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Mathematics

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ULearnBig
10 Views · 11 days ago

The documentary film "History of Mathematics" takes viewers on a fascinating journey through time to explore the evolution of mathematics in various civilizations. From ancient Egypt and Mesopotamia to Greece, China, India, and the Middle East, the film highlights the contributions of prominent mathematicians and their impact on the field.

The film delves into the use of decimal systems, the invention of the number zero and the concept of infinity, the creation of algebra, and the spread of Eastern knowledge to the West. With a combination of historical footage, expert interviews, and breathtaking visuals, this documentary brings to life the rich history of mathematics and its role in shaping the world we live in today..

1:20 - Mathematics in Egypt
19:30 - Mathematics in Mesopotamia
35:21 - Mathematics in Greece
54:21 - Mathematics in China
1:10:08 - Mathematics in India
1:35:36 - Mathematics in Europe

#mathematics #math #history #documentary

ULearnBig
6 Views · 21 days ago

Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org..../the-biggest-discove

00:05 Ramsey Numbers
One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935.
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../after-nearly-a-cent

06:21 Aperiodic Monotile
The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation.
CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com..../2023/03/23/its-a-sh
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../hobbyist-finds-math
- Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html

14:20 Three Arithmetic Progressions
Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern.
- Original story with links to research papers can be found here: https://www.quantamagazine.org..../surprise-computer-s

- VISIT our Website: https://www.quantamagazine.org

- LIKE us on Facebook: https://www.facebook.com/QuantaNews

- FOLLOW us Twitter: https://twitter.com/QuantaMagazine

Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/

ULearnBig
4 Views · 1 month ago

Adding Fractions?
Subtracting Fractions?
Multiplying Fractions?
Dividing Fractions?
Mixed Numbers?
Simplifying Fractions?

It's all here.

To support tecmath on Patreon: https://www.patreon.com/tecmath
It really helps and is appreciated!

ULearnBig
3 Views · 2 months ago

The most famous equation in finance, the Black-Scholes/Merton equation, came from physics. It launched an industry worth trillions of dollars and led to the world’s best investments. Go to https://www.eightsleep.com/veritasium and use the code Veritasium for $200 off your Pod Cover.

Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
https://ve42.co/PatreonDEB

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - https://ve42.co/SnatomsV

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A huge thank you to Prof. Andrew Lo (MIT) for speaking with us and helping with the script.

We would also like to thank the following:
Prof. Amanda Turner (University of Leeds)
Owen Maher (Electrify Video Partners)

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References:

The Man Who Solved the Market: How Jim Simons launched the quant revolution, Gregory Zuckerman. Penguin Publishing Group. - https://ve42.co/GZuckerman

The Physics of Finance: Predicting the Unpredictable: Can Science Beat the Market? James Owen Weatherall. Short Books. - https://ve42.co/FinancePhysics

The Statistical Mechanics of Financial Markets, J.Voigt. Springer. - https://ve42.co/Springer

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654. - https://ve42.co/BlackScholes

Cornell, B. (2020). Medallion fund: The ultimate counterexample?. The Journal of Portfolio Management, 46(4), 156-159. - https://ve42.co/Medallion

Images & Video:
Ed Thorp on The Tim Ferris Show - https://www.youtube.com/watch?v=CNvz91Jyzbg
Jim Simons on TED - https://www.youtube.com/watch?v=U5kIdtMJGc8
Jim Simons on Numberphile - https://www.youtube.com/watch?v=QNznD9hMEh0

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Special thanks to our Patreon supporters:
Adam Foreman, Anton Ragin, Balkrishna Heroor, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Diffbot, Evgeny Skvortsov, Garrett Mueller, Gnare, I.H., John H. Austin, Jr. ,john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures


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Directed by Will Wood and Derek Muller
Written by Will Wood, Emily Zhang, Petr Lebedev and Derek Muller
Camera operation by Raquel Nuno
Additional research by Gregor Čavlović
Edited by Jack Saxon and Trenton Oliver
Animated by Fabio Albertelli, Jakub Misiek, Ivy Tello, David Szakaly and Will Wood
Produced by Will Wood, Han Evans and Derek Muller

Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

ULearnBig
2 Views · 2 months ago

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015

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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman
SFX & Music: Jonny Hyman
Camerapeople: Derek Muller, Raquel Nuno
Editors: Derek Muller
Producers: Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett

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