Yet what's weirder than weird multiplication? Weird division!
Having initially studied economics at the University of Melbourne, Jonathan J. Crabtree is an autodidact, studying the history of mathematics since 1983.
His first paper was on the history of Euclid’s definition of multiplication ¹ whilst his next paper explored the writings of Descartes and Newton ². Another paper presented in Hungary ³ spanned the writings of Diophantus, Cardano, Euclid, Liu Hui and Brahmagupta.
Having reviewed original writings in Latin, Greek, Arabic and Sanskrit, Crabtree has also written magazine articles on mathematics history ⁴ and been a guest lecturer on the history of zero at Indian universities ⁵.
In 1968 at age 7 in Grade 2, Jonathan J. Crabtree noticed Euclid's definition of multiplication made no sense. Two added to itself three times is 8, not 6, as people have said for centuries. (HINT 2 added to itself once is 4.) Jonathan went on to explore hundreds of original source mathematics books & manuscripts spanning 16 languages. Euclid's definition of multiplication had been incorrectly translated into English in 1570 and was NEVER corrected!
RECENT ARTICLES & PAPERS
- A new reason negative multiplied by negative is positive Jonathan J Crabtree 2015 Vinculum 52 (3), 20
- A new model of multiplication via Euclid Jonathan J Crabtree 2016 Vinculum 53 (2), 16-18, 21
- Squaring the circle: A practical approach (i.e. via rope & straightedge) Jonathan J Crabtree 2016 Vinculum 53 (4), 7-9
- The Lost Logic of Elementary Mathematics and the Haberdasher who Kidnapped Kaizen Jonathan J Crabtree 2016 Mathematical Association of Victoria (MAV) Annual Conference 53, 98-106
- Fun in Podo’s Paddock: New Ways of Teaching Children the Laws of Sign for Multiplication and Division (and more!) Jonathan J Crabtree 2017 Challenges in Mathematics Education for the Next Decade. 14th International Conference of The Mathematics Education for the Future Project - Hungary.
- How mathematics teachers can explain multiplication and division in the manner of René Descartes and Isaac Newton. Jonathan J Crabtree 2017 Proceedings of the 26th Biennial Conference of the Australian Association of Mathematics Teachers.
Jonathan's paper and conference presentation titled, The Lost Logic of Elementary Mathematics reveals when why and how western mathematics education came to be filled with mis-truths, contradictions and inconsistencies.
1. Presented for and published 2016 in the Australian Proceedings of the Mathematical Association of Victoria (MAV) Annual Conference (double-blind reviewed).
2. Presented for and published 2017 in the Proceedings of the 26th Biennial Conference of the Australian Association of Mathematics Teachers.
3. Presented for and published 2017 by the 14th International Conference of the Mathematics Education for the Future Project.
4. Vinculum Magazine, published by the MAV (Mathematical Association of Victoria).
5. Jadavpur University Kolkata 2018 and Visva-Bharati University Santiniketan 2019.
- Free Gift for National Mathematics Day India 2018
- MISSING! Brahmagupta’s 18 Indian Laws of Maths
- Relaunching Indian Maths! (News & Interviews)
- Dear India, I'm visiting you to relaunch maths!
- Mathematics Education for the Future
- How to Rebuild Maths from Zero (Free Seminar)
- REGENESIS: Recompiling Math via Indian Logic
- Answer this. If 1⁰ = 1 and 1¹ = 1 does 0 = 1?
- Success Secrets for Teachers via China & India
- Fixing Flaws in Elementary Mathematics Teaching
- Missed math revealed! (Multiplication & Division)
- Multiplication via Descartes & Newton (Free Slides)
- The Lost Logic of Elementary Math
- Greening the Elementary Integer Math Matrix
- Saving Aha Moments from my Necktop Computer
- Multiplication ≠ Repeated Addition: Myth Busted!
- Reactions to my Mathematics Lessons, A-Z
- Questions to Santa about Multiplication
- Goldbach Conjecture FALSE for Big Numbers
- New Lattice/Gelosia Multiplication Template
- Multiplication after the War of Independence
- Multiplication – Addition = Keith Devlin
- Errata in the Multiplication/Exponentiation Data
- Truths of Math Mocked...
- Multiplication, in Italian, German & French
- MIRA IS DEAD! (Long Live PCV.)
- How al-Khwarizmi multiplied and divided fractions
- Ramanujan was wrong... 0/0 and the SCAM
- Pythagoras in the Chinese Chou Pei Suan Ching
- The first printed edition of Euclid's Elements
- Isaac Barrow's pocket size Elements of Euclid
- Versions of Euclid's multiplication definition
- How to memorise the world's largest known prime!
- A Radical '123' proposal for Real Numbers
- How to square a circle with peg & rope.
- Did Thales teach Pythagoras this?
- Theodorus of Cyrene, Pythagoras & Podo at Play!
- Why is negative left of zero & positive right?
- Why Positive Reals have 2 square roots
- The Financial 'Times Tables' on the Cartesian Plane
- Weirder than Weird Multiplication? Weird Division!
- Proofs for Multiplication on the Reals with a Circle
- The Master Key that Unlocks Science
- A proof ab = a added to itself b – 1 times
- 1565 Pierre Forcadel on Euclid's Multiplication
- 1555 Johann Scheubelon on Euclid's Multiplication
- 1543 Niccolo Tartaglia on Euclid's Multiplication
- Subtracting addition from multiplication...
- Why do numbers exist?
- The Oldest Manuscript of Euclid’s Elements 888CE
- Exponentiation as Repeated Multiplication
- Is this why are Chinese kids better at math?
- Henry the Haberdasher's Multiplication
- CCSS Drops Defective Definition of Multiplication
- When Multiplication is Repeated Subtraction