The Re-Invention of Mathematics.

Question 1

Vieta

Answer 1

1500s - invented the New Algebra!
Introduced the equals sign and cosa the unknown.
(Vieta sounds like a huge leap)

Question 2

Descartes

Answer 2

1650s - invented the New Geometry!
Equations of curves, coordinates.
Unified geometry and algebra.
(think Cartesian)

Question 3

Cardanno

Answer 3

Solved the cubic! Shortly thereafter, the quartic was solved.
(think spice upon Descartes)

Question 4

Galileo

Answer 4

Invented New Physics! I think.

Besides all the astronomy stuff, he began working on a way to find a tangent line to a point.

Question 5

Describe the Age of Algebra

Answer 5

An era brought upon by Vieta’s New Arithmetic and Descartes’ New Geometry.

Question 6

Describe the Age of Calculus

Answer 6

An era brought upon by a “thinktank” composed of Descartes, Galileo, Fermat, Newton, and Leibnitz
(Newton and Leibnitz have separate notations, and Descartes and Galileo were pioneers)

Question 7

What were Zeno’s Paradoxii?

Answer 7

Two paradoxes that stood in the way of the Age of Calculus.

1) The flying arrow never moves.
2) A point has no width.

Question 8

What’s the difference between an antiderivative/integral and a sum?

Answer 8

An anti-derivative is the definition of a derivative, but backwards.
A sum is when you add a bunch of little things.
The word you use really depends on the context.

Question 9

What was the first calculus formula?

Answer 9

Sum of dx from a to b is b - a! Yaaay!

Question 10

What were the differences between Leibnitz’ use of calculus and Newton’s use of calculus?

Answer 10

Leibnitz loved algebra. (It shows in his notation)

Newton wanted calculus for physics.

Question 11

Who’s Euler.

Answer 11

A very very very active mathematician.
Picked all the raisins out of the mathematical cake.
800 pages of new math per year.

Question 12

What was the big crisis in 1800?

Answer 12

Infinite series!

Calculus began returning nonsensical answers.

Question 13

Who’s Bishop Berkely?

Answer 13

1720s, questioned fluxions and infinitesimals.

Question 14

Who used fluxions and who used infintesimals?

Answer 14

Newton used fluxions and Leibnitz used infintesimals.

makes sense, infinitesimals smell like algebra and fluxions sound like physics

Question 15

What’s the difference between mathematics and science and physics?

Answer 15

Real world: Start with the real world and churn things we know to be true.
Mathematics: Start with complete doubt and churn out absolute truth! (epistemology)