ಹಳೆಯ ಹಳ್ಳಿಯ ಲೆಕ್ಕಗಳು

ಹಳೆಯ ಹಳ್ಳಿಯ ಲೆಕ್ಕಗಳು

ತೂಕ ಹಾಗೂ ಅಳತೆಗೆ ಸಂಬಂಧಿಸಿದಂತೆ
ಹಿಂದೆ ತೂಕವನ್ನು “ರೂಪಾಯಿ”ಗಳಿಂದಲೇ ಕಂಡುಕೊಂಡಿದ್ದು ನಮಗೆ ಕಂಡುಬರುತ್ತದೆ. ೨೪ ಬೆಳ್ಳಿ “ರೂಪಾಯಿ”ಗಳ ತೂಕವನ್ನು ಒಂದು “ಸೇರು” ಎಂದು ಮಾಡಿಕೊಂಡಿದ್ದರಿಂದ, ಅದರ ಅಳತೆಗೆ ತಕ್ಕಂತೆ ” ಸೇರಿ”ನ ಸೃಷ್ಟಿಯಾಗಿರುವುದನ್ನು ನಾವು ಗಮನಿಸುತ್ತೇವೆ. ಹೀಗೆ “ಪಾವು”, “ಚಟಾಕು”, “ಗಜ”, “ಅಂಗುಲ”, “ಮೈಲಿ”, “ಹರಿದಾರಿ” “ಎಕರೆ” ಮುಂತಾದ ಅಳತೆಮಾನಗಳು ಹಾಗೂ “ತೊಲ”, “ಪಲ್ಲ”, “ಖಂಡುಗ” ಮುಂತಾದ ತೂಕಮಾನಗಳು ಬಂದು ಸೇರಿಕೊಂಡಿವೆ. ಉದಾಹರಣೆಗೆ, ಒಂದು ಸೇರು ಎಂದರೆ, ೨೪ ಬೆಳ್ಳಿ “ರೂಪಾಯಿ”ಗಳ ತೂಕ ಅಥವಾ ನಾಲ್ಕು “ಪಾವು” ಎಂದೂ ಹಾಗೂ ಒಂದು “ಗಜ” ಎಂಬುದನ್ನು ಮೂರು “ಅಡಿ” ಎಂದು ಹೇಳಲಾಗುತ್ತದೆ. ಇವುಗಳ ಪ್ರಕಾರ ತೂಕ ಹಾಗು ಅಳತೆಗಳನ್ನು ನಾವು ಈ ರೀತಿ ವಿಂಗಡಿಸಬಹುದಾಗಿದೆ.
೧ ಬೆಳ್ಳಿ ರೂಪಯಿ ತೂಕ = ೧ ತೊಲ
೧ ಪಾವು = ೪ ಚಟಾಕು
೧ ಸೇರು = ೪ ಪಾವು ಅಥವ ೨೪ ಬೆಳ್ಳಿ ರೂಪಯಿಗಳ ತೂಕ
೧ ಇಬ್ಬಳಿಗೆ = ಐದೂವರೆ ಸೇರು (ದೊಡ್ದ ಇಬ್ಬಳಿಗೆಯಾದರೆ ೬ ಸೇರು)
೧ ಪಲ್ಲ = ೧೦೦ ಸೇರು
೧ ಕೊಳಗ = ೨ ಇಬ್ಬಳಿಗೆ ಅಥವ ೧೧ ಸೇರು
೧ ಖಂಡುಗ = ೪೦ ಇಬ್ಬಳಿಗೆ ಅಥವ ೨೦ ಕೊಳಗ
೧ ಅಡಿ = ೧೨ ಅಂಗುಲ ಅಥವ ಇಂಚು
೧ ಗಜ = ೩ ಅಡಿ ಅಥವ ೩೬ ಅಂಗುಲ
೧ ಗುಂಟೆ = ೨೨೦ ಚದರ ಗಜ
೧ ಎಕರೆ = ೪೦ ಗುಂಟೆ
೧ ಮೈಲಿ = ೮ ಫರ್ಲಾಂಗು
೧ ಹರಿದಾರಿ = ೪ ಮೈಲಿ
೧ ಗಾವುದ = ೧೨ ಹರಿದಾರಿ
ನಾನು ನೋಡಿದಂತೆ ಸಣ್ಣವನಾಗಿದ್ದಾಗ, ಅಪ್ಪ ಶಾಲಾ ಯೂನಿಫಾರಂ ಬಟ್ಟೆ ಹಾಕಲು ಅಂಗಡಿಗೆ ಕರೆದುಕೊಂಡು ಹೋಗುತ್ತಿದ್ದದ್ದು ಹಾಗೂ ಅಲ್ಲಿ ಬಟ್ಟೆಯನ್ನು ಗಜದಲ್ಲೇ ಅಳತೆ ಮಾಡುತ್ತಿದ್ದದ್ದು ನನಗೆ ನೆನಪಿದೆ. ಇನ್ನು ಭತ್ತದ ನಾಟಿಗೂ ಮೊದಲು ಪೈರಿನ ಹೊಟ್ಟಿಲಿಗೆ ಬಿತ್ತನೆ ಭತ್ತದ ಅಳತೆಯನ್ನು ಸೇರಿನಲ್ಲಿ ಈಗಲೂ ಅಳೆದು ಉಪಯೋಗಿಸುವುದು ಸಾಮಾನ್ಯವಾಗಿದೆ. ಹಳ್ಳಿಗಳಲ್ಲಿ ಒಂದು