| 1. | " The detractor of the Kalam cosmological
argument thus finds himself shouldered with an enormous burden of proof
if he is to carry his objection based on the existence of mathematical
infinites:..."
| Source: | Craig, William Lane. "A swift and simple refutation of the Kalam cosmological argument?" Religious Studies 35.1 Mar. 1 1999: 57-58
 |
|
| 2. | "... to
satisfy their own curiosity rather than to please the teacher, a
phenomenon that seems to appear more often in workshops than during
other mathematical activities
* Increase in innovative thinking and creative inquiries, such as
balancing teddy-bear counters to..."
| Source: | Heuser, Daniel. "MATHEMATICS WORKSHOP: Mathematics Class Becomes Learner Centered" Teaching Children Mathematics 6.5 Jan. 1 2000: 288
|
|
| 3. | "
Now that the low-hanging fruits have been picked from the
mathematics tree, the remaining conjectures are requiring very long
proofs that are prone to error, both in their construction and in the
necessary checking by other mathematicians."
| Source: | Gualtieri, Devlin M. "Proof and truth in mathematics" Phi Kappa Phi Forum 83.4 Sept. 22 2003: 6-8
|
|
| 4. | "... arguments to the effect
that the arguments found in mathematics cannot reach an absolute truth,
but it is certainly possible, as demonstrated by the existence of Paul
Ernest's Social Constructivism as a Philosophy of Mathematics
(1998)."
| Source: | Franklin, James. "Imre Lakatos and Paul Feyerabend" New Criterion 18.9 May 1 2000: 74
|
|
| 5. | " The
study explored four issues: preservice teachers'
experiences/exposure to proof, their beliefs about what constitutes a
proof and the role of proof in mathematics, and their beliefs about when
proof should..."
| Source: | Mingus, Tabitha T. Y.,Grassl, Richard M. "Preservice Teacher Beliefs About Proofs" School Science and Mathematics 99.8 Dec. 1 1999: 438
|
|
| 6. | " In "The Role of Tasks in Developing Communities of
Mathematical Inquiry," researchers report their analyses of
children's responses to a mathematically rich task and suggest how
to select and use such tasks to stimulate children's mathematical
inquiry."
| Source: | Fuys, David,Huinker, DeAnn. "Children as Mathematicians" Teaching Children Mathematics 6.6 Feb. 1 2000: 341
|
|
| 7. | "... * Using multiple representations (literal, symbolic, graphic) to
represent problems and solutions;
* Understanding the role of definitions, proofs, and
counterexamples in mathematical reasoning; constructing simple proofs;
* Using the special symbols of mathematics correctly..."
| Source: | . "Ready or not: mathematics benchmarks from the American Diploma Project" Peer Review 6.4 June 22 2004: 22-26
|
|
| 8. | "
While appreciating the powerful role that curriculum materials can
play in extending preservice teachers' mathematical conceptions, we
must also bear in mind..."
| Source: | LLOYD, GWENDOLYN M.,FRYKHOLM, JEFFREY A. "HOW INNOVATIVE MIDDLE SCHOOL MATHEMATICS CAN CHANGE PROSPECTIVE ELEMENTARY TEACHERS' CONCEPTIONS" Education 120.3 Mar. 22 2000: 575
|
|
| 9. | "... programs from prekindergarten through grade 12
should enable all students to--
* recognize reasoning and proof as fundamental aspects of
mathematics;
* make and investigate mathematical conjectures;
* develop and evaluate mathematical arguments and proofs;
* select and use..."
| Source: | Niess, Margaret L.,Lederman, Norman G. "A Call for Action With the Principles and Standards for School Mathematics" School Science and Mathematics 100.5 May 1 2000: 256
|
|
| 10. | "
The National Council of Teachers of Mathematics (NCTM, 1991) has
called on teachers to facilitate students' deep understanding of
mathematical concepts rather than apply old models that primarily
emphasize mathematical manipulation and formal proof development."
| Source: | Schwalbach, Eileen M.,Dosemagen, Debra M. "Developing Student Understanding: Contextualizing Calculus Concepts" School Science and Mathematics 100.2 Feb. 1 2000: 90
|
|
| 11. | "
The proof of the theorem "in full generality represents a
milestone in algebraic number theory," mathematician Jonathan
Rogawski of the University of California, Los Angeles remarks in the
January NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY.
"
| Source: | I.P. "Squares, primes, and proofs" Science News 157.3 Jan. 15 2000: 47
|
|
| 12. | "
Mathematics & Computers
* Four mathematicians proved the Taniyama-Shimura conjecture
regarding elliptical curves, extending work that had previously led to a
proof of Fermat's last theorem (156: 221).
