^TagMathematics

^{Type
post

Author
Jonathan Bartlett
Date
March 21, 2022

Categorized
Education, Mathematics

Tagged
Mathematics, mathematics education}

What Do We Want With Mathematics Curriculum?

_{If we are going to dedicate such a large portion of our children's lives to learning mathematics, we had better know why} _{Jonathan Bartlett

March 21, 2022

Education, Mathematics}

Modern policy discussions in America almost always leave out the biggest question – why are we doing what we are doing in the first place? Leaving out first principles always leaves people trying to find the most practical way to accomplish nothing in particular. We have become accustomed to not asking questions about first principles because they always sound too doctrinaire, but then we wind up, at best, making the misplaced assumption that everyone is reaching for the same goal, or, far worse, viewing the activities themselves as the goals. One place where this problem repeatedly rears its ugly head is education, and especially mathematics education. Why are we teaching math? What do we want people to get out of…

child hands showing a colorful 123 numbers agains wooden table. Concept of Child education, learning mathematics and counting

^{Type
post

Author
Jonathan Bartlett
Date
March 31, 2021

Categorized
Education, Mathematics

Tagged
Common Core math, math curriculum, Mathematics, mathematics education, Mathematics education reform, New Math}

The Fundamental Problem With Common Core Math

_{Intuition relies on skill, not the other way around} _{Jonathan Bartlett

March 31, 2021

Education, Mathematics}

In 2010, a bold effort to reform math curriculum was adopted by the majority of the United States. Known as “Common Core Math,” the goal of this endeavor was to establish a common foundation of mathematics education across the country, and to help bolster not only students’ mathematical abilities, but also their mathematical intuition. The goal was to help students think about math more deeply, believing that this will help them work with mathematics better in later years. Before discussing problems with this approach, I want to say that I appreciate the idea of helping students think more deeply about mathematics. After years and years and years of mathematics education, many students wind up thinking about mathematics as merely a set…

group of school kids raising hands in classroom

^{Type
post

Author
Jonathan Bartlett
Date
March 30, 2021

Categorized
Education, Mathematics

Tagged
education, math facts, Mathematics, mathematics education, number knock-out, skip counting, speed of recall, speed testing}

Practicing the Basics: Teaching Math Facts in the Classroom

_{How to help students make deeper connections within mathematics with creative games.} _{Jonathan Bartlett

March 30, 2021

Education, Mathematics}

Many people learn to hate math early on. One of the places where people learn to hate math first is in high-stakes speed testing for math facts. This has caused quite a bit of angst in mathematics education for people on both sides of this issue. On the one hand, some have advocated for getting rid of math facts memorization altogether. On the other hand, others have doubled-down, saying that we need speed tests in order to make sure that the cognitive load of arithmetic is limited for later mathematics work. While I fall more into the latter camp than the former, I do think that a more balanced approach to mathematics education may help students in the long run. …

Silhouette of a man, with thoughts in the form of physico-mathematical formulas. The concept of scientific and education topics.

^{Type
podcast

Author
Robert J. Marks
Date
March 18, 2021

Tagged
academia, Artificial Intelligence, Fermat's Last Theorem, Mathematics, scholarship}

The Chaitin Interview III: The Changing Landscape for Mathematics

_{Robert J. Marks

March 18, 2021}

How are the fields of mathematics and academic research different today compared to years past? In this week’s podcast, Robert J. Marks and Gregory Chaitin discuss the challenges many mathematicians face today and the unfortunate trend toward bureaucracy that makes academic research difficult. Dropping names of mathematical geniuses past and present, they explore how technology and artificial intelligence are changing…

Close up cute little child girl spinning a coin to make decision. Heads or tails game.

^{Type
podcast

Author
Robert J. Marks
Date
March 11, 2021

Tagged
Algorithmic Information Theory, Computer science, Fermat's Last Theorem, Gregory Chaitin, Kurt Gödel, Mathematics, Randomness}

The Chaitin Interview II: Defining Randomness

_{Robert J. Marks

March 11, 2021}

In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Listen in as Robert J. Marks explores that paper with Chaitin, covering Chaitin’s definition of randomness and his philosophical interest in algorithmic information theory. Show Notes 00:27…

^{Type
post

Author
Jonathan Bartlett
Date
March 8, 2021

Categorized
Mathematics

Tagged
Algebra, calculus, George Berkeley (1685–1753), Mathematics}

The Needless Complexity of Modern Calculus

_{How 18th century mathematicians complicated calculus to avoid the criticisms of a bishop} _{Jonathan Bartlett

March 8, 2021

Mathematics}

Would you be surprised if I told you that the essentials of calculus are actually very straightforward and simple? Read More ›

Close-up Shot of a Hand Holding Chalk and Writing Complex and Sophisticated Mathematical Formula/ Equation on the Blackboard.