ಎಕರೆಗೆ ಸುಮಾರು ಮೂವತ್ತು ಸೇರು ಬಿತ್ತನೆ ಭತ್ತವನ್ನು ಉಪಯೋಗಿಸುತ್ತಾರೆ. ಇನ್ನು ತೂಕದಲ್ಲಿ ನೋಡಿದರೆ, ಬೆಣ್ಣೆ, ತುಪ್ಪ ಮುಂತಾದ ಖಾದ್ಯಗಳನ್ನು “ಸೇರು”, “ಪಾವು” ಎಂದೇ ತೂಗುವುದು ವಾಡಿಕೆಯಾಗಿತ್ತು. ಅದಕ್ಕಾಗಿಯೇ ತೂಕದ ಕಲ್ಲುಗಳನ್ನು ಉಪಯೋಗಿಸುತ್ತಿದ್ದರು. ಉದಾಹರಣೆಗೆ,
ಅಚ್ಚೇರು ಬೆಣ್ಣೆ = ಅರ್ಧ ಸೇರು ಬೆಣ್ಣೆ = ೧೨ ಬೆಳ್ಳಿ ರೂಪಾಯಿಗಳ ತೂಕ ಅಥವ ೨ ಪಾವು
ಅರ್ಪಾವು ತುಪ್ಪ = ಅರ್ಧ ಪಾವು ತುಪ್ಪ
ಹಳ್ಳಿ ಅಳತೆಯಲ್ಲಿ ಕಾಣಬಹುದಾದ ಇನ್ನೊಂದು ವಿಷೇಶ ಎಂದರೆ, ಸೇರು, ಪಾವು, ಇಬ್ಬಳಿಗೆ, ಕೊಳಗ ಹೀಗೆ ಯಾವುದನ್ನೇ ಉಪಯೋಗಿಸಿ ಭತ್ತ, ರಾಗಿ ಅಥವಾ ಬೇರೆ ಯಾವುದೇ ಧಾನ್ಯಗಳನ್ನು ಅಳೆಯುವಾಗ “ಹೆಚ್ಚಲಿ” ಎಂಬ ಪದವನ್ನು ಸಾಮಾನ್ಯವಾಗಿ ಉಪಯೋಗಿಸುತ್ತಿರುತ್ತಿದ್ದರು. ಅದಕ್ಕೆ ಎರಡು ಕಾರಣಗಳಿವೆ. ಮೊದಲನೆಯದಾಗಿ ಧಾನ್ಯ ಹಾಗೇ ಹೆಚ್ಚಲಿ ಎಂಬುದು. ಎರಡನೆಯದಾಗಿ ೭, ೧೧ ಮತ್ತು ೧೭ ಸಂಖ್ಯೆಗಳು ಅಶುಭ ಹಾಗು ಅವುಗಳನ್ನು ಉಪಯೋಗಿಸಬಾರದೆಂಬ ನಂಬಿಕೆ. ಈ ಕಾರಣಗಳಿಂದ, “ಆರು” ಆದ ನಂತರ “ಹೆಚ್ಚಲಿ” ನಂತರ “ಎಂಟು” ಎಂದೂ, ಹತ್ತಾದ ನಂತರ “ಹೆಚ್ಚಲಿ” ನಂತರ “ಹನ್ನೆರಡು ಎಂದೂ, “ಹದಿನಾರು” ಆದ ನಂತರ “ಹೆಚ್ಚಲಿ” ನಂತರ “ಹದಿನೆಂಟು” ಎಂದೂ ಬಳಸುತ್ತಿದ್ದರು. ಹೀಗೆ ಏಳು, ಹನ್ನೊಂದು ಮತ್ತು ಹದಿನೇಳು ಸಂಖ್ಯೆಗಳನ್ನು ಉಪಯೋಗಿಸುತ್ತಿರಲಿಲ್ಲ. ಹಾಗೇ ಕೆಲವು ಸಂಖ್ಯೆಗಳನ್ನು ಶುಭ ಸಂಖ್ಯೆಗಳೆಂದು ನಂಬಿ ಉಪಯೋಗಿಸುತ್ತಿದ್ದದ್ದೂ ಉಂಟು. ಅವು ಯಾವುವೆಂದರೆ, ಐದು, ಒಂಬತ್ತು ಮತ್ತು ಹನ್ನೆರಡು.
ಹಣಕ್ಕೆ ಸಂಬಂಧಿಸಿದಂತೆ
ಈ ಮೊದಲೇ ಹೇಳಿದಂತೆ ಹಿಂದೆ “ಕಾಸು”ಗಳು ಬಹುಪಾಲು ಎಲ್ಲಾ ಅಳತೆಗಳಲ್ಲೂ ಪ್ರಧಾನ ಪಾತ್ರ ವಹಿಸುತ್ತಿದ್ದದ್ದು ನಮಗೆ ಕಾಣುತ್ತದೆ. ಮೂರು ಕಾಸಿನ ಒಂದು ಬಿಲ್ಲೆ, ಇಂಥ ನಾಲ್ಕು ಬಿಲ್ಲೆಗಳು ಸೇರಿದರೆ ಹನ್ನೆರಡು “ಕಾಸು” ಅಥವಾ ಒಂದು “ಆಣೆ”ಯಾಗುತ್ತದೆ. ಇಂದಿನ “ನಾಲ್ಕಾಣೆ”, “ಎಂಟಾಣೆ”, “ಹನ್ನೆರಡಾಣೆ”, “ಹದಿನಾರಾಣೆ”ಗಳು ಈ ಹಿನ್ನಲೆಯಿಂದಲೇ ಬಂದಿರುವುದು ನಮಗೆ ತಿಳಿದ ಸಂಗತಿಯಾಗಿದೆ. ಈಗಲೂ ನಾವು ಈ “ಆಣೆ”ಗಳನ್ನು ಉಪಯೋಗಿಸುತ್ತೇವೆ. ಇದರ ಪ್ರಕಾರ ನಾವು ನಾಣ್ಯಗಳನ್ನು ಈ ಕೆಳಗೆ ಹೇಳಿರುವ ರೀತಿ ವಿಂಗಡಿಸಬಹುದಾಗಿದೆ.
