Edited by Eric Dietrich State University of New York at Binghamton About this topic Summary This category is about whether or not computers, robots, and software agents can literally be said to think. Humans think, chimps think, dogs think, cats and birds think. Is your computer thinking now? Perhaps only specially programmed computers think?

This is primarily a list of Greatest Mathematicians of the Past, but I use birth as an arbitrary cutoff, and two of the "Top " are still alive now.

Click here for a longer List of including many more 20th-century mathematicians.

Click for a discussion of certain omissions. Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different.

Please e-mail and tell me! Following are the top mathematicians in chronological birth-year order. By the way, the ranking assigned to a mathematician will appear if you place the cursor atop the name at the top of his mini-bio.

Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic.

The markings include six prime numbers 5, 7, 11, 13, 17, 19 in order, though this is probably coincidence. By years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms and trig functions, using a primitive place-value system in base 60, not The Greeks borrowed from Babylonian mathematics, which was the most advanced of any before the Greeks; but there is no ancient Babylonian mathematician whose name is known.

Also at least years ago, the Egyptian scribe Ahmes produced a famous manuscript now called the Rhind Papyrusitself a copy of a late Can machines think turing essay Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions.

Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. The Pyramids demonstrate that Egyptians were adept at geometry, though little written evidence survives. Babylon was much more advanced than Egypt at arithmetic and algebra; this was probably due, at least in part, to their place-value system.

But although their base system survives e. The Vedics understood relationships between geometry and arithmetic, developed astronomy, astrology, calendars, and used mathematical forms in some religious rituals.

The earliest mathematician to whom definite teachings can be ascribed was Lagadha, who apparently lived about BC and used geometry and elementary trigonometry for his astronomy.

Apastambha did work summarized below; other early Vedic mathematicians solved quadratic and simultaneous equations. Other early cultures also developed some mathematics.

The ancient Mayans apparently had a place-value system with zero before the Hindus did; Aztec architecture implies practical geometry skills. Ancient China certainly developed mathematics, in fact the first known proof of the Pythagorean Theorem is found in a Chinese book Zhoubi Suanjing which might have been written about BC.

Thales may have invented the notion of compass-and-straightedge construction. Thales was also an astronomer; he invented the day calendar, introduced the use of Ursa Minor for finding North, invented the gnomonic map projection the first of many methods known today to map part of the surface of a sphere to a plane, and is the first person believed to have correctly predicted a solar eclipse.

His theories of physics would seem quaint today, but he seems to have been the first to describe magnetism and static electricity. Aristotle said, "To Thales the primary question was not what do we know, but how do we know it.

It is said he once leased all available olive presses after predicting a good olive season; he did this not for the wealth itself, but as a demonstration of the use of intelligence in business.

Since his famous theorems of geometry were probably already known in ancient Babylon, his importance derives from imparting the notions of mathematical proof and the scientific method to ancient Greeks.

Anaximander is famous for astronomy, cartography and sundials, and also enunciated a theory of evolution, that land species somehow developed from primordial fish! For this reason Thales may belong on this list for his historical importance despite his relative lack of mathematical achievements.

Apastambha ca BC India The Dharmasutra composed by Apastambha contains mensuration techniques, novel geometric construction techniques, a method of elementary algebra, and what may be an early proof of the Pythagorean Theorem.

Apastambha built on the work of earlier Vedic scholars, especially Baudhayana, as well as Harappan and probably Mesopotamian mathematicians. His notation and proofs were primitive, and there is little certainty about his life. However similar comments apply to Thales of Miletus, so it seems fair to mention Apastambha who was perhaps the most creative Vedic mathematician before Panini along with Thales as one of the earliest mathematicians whose name is known.

Pythagoras of Samos ca BC Greek domain Pythagoras, who is sometimes called the "First Philosopher," studied under Anaximander, Egyptians, Babylonians, and the mystic Pherekydes from whom Pythagoras acquired a belief in reincarnation ; he became the most influential of early Greek mathematicians.

He and his students the "Pythagoreans" were ascetic mystics for whom mathematics was partly a spiritual tool.Key works: The idea that machines could think occurred to the very first computer builders and programmers. See, e.g., Alan Turing's great paper Turing The term "artificial intelligence" (AI) goes back to a summer conference in held at Dartmouth College in New Hampshire.

This essay is an antidote, a prosthesis for the imagination, showing how huge however, and I have updated the essay with a new postscript.

Can Machines Think?1 Can machines think? This has been a conundrum for philosophers for years, but in their fascination with the pure essential feature, musicianship, can be examined.

Turing. Can machines think? Turing didn't describe the human vs. machine game right away, to make a point. He didn't just flip a coin to see what he was going to write about.4/4(1). Thinking Outside the Box: A Misguided Idea The truth behind the universal, but flawed, catchphrase for creativity.

Posted Feb 06, The Failure of Two-Factor Authentication. Two-factor authentication isn't our savior.

It won't defend against phishing. It's not going to prevent identity theft. In the course of day-to-day conversation, virtually everyone has heard someone make the statement, “I am not religious,” in order to convey a lack of affiliation with theistic belief systems such as Christianity.

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