Abhishek Gopal (Himalaya)

Do you ever feel like math just isn’t your thing? A short video by Courtney Gibbons, a math professor at Hamilton College. Another video and article titled "Here's A Big Secret To Being Good At Math" by Grunge. One-line summary: "Being good at math is being good at being stuck."

• Meet a Mathematician!: Meet a Mathematician's mission is to share the stories of mathematicians from various backgrounds, particularly those from historically excluded groups, with the aim of introducing students to role models and fostering a sense of community. Meet a Mathematician is committed to increasing the voice and visibility of academic mathematicians from underrepresented groups while advocating for a more inclusive math community that reflects diversity in the world.

• Quanta, also its YouTube channel: Quanta Magazine is one of two websites published by the Simons Foundation, the vehicle for the philanthropic charity of hedge fund founder James Simons. Quanta focuses on mathematics, physics, computer science, and biology. The other publication is Spectrum News, which covers autism research. Undark Magazine described Quanta Magazine as "highly regarded for its masterful coverage of complex topics in science and math."

• My Favorite Theorem: A monthly podcast dedicated to sharing their guest's favorite mathematical results hosted by Kevin Knudson and Evelyn Lamb. You can also follow their individual blogs (150+).

• YouTube channels for mathematics: These channels really offer great graphics, provide visualizations, one can hardly imagine. These are an element of truth - videos about science, education, and anything else I find interesting. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. They are Insights into Mathematics, The Math Sorcerer, Numberphile, 3Blue1Brown, Mathologer, Stand-up Maths, MindYourDecisions, Veritasium, and Tibees.

• Movies featuring mathematics: Well, from the above-mentioned link, my favorite ones are; A Beautiful Mind (2001), X+Y: A Brilliant Young Mind (2014), The Man Who Knew Infinity (2015), The Imitation Game (2014), The Theory of Everything (2014), Good Will Hunting (1997), Pi (1998), Hidden Figures (2016), Gifted (2017), and a few more.

  The MMDb (The Mathematical Movie Database) contains a list of titles and short descriptions of about 800 movies that contain mathematics. Also included are links to the respective entries in the International Movie Database (IMDB) and links to clips from some of the movies. Oliver Knill, Harvard has also maintained a collection of clips.

• Blogs: The following blogs by people or group are fun to read
• Cantor’s Paradise by Medium
• Undark
• Nautilus
• Terence Tao Blogs
• Quantum Calculus by Oliver Knill
Topology
• Low-Dimensional Topology by Ryan Budney, Nathan Dunfield, Jesse Johnson, Daniel Moskovich and Henry Wilton, for recent progress and open problems.
• sketches of topology: visualizations of low dimensional topology by Kenneth Baker.

Indiana University Bloomington

• Topology Seminar
• Graduate Student Seminar
• Topology and Friends Graduate Student Seminar (TopFrogs)

Boston College (and other events in Boston area)

• Geometry / Topology / Dynamics Seminar (Boston College)
• HyperboliciTea (Boston College)
• Getting Into Some Theorem (GIST) Seminar (Boston College)
• Geometry & Topology Seminar (MIT)
• Gauge Theory and Topology Seminar (Harvard)
• Dynamics, Geometry and Moduli Spaces (Harvard)

The following list will help you locate upcoming conferences, workshops, and summer schools.

• researchseminars.org (for any subject, any field)
• MathMeetings.net
• COMS operated by COMS, Dienstleistungen in der automatischen Datenverarbeitung und Informationstechnik.
• Low Dimensional Topology Conferences
• Links to low-dimensional topology (this might be outdated)
• Seminars on knot theory and related topics (for knot theory and quantum topology; online)

Resources for those new to mathematics or exploring the field for the first time.

• Wolfram Alpha: It is the best free online math calculator that I know of. It can do everything from basic arithmetic to factoring polynomials, computing derivatives, solving multiple integrations, dealing with systems of differential equations, finding matrix decomposition, and more. Odds are that if you have a straightforward computational math problem, there is some way you can get Wolfram to calculate it for you.

• GeoGebra: GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics, and calculus in one easy-to-use package. It is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering, and mathematics (STEM) education and innovations in teaching and learning worldwide.

• Overleaf: Overleaf is a free online LaTeX editor. LaTeX is universally used by professional mathematicians for typesetting mathematics. It is especially good for making clean documents or presentations, particularly if they contain technical math content. Provides a good interface and many free templates for your documentation needs in LaTeX. The help and LaTeX guide is exceptional and it is useful whether you are using LaTeX in Overleaf or not.

• MathOverflow and Math.StackExchange: Both are question-and-answer (Q&A) websites, which serve as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. In its current state, any post including "Math Mode" (text between $'s) will translate into proper mathematical notation. They allow users to donate some of their reputations to help questions receive answers or better answers, as well as to incentivize users to answer.