ಚಲಾವಣೆಯಲ್ಲಿದ್ದ ನಾಣ್ಯಗಳು ಮತ್ತು ಉಪಯೋಗಿಸುತ್ತಿದ್ದ ಲೋಹಗಳು:
೧ ಕಾಸು (ತಾಮ್ರ)
೩ ಕಾಸು (ತಾಮ್ರ)
೬ ಕಾಸು (ನಿಕ್ಕಲ್)
೧ ಆಣೆ = ೧೨ ಕಾಸು (ನಿಕ್ಕಲ್)
೨ ಆಣೆ = ೨೪ ಕಾಸು (ನಿಕ್ಕಲ್)
೪ ಆಣೆ (ಬೆಳ್ಳಿ)
೮ ಆಣೆ (ಬೆಳ್ಳಿ)
೧ ರೂಪಾಯಿ = ೧೯೨ ಕಾಸು (ಬೆಳ್ಳಿ)
ಜೊತೆಗೆ ನಾಣ್ಯವಲ್ಲದಿದ್ದರೂ “ದುಡ್ಡು”, “ಪಾವಲಿ” “ಹಣ ಅಥವ ವರಹ” ಹಾಗು “ದುಗ್ಗಾಣಿ” ಎಂಬ ಪದಗಳು ವ್ಯವಹಾರಿಕವಾಗಿ ಉಪಯೋಗಿಸಲ್ಪಡುತ್ತಿದ್ದವು. ಇವುಗಳನ್ನು “ಕಾಸು” ಮತ್ತು “ಆಣೆ”ಗಳಲ್ಲಿ ಹೇಳಬಹುದಾದರೆ:
೧ ದುಡ್ಡು = ೪ ಕಾಸು
೧ ಪಾವಲಿ = ೪ ಆಣೆ
೧ ಹಣ ಅಥವ ವರಹ= ೪ ಆಣೆ ಪಾವಲಿ
೧ ದುಗ್ಗಾಣಿ = ೮ ಕಾಸು ಅಥವಾ ೨ ದುಡ್ಡು ಎಂದು ಹೇಳಲಾಗುತ್ತಿತ್ತು.
ಈಗಿನ ಖೋಟಾ ನೋಟುಗಳು ಇರುವಂತೆ, ಹಿಂದೆಯೂ ನಾಣ್ಯಗಳ ನಕಲು ಮಾಡಲಾಗುತ್ತಿತ್ತು. ಬೆಳ್ಳಿಕಾಸಿನ ನಕಲನ್ನು “ಸೀಸ”ದಲ್ಲಿ ಮಾಡುತ್ತಿದ್ದರು. ಆದುದರಿಂದ, ನಾಣ್ಯವನ್ನು ಚಿಮ್ಮಿಸಿ ಅದರ ಶಬ್ಧದ ಆಧಾರದ ಮೇಲೆ ಅದು “ಬೆಳ್ಳಿ” ಅಥವ “ಸೀಸ”ದಿಂದ ಮಾಡಲ್ಪಟ್ಟಿದೆ ಎಂಬುದನ್ನು ಗುರುತಿಸುತ್ತಿದ್ದರು. “ಹಣ”, “ವರಹ” ಎಂಬ ಪದಗಳನ್ನು ಸಾಮಾನ್ಯವಾಗಿ ಮದುವೆ ಮುಂತಾದ ಸಮಾರಂಭಗಲ್ಲಿ ಹೆಚ್ಚು ಉಪಯೋಗಿಸುತ್ತಿದ್ದರು. ಮದುವೆಗಳಲ್ಲಿ ನೀಡುವ ಉಡುಗೊರೆಯ ಹಣದ (ಮುಯ್ಯಿ) ಪಟ್ಟಿ ಬರೆಯುವಾಗ “ವಧುವಿಗೆ ಸೋದರಮಾವನಿಂದ ನಾಲ್ಕು ವರಹ” ಅಥವಾ “ವರನಿಗೆ ಚಿಕ್ಕಪ್ಪನಿಂದ ಹತ್ತು ಹಣ” ಎಂದು ಹೇಳುತ್ತಿದ್ದರು. ಕೆಲವು ಭಾಗಗಳಲ್ಲಿ “ಆಗ”, “ಅಡ್ಡ” ಮುಂತಾದ ಪದಗಳನ್ನು ಈ ಕೆಳಗಿನ ಅರ್ಥದಲ್ಲಿ ಉಪಯೋಗಿಸುತ್ತಿದ್ದರು.
ಆಗ = ಒಂದು
ಅಡ್ಡ = ಎರಡು
ದುಡ್ಡು = ನಾಲ್ಕು
ದುಗ್ಗಾಣಿ = ಎಂಟು