* A hexagonal lattice represents the..."
| Source: | Miller, Julie Ann. "SCIENCE NEWS of the Year" Science News Dec. 18 1999: 392
|
|
| 13. | " No one has ever
discovered Fermat's original proof (if it ever existed) and the
theorem remained unsolved until 1993 when Andrew Wiles, a Princeton
professor, stunned the international mathematics community when he
announced that he had a proof."
| Source: | Levinson, Martin H. "Did Nike Say to `Just Do It" ETC.: A Review of General Semantics v55.n2 June 22 1998: 227-229
|
|
| 14. | "
Mathematical proofs of conjectures, however, require more than
overwhelming numerical evidence."
| Source: | Peterson, I. "Prime conjecture verified to new heights" Science News 158.7 Aug. 12 2000: 103
|
|
| 15. | "... The play focuses on a great mathematics professor's
daughter who, just as those around her begin to have doubts about her
sanity, unearths a saving validation in the form of a notebook
containing what may be her father's greatest proof."
| Source: | Congdon, Constance. "God Is in the Numbers" American Theatre 17.7 Sept. 1 2000: 72
|
|
| 16. | " As
Timothy J. Reiss demonstrates, Galileo ultimately concludes that the
only way of achieving certain proof is through mathematics. [31] Thus,
in..."
| Source: | SPILLER, ELIZABETH A. "Reading through Galileo's Telescope. Margaret Cavendish and the Experience of Reading [*]" Renaissance Quarterly 53.1 Mar. 22 2000: 192
|
|
| 17. | " Polya emphasized clear understanding and
presentation of mathematical proofs, so it is appropriate to review his
biography with Mathematical Fallacies, Flaws, and Flimflam, another
title in the same series."
| Source: | Thompson, William J. "How Not to Solve It" American Scientist 88.5 Sept. 1 2000: 465
|
|
| 18. | " Similar considerations explain Plateau's other
principle, although a fully rigorous mathematical proof of them was not
given until 1976 by the Rutgers University mathematician Jean Taylor."
| Source: | Klarreich, Erica G. "Foams and Honeycombs" American Scientist 88.2 Mar. 1 2000: 152
|
|
| 19. | " In New York, at the
Manhattan Theatre Club, we've lately seen Shelagh Stevenson's
An Experiment With an Air Pump (about the ethics of medical
experimentation), Arthur Kopit's Y2K (about computer technology)
and David Auburn's Proof (about mathematics)."
| Source: | ROCAMORA, CAROL. "Scientific Dramaturgy" Nation 270.22 June 5 2000: 49
|
|
| 20. | " Mathematicians often formulate and extend their
"hunches" to check their conjectures before they offer
deductive proof of the validity of these conjectures as a final step."
| Source: | Steele, Diana F. "Enthusiastic Voices from YOUNG MATHEMATICIANS" Teaching Children Mathematics 6.7 Mar. 1 2000: 464
|
|
| 21. | " Accordingly, the summed elasticities of transitions coming
into and going out of a node are identical (see van Groenendael et al.
[1994] for mathematical proof),..."
| Source: | KROON, HANS DE,GROENENDAEL, JAN VAN,EHRLEN, JOHAN. "ELASTICITIES A REVIEW OF METHODS AND MODEL LIMITATIONS" Ecology 81.3 Mar. 1 2000: 607
|
|
| 22. | "
For those who think all mathematical proofs are boring, Appendix A
nicely proves that Winston Churchill was a carrot."
| Source: | Hammel, Sara,Stratton, David. "Top Picks" U.S. News & World Report 128.8 Feb. 28 2000: 86
|
|
| 23. | "... See for example, McCloskey (1996: chapter 3), who argues that
the current focus by economists on logic and mathematical proofs
relating assumptions to predictions serves to remove economists from a
concern for issues flowing from economic reality."
| Source: | Altman, Morris. "The Methodology of Economics and the Survival Principle Revisited and Revised: Some Welfare and Public Policy Implications of Modeling the Economic Agent" Review of Social Economy 57.4 Dec. 1 1999: 427
|
|
| 24. | " The novelty of Pyatt's
formula is that it can be exactly decomposed into three separable
components if the population is divided into classes (for more
discussion and mathematical proofs, see Yao [1998])."
| Source: | Yao, Shujie. "Economic growth, income inequality and poverty in China under economic reforms" Journal of Development Studies 35.6 Aug. 1 1999: 104-106
|
|
| 25. | " A concert pianist, he is also the
author of three books on the history and philosophy of mathematics and
science: "Abel's Proof" (2003), "Seeing Double"
(2002), and "Labyrinth" (2000).
"
| Source: | Pesic, Peter. "The bell & the buzzer: on the meaning of science" Daedalus 132.4 Sept. 22 2003: 35-45
|
|
back to top