Channel Description: Insights into Mathematics

Welcome! This channel aims to lay out a good part of modern mathematics, from the ground up. It provides careful and novel treatments of a wide spectrum of mathematical topics, from Rational Trigonometry to Differential Geometry to Probability and Statistics.

The video includes some biographical info about me, and summarizes my orientation towards modern pure mathematics and mathematics education.

I then give a brief description of the Playlists: ElemMathK-6, MathHistory, WildTrig, FamousMathProbs, WildLinAlg, ProbStats, UnivHypGeom, DiffGeom, MathFoundations and MathSeminars.

I hope that if you have an interest in mathematics or a desire to appreciate it at a deeper level, you will find something here to engage your interest, with new videos appearing regularly each week. Become a subscriber, and take your understanding of mathematics to a new level! [A correction: I have been at UNSW since 1990, not 2000!--how time flies.]

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Here are the Insights into Mathematics Playlists:

Here are the Wild Egg Maths Playlists (some available only to Members!)

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[crittinger]

I left university mathematics unsatisfied, and have resolved to learn it on my own. Your channel has been a big help and a source of much inspiration for me. I tutor mathematics and am always trying to be better at teaching, so I thank you (and YouTube) for this

[MrJosephArthur]

An admirable intellectual effort of Prof. Wildberger in order to develop, expose and teach mathematics for the world. By applying his mathematical personality and his own criteria on understanding many fundamental concepts of mathematics, Prof. Wildberger is creating a sort of new school of mathematics for the world. All people who are interested in pure and/or applied mathematics will find this site extremely interesting for their intellectual and/or practical purposes. At least, for all those who feel an emotional intimate pleasure of doing mathematics.

[njwildberger]

I would suggest that philosophy might also contribute in clarifying how it is that the last few generations have willfully fooled themselves into believing this sugar coated version of mathematics, where concepts are brought into being by essentially grammatical constructions, and where the obvious divergences between theory and practice are simply ignored. How can we have so effectively fooled ourselves?? Maybe this is a question of sociology too.

[njwildberger]

Thanks for the nice comment. I do hope to do something in the direction of group theory some day!

[njwildberger]

Nice to hear from you--great that you are dedicated to learning more.

[njwildberger]

It's a pleasure. Thanks for all your contributions to the channel.

[njwildberger]

It will still be complicated, but it will open quite a few new avenues for amateurs. In fact the mathematics of this coming century will have lots of opportunities for amateurs to grapple with--particularly the areas of geometry opened up by this channel!

[TimeWithinTime]

Prof. Wildberger, I want to thank you for having such a valuable channel for people to benefit from.

[postbodzapism]

I got into your channel because of your wildtrig video about projective geometry, and your other videos have turned my interest from chemistry back to mathematics. Thank you for showing us that mathematics is not just about drilling and exercising and its rigour can be questioned. You have made me love maths so much!

[njwildberger]

That's an excellent question. Categorical thinking is very powerful and general, and is an important tool for a modern mathematician. On the other hand, speaking honestly, the current foundations for that subject, currently residing in `set theory', are logically a shambles. So there is a lot of work to be done in straightening out that theory.

I believe computer scientists are the ones to help with that: they like to think categorically too, in a way.

[njwildberger]

Maybe not more difficult, but perhaps more advanced, and certainly the novelty aspect can prove a challenge for viewers with traditional orientations.

[felixgraphx]

Got hooked on this channel because of the math history playlist. Math is so much easier to grasp and remember when you can relate its parts to stories, historical events and context. Many thanks again!

[njwildberger]

Hi Paul, By the new year I should be back with more in the MathFoundations series. Also the Basel problem is one I will tackle eventually in the FamousMathProbs series. My take on it might not be the standard one though.

[peterhi]

Thank you for your contributions, Norman. Your videos are uniformly outstanding and show what an excellent teacher and human being you are. Best.

[njwildberger]

Thanks Pavlos. Nice to hear that there are philosophers opposed to the imaginative meanderings of infinite set theory and so-called real numbers.

[pklimatsakis]

Dear Professor,

I am indebted to you for your contributions to the understanding of mathematics by a more general public. As a philosopher of Hegelian descent I share your disinclination to the notions of the real number and foremost of the infinite by modern mathematics (Cantors infinite sets). As a Greek I also thank you also for the presentation of Greek Mathematics in the HistofMath Course. Waiting for its continuance. all in all GREAT WORK!

[njwildberger]

Hi, Yes I will be talking about Godel's work, certainly in the MathFoundations series eventually, but likely also in the FamousMathProbs series. I think his work has been misconstrued by many as implying that mathematics swims in a sea of ambiguity (i.e. it all depends on your assumptions/axioms). This is a kind of thinking I need to reverse.

[njwildberger]

Thanks for the comment. As for the logical difficulties in pure mathematics re the continuum and real numbers: while applied maths is fine, the theoretical development of pure maths can see big improvements once these logical difficulties are removed. For example, in geometry, rational trigonometry opens the doors to a new way of understanding Euclidean geometry, it allows the discovery of chromogeometry, which is very very cool, and it motivates universal hyperbolic geometry--much better!

[JPaulDiLucci]

This is channel is what YT was made for! I am very much looking forward to the continuation of the Foundations series and (hopefully) Euler's solution to the Basel Problem in FamousMathProbs. Thanks for sharing your wisdom Professor.

[sijojosephdr]

I take this opportunity to be the first person to make a comment on this video. Thank you professor. I am a regular viewer of your video, always I am interested in mathematics, for me it is a blessing that if I get professors like you. I think that your lectures have some sorts of magical power.