ಪ್ರಾಣಿಗಳ ಮೈಮೇಲಿನ ಚಿತ್ರವೂ..........ಗಣಿತವೂ.......

Mathematical model for animal stripes

Summary:

The back of a tiger could have been a blank canvas. Instead, nature painted the big cat with parallel stripes, evenly spaced and perpendicular to the spine. Scientists don't know exactly how stripes develop, but since the 1950s, mathematicians have been modeling possible scenarios. Now researchers assemble a range of these models into a single equation to identify what variables control stripe formation in living things.

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This image shows simulations of Turing stripes. On the left, stripes are evenly spaced, but their direction is variable. On the right, a signaling gradient has made the stripes align in the same direction.

Credit: Tom Hiscock

The back of a tiger could have been a blank canvas. Instead, nature painted the big cat with parallel stripes, evenly spaced and perpendicular to the spine. Scientists don't know exactly how stripes develop, but since the 1950s, mathematicians have been modeling possible scenarios. In Cell Systems on December 23, Harvard researchers assemble a range of these models into a single equation to identify what variables control stripe formation in living things.

"We wanted a very simple model in hopes that it would be big picture enough to include all of these different explanations," says lead author Tom Hiscock, a PhD student in Sean Megason's systems biology lab at Harvard Medical School. "We now get to ask what is common among molecular, cellular, and mechanical hypotheses for how living things orient the directions of stripes, which can then tell you what kinds of experiments will (or won't) distinguish between them."

Stripes are surprisingly simple to model mathematically (and much of the early work on the subject was by Alan Turing of "The Imitation Game" fame). These patterns emerge when interacting substances create waves of high and low concentrations of, for example, a pigment, chemical, or type of cell. What Turing's model doesn't explain is how stripes orient themselves in one particular direction.

