Here is my collection of experimental mathematical games, simulations, and other apps I have written (or supervised) over the years.
— Algebra —
- A preliminary demo of an algebra game in Scratch (discussion here), solving a single (randomly selected) linear equation in one unknown using two operations.
- A more developed version of the same game, still programmed in Scratch, with 12 levels, with a focus on making challenging and entertaining problems rather than on basic algebra skills. (Discussion here)
- A variant of the above game with 12 random levels, with the n^th level formed by performing n moves in reverse.
— Logic —
- A solver for Lewis Carroll logic puzzles in Scratch (discussion here).
- An interactive textbook for first-order logic in Javascript (and also CSS and HTML); discussion here and here, and code here.
— Linear algebra —
These Java apps were coded by Kim Chi Tran under my supervision.
- Vector calculator
- Gaussian elimination
- Matrix calculator
- Linear transformations in R^2
- Eigenvalues and Eigenvectors
- The Gram-Schmidt orthogonalisation process
— Complex analysis —
- The complex plane
- Elementary complex maps
- Mobius transforms
- Multi-valued functions
- The complex derivative
- The complex integral
- Taylor and Laurent series
- The fundamental theorem of calculus
- The residue theorem
- The argument principle
— Miscellaneous —
Some miscellaneous Java applets:
- Besicovitch sets
- Conformal compactification
- Honeycombs (with Allen Knutson)
- Exponent Calculator
- Multiple choice applet (now a wiki; see also these two discussions).
Source code for the java applets can be found here.
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11 comments
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18 September, 2016 at 11:36 pm
Bhargav Baruah
Hi Terry, This is Bhargav from India…..
You are truly one of the most outstanding, mind-blowing mathematician the world has ever produced.
3 July, 2017 at 7:42 am
Michael M. Ross
Four Excel calculators/graphing tools (written in VBA):
–Collatz Odd Number Calculator (with Factors and Graphing)
–Goldbach “Stress Test”
–Legendre’s (Linear Parity)
–Legendre’s (Fractional Elimination)
These are macro-enabled worksheets (enable content, enable macros).
https://mathrodite.quora.com/Excel-Calculators-Visualizations
28 January, 2018 at 4:18 pm
David Binner
Hi, Professor Tao.
You’ve started building a nice selection of applets here, and work seems to be ongoing; the “Vector calculator” page includes the statement, “We’re still ironing out the kinks in the code, so bear with us for the moment!” I look forward to seeing more of this work as it progresses.
I write similar applets that may be of interest to you and your readers:
http://www.akiti.ca/Mathfxns.html
Presently, JavaScript programs are posted that solve N Equations in N Unknowns, compute Eigenvalues and Eigenvectors of a real general matrix, and perform a Cholesky Decomposition on a real symmetric matrix, to name a few. Source code is viewable (I have done nothing to obfuscate the JavaScript code; furthermore, C++ source code for the programs is being posted on GitHub.) Several more programs are in the works and I am open to suggestions as to what other sorts of discrete math applets could be written that would be useful.
26 May, 2020 at 9:39 pm
Usman Nizami
Can you give me link of c++ code ?
28 September, 2018 at 11:34 am
Kipperock
Dear Prof. Tao,I took the liberty of checking most links(but not all of them), and the following are broken/out of date/other problem:
-“Encyclopedia of mathematics” webpage is empty
-MAA MinuteMath have ceased to update their page
-LMFDB is posted twice:between “Libres pensées . . ” and “LMS blog page”, and between “The Geomblog” and “The mathematics literature project”
-“Patterns of Ideas” has been moved to GitHub, and there’s a link at the old one.
-The mathematics literature project shows a 404 error.
-The blog by James Colliander is down.
-“The capacity to be alone” has been deleted.
-“London number theory” has been deleted.
-“Blog on mathematical journals” is down.
-“PDE blog” webpage is empty,seems it’s been deleted.
-All blogs in “tosio.math.utoronto.ca” are down, including: “Analysis and PDE conferences”, “DispersiveWiki”, and the blog by James Colliander.
-Mathonline blog is currently down, perhaps temporarily
-“Mixedmath” has been moved to http://davidlowryduda.com/ (in 2014).
I didn’t know where to post this other than in this less crowded section.
Also, there may be other lemons.
[Links corrected/deleted, thanks – T.]
21 June, 2019 at 8:31 am
Kipperock
Dear prof. Tao, when one presses the “Subscribe to RSS feed” button there is a bug, and instead of a window which allows one to enter an email address and sign up for the feed, there pops up a window full of code and nothing can be done – besides going back to the blog.
5 December, 2023 at 12:23 am
Anonymous
Why are hard problems more entertaining? Are you relating hard to being more intelligent and/or arousing? If that’s true, you do hard problems for your ego or trying to “get smarter” instead of having fun and being curious. If problems are hard, you force it. You should step back..
29 November, 2024 at 1:12 am
Anonymous
I don’t know if it’s only me but at the moment 29/11/2024 complex analysis applets does not work. Has someone experienced the same and has a fix for that? Thank you very much!
29 November, 2024 at 11:43 am
Terence Tao
The applets were written in Java 1.0, which is a language that is not generally supported by modern browsers. I unfortunately do not have the time available to port them to a more modern language, but I have no objection to others using the code (or the concept) for their own purposes.
31 May, 2025 at 1:44 pm
Anonymous
Hello Tao!
If you’re able to share the source code, I’d be more than happy to help migrate it to a more recent version of Java!
[The source code is available at https://www.math.ucla.edu/~tao/java/ -T.]
5 April, 2026 at 7:35 am
Orlando Ramirez Rodriguez
Hi, esteemed Professor Tao.
I am a mathematics teacher in Colombia, at both the secondary and university levels, and I’ve been following you on this platform you’ve created to share knowledge. I admire you for everything you do. Congratulations.
I’ve also created some GeoGebra applets, which are used to model certain concepts. Here I’m sharing one about the constant π.
Applet_pi: https://www.geogebra.org/m/txsajjbp