• SageMath: SageMath, or simply Sage, is an open-source mathematics software system built to provide a comprehensive, unified environment for mathematical computation. It is designed for a wide range of applications in mathematics, from basic algebra and calculus to advanced number theory, cryptography, and numerical computation.

• Additional Math Tools: Desmos, Mathematica by Wolfram, etc.

For those who are already knee-deep in the field.

• MathCurve: Encyclopedia of Remarkable Mathematical Forms: The website is grouped into 5 themes: 2D curves, 3D curves (which is more "in" than plane curve and left curve...), surfaces, fractals and polyhedra.

• 3DXM Virtual Math Museum: A part of 3D-XplorMath, a program for visualizing and experimenting with a variety of mathematical objects.

• 3-Dimensional Space by Rémi Coulon, Sabetta Matsumoto, Henry Segerman, and Steve Trettel, to render accurate images of the eight Thurston geometries and their quotients.

• GroupNames.org by Tim Dokchitser, is a database, under construction, of names, extensions, properties and character tables of finite groups of small order. Currently, it includes all 16309 finite groups that have order ≤500 and not 256 or 384.

• 3D Models and Printing (download files and build them with your 3D printer, laser cutter, or CNC):
• Henry Segerman is a recreational mathematician and mathematical artist with expertise in virtual reality. Book: Visualizing Mathematics with 3D Printing.
• DesignByNumbers by Jason Cantarella for 3D files of knots and links.

• Below is a collection of programs and online databases that are helpful for knot theory research. Naturally, this compilation is not exhaustive and reflects my personal preferences. Please feel free to suggest any additions.

  Online Databases

  • KnotInfo by Charles Livingston and Allison H. Moore, provides an online database containing many different properties of the knots with at most 13 crossings.
  • Knot Atlas by Dror Bar-Natan, features an online tables of knots and links with pictures and polynomial invariants. Also includes a Mathematica package for computing polynomial invariants of knots and links which contains the information in the tables.
  • CompuTop.org by Nathan Dunfield, a site containing list of softwares and packages for people doing computational stuff with low-dimensional topology.
  • Knot Data Tables by Alexander Stoimenow
  • Knotorious by Maciej Borodzik and Stefan Friedl to compute various lower and upper bounds on the algebraic unknotting number.
  • Regina by Benjamin Burton, Ryan Budney, and William Pettersson, is a software package for 3-manifold and 4-manifold topologists, with a focus on triangulations, knots and links, normal surfaces, and angle structures.
  • Knot Tables provides the tables of all 352,152,252 prime non-trivial knots with up to 19 crossings.

  General Purpose Programs and Packages

  • KnotTheory` by Dror Bar-Natan, is a Mathematica package KnotTheory`, the main tool used to produce The Knot Atlas.
  • KnotScape by Jim Hoste and Morwen Thistletwaite, is an interactive program for the study of knots.
  • LinKnot by S. Jablan, R. Sazdanovic, is a Mathematica-based program for Windows LinKnot is the knot theory program that works with knots and links given in Conway notation.
  • KnotFolio by Kyle Miller, is a browser-based program for drawing and manipulating topological knots and links.

  Knot Homology Calculators

  • Gridlinkby Marc Culler, is a tool for manipulating the rectangular link diagrams or Grid diagram which were introduced as variant forms of arc presentations
  • HFKcalc by by Peter Ozsváth and Zoltán Szabó, is a program to compute knot Floer homology
  • BordProg is a program BordProg for computing Heegaard Floer homology using the bordered theory of Lipshitz, Ozsváth, and D. Thurston.

  Programs for Other Specific Purposes

  • SnapPea and SnapPy by Marc Culler and Nathan Dunfield, using Jeff Weeks's original kernel, is a general purpose program for manipulation of 3-manifolds, with an emphasis on finite volume hyperbolic 3-manifolds.
  • SeifertView by Jarke van Wijk for visualizing Seifert surfaces for knots in the 3-sphere.
  • Braid programme by Roger Fenn to calculate matrix representations of virtual braid groups.

I spent 3 years, 5 months, and 1 day in Bloomington. Here is a list of things to do in Bloomington—including local food spots, lakes, and nearby state parks—whether you're in your first year of school or just visiting Bloomington.

I have just arrived in Boston. Here is the list of places I have figured out and enjoyed so far. I'm always looking for new places to eat, so if you have any recommendations, please let me know.

Fun fact for mathematicians: Despite the name, the Boston cream doughnut has no hole, and Boston cream pie is not a pie but a cake.

(Back to top...)

Last updated: March 2026