Lesson 17: Modern Algebra and the Future of Mathematics Quiz

How can mathematics be classified according to its subject matter?

• By its taste, smell, and texture

• By its subject matter, questions, and techniques

• By its color, shape, and size

• By its location, temperature, and humidity

What is the term used to refer to the study of mathematical structures such as groups, rings, vector spaces, and algebras using the axiomatic method?

• Concrete Algebra

• Modern Algebra

• Ancient Algebra

• Traditional Algebra

Who influenced the 20th-century mathematics with his 23 problems lecture in 1900?

• Emil Aron

• Henri Poincaré

• Emmy Noether

• David Hilbert

What is the main tool kit of an algebraist?

• Basic algebra, linear algebra, and general knowledge of history

• Facility with programming and use of mathematical software

• General knowledge of maps, morphisms, and some category theory

• All of the above

What is the significance of the future of mathematics according to Henri Poincaré?

• It lies in the practical consequences of mathematical theorems

• It lies in the significance of the mathematical ideas which it connects

• It lies in the study of its history and its present state

• It lies in the size of the community and mathematical research activity

What did Stanislaw Ulam say when asked about the future of mathematics during his lecture?

• He gave a completely mundane mathematical talk

• He discussed the influence of computers and information technology

• He talked about problems, lemmas, theorems, and conjectures

• He insisted that the future would only come at a later time

What is the title of the celebrated essay by mathematical biologist Joel Cohen?

• The Future of Mathematics

• A Mathematician’s Apology

• Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

• The Two Cultures of Mathematics

What is the main motivation shaping the future of math according to the text?

• None of the above

• Desire to clarify, update and extrapolate the way that sub-disciplines relate to the general discipline of math

• Both A and B

• Desire to set a research agenda to direct efforts to specific problems

What did Ulam insist when asked about the future of mathematics during his lecture?

• These questions were misguided since the future would only come at a later time

• He talked about problems, lemmas, theorems, and conjectures

• He gave a completely mundane mathematical talk

• He discussed the influence of computers and information technology

What is the future of math shaped by according to the text?

• None of the above

• Both A and B

• Highly significant developments in math

• Unexpected union between its diverse parts