^{Type
podcast

Author
Robert J. Marks
Date
March 4, 2021

Tagged
Algorithmic Information Theory, Computer science, Gregory Chaitin, Kurt Gödel, Leonard Euler, Mathematics}

The Chaitin Interview I: Chaitin Chats with Kurt Gödel

_{Robert J. Marks

March 4, 2021}

In this week’s Mind Matters episode, Robert J. Marks begins a conversation with mathematician and computer scientist Gregory Chaitin. The two discuss Chaitin’s beginnings in computer science, his thoughts on historic scientists in his field such as Leonard Euler and Kurt Gödel, and even the story of how a cold call to Gödel almost led to Chaitin meeting the famed…

The robot writes with a pen and looks at the computer monitor. Artificial Intelligence

^{Type
podcast

Author
Robert J. Marks
Date
September 24, 2020

Tagged
Abstract thought, Ada Lovelace, Alan Turing, Algorithm-of-the-Gaps, AlphaGo, Charles Babbage, Claude Shannon, Cognition, computer, Computers, Consciousness, Creativity, David Gelernter, disjunctive syllogism, Eugene Goostman, Gottfried Wilhelm Leibniz, Kurt Gödel, Language, Lovelace test, Marcel Proust, Mathematics, Natural Language Generation, Natural Language Processing, non-algorithmic, novels, ontological argument, ontological proof, Ray Kurzweil, Saint Anselm, Selmer Bringsjord, Singularity, Sports, Theorems, Turing Test}

Bingecast: Selmer Bringsjord on the Lovelace Test

_{Robert J. Marks

September 24, 2020}

The Turing test, developed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behaviour indistinguishable from a human. Many think that Turing’s proposal for intelligence, especially creativity, has been proven inadequate. Is the Lovelace test a better alternative? What are the capabilities and limitations of AI? Robert J. Marks and Dr. Selmer Bringsjord discuss…

Groupe de Bonobos autour d'un hôtel à insectes

^{Type
post

Author
Michael Egnor
Date
July 12, 2020

Categorized
Mathematics, Natural Intelligence, Philosophy of Mind

Tagged
___longform, Abstractions, Animal Intelligence, Bonobos, Designators, Featured, Gay A. Bradshaw, Language, Mathematics, Sue Savage-Rumbaugh, symbols}

Can Animal Minds Rival Humans Under the Right Circumstances?

_{Are we just not being fair to animals, as some researchers think?} _{Michael Egnor

July 12, 2020

Mathematics, Natural Intelligence, Philosophy of Mind}

In 2007, Sue Savage-Rumbaugh, a psychologist and primatologist , published a paper in the Journal of Applied Animal Welfare Science with a remarkable citation: Sue Savage-Rumbaugh, Kanzi Wamba, Panbanisha Wamba, and Nyota Wamba, “Welfare of Apes in Captive Environments: Comments on, and by, a Specific Group of Apes,” Journal of Applied Animal Welfare Science 10:1 (2007): 7–19. What is remarkable about the paper is not the text but the authorship statement. Kanzi, Panbanisha, and Nyota Wamba are not co-author colleagues—they’re apes, bonobos to be specific. Dr. Savage-Rumbaugh (right) is a controversial scientist who believes that animals have intellectual powers that can, under the right circumstances, rival the human intellect. She included her ape subjects as co-authors on the paper because…

If Then logic statement written in white chalk on a black chalkboard isolated on white

^{Type
post

Author
News
Date
May 10, 2020

Categorized
Artificial Intelligence, Mathematics, Religion

Tagged
___longform, Featured, Formal logic, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, Rene Descartes, Robert J. Marks, Saint Anselm, Selmer Bringsjord}

Gödel and God: A Surprising History

_{A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God} _{News

May 10, 2020

Artificial Intelligence, Mathematics, Religion}

In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test.

