a deck of cards, such that each card contains a digit on one side and an English letter on the other. We are dealing four cards, with the following result:

We are told that behind every vowel there is an even digit. Which of the four cards should we flip to check whether this claim is true?

I suspect that most mathematicians would only need a few seconds to answer this. On the other hand, people who are not used to mathematical logic would probably need a minute to get to the correct answer.

Problem 2. A cop walks into a bar to check for underage drinking and sees four people drinking. From a first glance, the cop notices that the first is a teenager, the second drinks water, the third is middle aged, and the fourth is drinking beer. Which of the four people should the cop check more carefully?

Most people would probably answer this problem immediately. This is interesting, since the two problems are completely identical! The only difference is that the second problem has a social context while the first is abstract. Even experienced mathematicians probably need to think for a couple of seconds to solve the first problem, but not the second.

This is a nice demonstration of why it is difficult to start studying advanced math. I will definitely use it when teaching proofs classes.

Here is another example of abstract things being hard to get:

Linear Algebra Riddle

I’d like to tell you about a nice riddle, which I heard from Bob Krueger (one of our current REU participants, who already has four papers on arXiv!!). The riddle requires very basic linear algebra and is in the spirit of the previous post.

Riddle. A library has books and subscribers. Each subscriber read at least one book from the library. Prove that there must exist two disjoint sets of subscribers who read exactly the same books (that is, the union of the books read by the subscribers in each set is the same).

Hint: Very basic linear algebra. Try the first thing that comes to mind.

The Math Art of Gábor Damásdi

You may have noticed that the credit for the drawing in my previous post went to Gábor Damásdi. Gábor is a PhD student at the Hebrew University of Jerusalem. He is also one of the top math art creators I have met.

Gábor Damásdi.

I think it took Gábor less than two minutes to prepare the drawing for the previous post, and this is one of his least interesting creations. Check out his site, which contains many more interesting things. You can find there drawings and animation of many mathematical results. Here is an animation of Pascal’s theorem:

Here is a Voronoi diagram of moving points:

I hope that in the future we’d have more of Gábor’s creations in this blog!

Child Care at STOC 2018 + Riddle

I’ve been asked to post the following message by the STOC 2018 local arrangements chairs – Ilias Diakonikolas and David Kempe.

We are pleased to announce that we will provide pooled, subsidized
child care at STOC 2018. The cost will be $40 per day per child for
regular conference attendees, and $20 per day per child for students.
For more detailed information, including how to register for STOC 2018
childcare, see http://acm-stoc.org/stoc2018/childcare.html

To have something slightly mathematical in this post, here’s a cute riddle: 100 passengers enter an airplane one at a time. The plane contains 100 seats and every passanger has a ticket with a seat number. The first passanger lost his ticket, so he randomly chooses a seat (uniformly). When any other passanger enters, if their seat is available they use it, and otherwise they randomly choose one of the available seats (uniformly). What is the probability that the last passanger got their correct seat.

Finally the name of this blog makes sense!

A New Discrete Geometry Group!

This year I moved to Baruch College (which is part of CUNY – the City University of New York), and I’m constantly surprised about wonderful things that keep happening here. In this post I’d like to write about just a couple of these. First, we just hired two additional Discrete Geometers! Together with myself and Rados Radoicic who are already here, we will have quite a large Discrete Geometry group. We have plenty of plans for what to do with this group, and hope that we’ll manage to establish a strong and well-known Discrete Geometry center.

The Discrete Geometers who will be joining us are

• Frank de Zeeuw – working mainly on polynomial methods in Discrete Geometry. Frank has very impressive results concerning expanding polynoamials, and the current best bound for the Szemerédi–Trotter theorem over finite fields.
• Pablo Soberon – working mainly on central ideas in convex geometry, such as Tverberg’s theorem and Helly’s theorem. Pablo also has an impressive background in the world of math competitions.

Frank de Zeeuw, Pablo Soberon, Yumeng Ou, and Andrew Obus.

If the above is not enough for you, we just hired two additional amazing mathematicians! With these four new hires, the pure part of our math department is receiving a huge boost.

The two additional new hires are:

• Yumeng Ou – working in Harmonic Analysis and more specifically on restriction problems and related topics. Personally, I’m very interested in her works involving polynomial methods and Falconer’s distance problem.
• Andrew Obus – working in Algebraic Geometery and Number Theory. I can write more but I’m afraid of getting the details wrong. So just look at Andrew’s webpage to see his impressive works.

By some weird coincidence I am interested in the works of all four people, and I cannot wait to interact with all of them! The future here looks exciting!