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# The Journey of Mathematics

This is a presentation on the discovery and the development of the subject of Mathematics, through five thousand years! However, do not present this unless you're me - there are parts that need my transcript.
by

## Roger Wilshaw

on 4 May 2015

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#### Transcript of The Journey of Mathematics

The Journey of Maths
Egypt
3000 BC*
3000 BC*
The Egyptian Number System
Multiplying
Fractions
Mesopotamia (now called Iraq)
1500 BC*
1500 BC*
1 10
0
India
600 BC*
600 BC*
Greece
550 BC*
550 BC*
a²=b²+c²
a
b
c
China
Dates with asterisks (*) after them are approximate.
Pictures are from other sources unless otherwise specified. I take no credit for those photos.
Persia (now called Iran)
Al-Kitāb al-mukhtasar fī hīsāb al-ğabr wa’l-muqābala
The Compendious Book on Calculation by Completion and Balancing
Italy
France
England
Germany
Descartes' Co-ordinates
Calculus
60s
1s
3600s
60s
1s
Europe
Topology
Primes for Codes
1. The Continuum Hypothesis: there is no set whose size is strictly between that of the integers and that of the real numbers
2. Prove that the axioms of logic are consistent
3. Given two polyhedra of equal volume, can we always cut the first into finitely many pieces that can be reassembled to yield the second
4. Construct all metrics whose lines are geodesics
5. Are continuous groups automatically differential groups?
6. Axiomatise all of physics
7. Is ab always transcendental for algebraic a ≠ 0, 1 and irrational algebraic b?
8. The Riemann hypothesis: prove that the real part of any non-trivial zero of the Riemann zeta function is ½
9. Find the most general law of reciprocity theorem in any algebraic number field
10. Find an algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution
11. Solve quadratic fields with algebraic numerical coefficients
12. Extend the Kronecker-Weber theorem on abelian extensions of the rational numbers to any base number field
13. Solve all 7th-degree equations using functions of two variables
14. Prove the finiteness of certain systems of functions
15. Provide a rigorous foundation for Schubert's enumerative calculus
16. Study the topology of algebraic curves and surfaces
17. Express a definite rational function as a quotient of sums of squares
18. Is there a non-regular space-filling polyhedron? What is the densest sphere packing?
19. Are the solutions of Lagrangians always analytic?
20. Do all variational problems with certain boundary conditions have solutions?
21. Prove the existence of linear differential equations with a prescribedmonodromy group
22. Uniformization of analytic relations by means of automorphic forms
23. Extend the methods of the calculus of variations
8. The Riemann hypothesis: prove that the real part of any non-trivial zero of the Riemann zeta function is ½
NOW!
Egyptian numbers
Multiplying
Fractions
Place Value
The Sexagesimal System
The Placeholder Zero
The Real Zero
Pythagoras' Theorem
The Ten System
Algebra
Perspective
Co-ordinates
Calculus
Topology
Primes For Codes
Hilbert's Problems
Goodbye! :-)
these are my photos
these are my photos
Fascinating
Facts!
Fascinating
Fact No. 1
In Egypt, the 'unlucky' number 13 was a symbol of eternal life. They believed that life was in twelve stages; the thirteenth being immortal life.
Fascinating
Fact No. 2
The Mesopotamian 'Long Count' Calendar predicted that the world would end on the 21st of December last year - but luckily for us it was wrong!
Fascinating
Fact No. 3
Ancient China also liked the number 13. As it is pronounced 'shisan', it sounds extremely like the word for 'assured growth' or 'definitely vibrant'. Cool!
Fascinating
Fact No. 4
Did you know that until 1751, the British followed the 'Julian' Calendar, meaning that the New Year started on the 25th of May! Now everyone is on the modern 'Gregorian' Calendar.
Fascinating
Fact No. 5
In Britain, football shirts with numbers on were first worn in 1928, in the matches: Sheffield Wednesday vs Arsenal; and
Chelsea vs Swansea Town.
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