^{Type
podcast

Author
Robert J. Marks
Date
May 7, 2020

Tagged
disjunctive syllogism, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, ontological argument, ontological proof, Saint Anselm, Selmer Bringsjord, Theorems}

Kurt Gödel’s Proof of the Existence of God

_{Robert J. Marks

May 7, 2020}

Kurt Gödel toppled a tall tower of mathematical reasoning with publication of his work showing no formal system of math could be both complete and consistent. He also gave a mathematical proof of the existence of God. Is Gödel’s proof valid? Robert J. Marks and Dr. Selmer Bringsjord discuss mathematics, Kurt Gödel, and the ontological argument. Show Notes 01:05 |…

^{Type
post

Author
Jonathan Bartlett
Date
October 4, 2019

Categorized
Education

Tagged
Curves, Mathematics}

Don’t Leave Home Without These Three Curves

_{Three mathematical curves explain a lot of what happens—and doesn’t happen—in everyday life} _{Jonathan Bartlett

October 4, 2019

Education}

One of the problems with modern secondary mathematics education is that it teaches lots of details about how to solve problems but provides very little insight into how to understand problems. You may have learned to solve a quadratic equation but you may not have learned what life situations generate a quadratic equation.

^{Type
post

Author
Jonathan Bartlett
Date
August 19, 2019

Categorized
Education

Tagged
calculus, Calculus from the Ground Up (book), Mathematics}

Doing the Impossible: A Step-by-Step Guide

_{Often, in life as in calculus, when our implicit assumptions as to why something can’t be done are made explicit, they can be disproven} _{Jonathan Bartlett

August 19, 2019

Education}

Calculus textbooks are the most dry and boring presentations of mathematics I have ever seen, even though calculus offers some of the most amazing insights. Unfortunately, most mathematics texts teach only the mathematics, never the insights. Read More ›

Detail of an old office machine used for calculations

^{Type
post

Author
Jonathan Bartlett
Date
June 8, 2019

Categorized
Artificial Intelligence, Machine Learning

Tagged
History of Ideas, Mathematics}

Machine Learning Dates Back To at Least 300 BC

_{The key to machine learning is not machines but mathematics} _{Jonathan Bartlett

June 8, 2019

Artificial Intelligence, Machine Learning}

Machine learning is not a new technique, but is simply a modern extension of a tool that we have had in our toolbox since the days of the Babylonians. It continues to serve us well to help us extrapolate our data to estimate the value of unknown results and to help find the signal in noisy data.

^{Type
post

Author
News
Date
April 10, 2019

Categorized
Mathematics, Work

Tagged
calculus, education, Jonathan Bartlett, Mathematics, philosophy of math, presuppositions}

Walter Bradley Center Fellow Discovers Longstanding Flaw in an Aspect of Elementary Calculus

_{The flaw doesn't lead directly to wrong answers but it does create confusion} _{News

April 10, 2019

Mathematics, Work}

The lead author, Jonathan Bartlett, noted that the likely source of the bad notation was a philosophical issue. Because no one wanted to give differentials that same ontological status as other numbers, everyone presumed that the notational problems were simply the result of this fact, and no one pursued it further.

blue digital binary data on computer screen. Close-up shallow DOF

^{Type
post

Author
Eric Holloway
Date
March 28, 2019

Categorized
Artificial Intelligence, Philosophy of Mind

Tagged
halting oracle, Mathematics}

The Flawed Logic behind “Thinking” Computers, Part II

_{There is another way to prove a negative besides exhaustively enumerating the possibilities} _{Eric Holloway

March 28, 2019

Artificial Intelligence, Philosophy of Mind}

I am publishing, in three parts and with his permission, an exchange with Querius, who is looking for answers as to whether computers can someday think like people. In the first part, we discussed why human thinking cannot be indefinitely compressed. Here is the second part: Recapping for myself what I said in Part I and mulling it over: “If all symbol strings do have a shorter representation, then so must their shorter representations. Thus, we’d end up concluding that all symbol strings can be represented by nothing, which is incoherent.” Wait, I’m getting lost. “Therefore, we conclude that only some symbol strings have a compressed representation. As a consequence, compression intelligence is only true if the physical effects of…