MF77: Object-oriented versus expression-oriented mathematics

[omicron8251]

That is what's known as the mathematical seed that blossoms.

[DanPartelly]

Really cool how simple you can extend Int B to present partial derivatives and their directional generalization.

[peterhi503]

Wldberger, what led you to interpretation C? It seems non-obvious and quite important. Are there any other useful or interesting interpretations? Hardy.

[njwildberger]

@peterhi503 Hi Hardy, Interpretation C arises naturally both from a geometrical and a linear algebra perspective. It is intimately connected with a crucial idea of projective geometry called polarity, and with the linear algebra notion of inner product, or dot product, or scalar product, or bilinear form. If you have done some Linear Algebra, you can think about the difference between Int A and Int C as comparable to the difference between quadratic and bilinear forms.

[njwildberger]

@peterhi503 I should also have mentioned that indeed there are at least two further useful and interesting interpretations of the unit circle. One of these involves a projective interpretation, and the other extends things to the rational complex numbers. I'll talk about both of these things later on.

[redpictureLA]

Can't wait for MF78. Nice cliffhanger!

[njwildberger]

Thanks everyone for the nice comments, appreciated!

[peterhi503]

Wildberger, your work continues to be first rate. You may be the finest expositor of mathematics of whom I am aware today. Well done, man. Hardy.

[Toxie207]

I felt something click in my brain when I got to around 30:00! Thanks.

[Lewclan]

Fantastic video. Thank for this

[MrSdplissken]

Dr in what ways whould this be used Pilots Astronauts?

as far as jobs go

[QuickR]

Another great lecture.  Thank you.

[danodet]

Math is a one player game with rules so well defined that a computer can referee a game.

[njwildberger]

@danodet I like it!

[Tr3xKuro]

Is this 76 or 77?  I didn't see 76 on my front page

[Waranle]

Thank you Dr Wildberger