Hiscock's investigation focused on orientation--e.g., why tiger stripes are perpendicular to its body while zebrafish stripes are horizontal. One surprise from his integrated model is that it takes only a small change to the model to switch whether the stripes are vertical or horizontal. What we don't know is how this translates to living things--so, for a tiger, what is the variable that pushes the development of perpendicular stripes?

"We can describe what happens in stripe formation using this simple mathematical equation, but I don't think we know the nitty-gritty details of exactly what molecules or cells are mapping the formation of stripes," Hiscock says. Genetic mutants exist that can't form stripes or make spots instead, such as in zebrafish, but "the problem is you have a big network of interactions, and so any number of parameters can change the pattern," he adds.

His master model predicts three main perturbations that can affect how stripes orient: one is a change in "production gradient," which would be a substance that amplifies stripe pattern density; second is a change in "parameter gradient," a substance that changes one of the parameters involved in forming the stripe; and the last is a physical change in the direction of the molecular, cellular, or mechanical origin of the stripe.

Although this paper is based in theory, Hiscock believes that we are close to having the experimental tools that can decipher whether the math holds true in living systems.

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Story Source:

The above post is reprinted from materials provided by Cell Press. Note: Materials may be edited for content and length.

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ಗಣಿತಕುರಿತ ಹೇಳಿಕಗಳು...........

Mathematics Quotes and Quotation

• "A mathematician is a blind man in a dark room looking for a black cat which isn't there." --Charles Darwin
• "A topologist is one who doesn't know the difference between a doughnut and a coffee cup." --John Kelley
• "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." --Albert Einstein
• "As long as algebra is taught in school, there will be prayer in school." --Cokie Roberts
• "Do not worry about your problems with mathematics, I assure you mine are far greater." --Albert Einstein
• "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." --Sir James Jeans
• "God does arithmetic." --Karl Friedrich Gauss
• "God does not care about our mathematical difficulties. He integrates empirically." --Albert Einstein
• "He uses statistics as a drunken man uses lamp posts." -- for support rather than illumination." --Andrew Lang
• "He who can properly define and divide is to be considered a god." --Plato
• "How dare we speak of the laws of chance? Is not chance the antithesis of all law?" --Bertrand Russell
• "I admit that mathematical science is a good thing. But excessive devotion to it is a bad thing." --Aldous Huxley
• "I don't believe in mathematics." --Albert Einstein
• "I have hardly ever known a mathematician who was capable of reasoning." --Plato
• "I have no faith in political arithmetic." --Adam Smith
• "If your experiment needs statistics, you ought to have done a better experiment." --Ernest Rutherford
• "Life is good for only two things, discovering mathematics and teaching mathematics." --Simeon Poisson
• "Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning." --John Locke
• "Mathematics consists of proving the most obvious thing in the least obvious way." --George Polye
• "Mathematics is a game played according to certain simple rules with meaningless marks on paper." --David Hilbert
• "[Mathematics] is an independent world created out of pure intelligence." --William Wordsworth
• "Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state." --Plato
• "Mathematics is not yet capable of coping with the naïveté of the mathematician himself." --Abraham Kaplan
• "Mathematics is the art of giving the same name to different things." --Jules Henri Poincare
• "Mathematics is the only instructional material that can be presented in an entirely undogmatic way." --Max Dehn
• "Mathematics is the science of what is clear by itself." --Carl Jacobi
• "Mathematics seems to endow one with something like a new sense." --Charles Darwin
• "Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform." --Bertrand Russell
• "Measure what is measurable, and make measurable what is not so." --Galileo Galilei
• "Medicine makes people ill, mathematics make them sad and theology makes them sinful." --Martin Luther
• "No human investigation can be called real science if it cannot be demonstrated mathematically." --Leonardo da Vinci
• "Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important... The knowledge doesn't make life any sweeter or happier, does it?" --Helen Keller
• "Perfect numbers like perfect men are very rare." --Rene Descartes
• "Pure mathematics, may it never be of any use to anyone." --Henry John Stephen Smith
• "Sex is the mathematics urge sublimated." --M. C. Reed
• "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." --Albert Einstein
• "Statistics: the mathematical theory of ignorance." --Morris Kline
• "The art of doing mathematics consists in finding that special case which contains all the germs of generality." --David Hilbert
• "The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being." --Gottfried Whilhem Liebniz
• "The infinite! No other question has ever moved so profoundly the spirit of man." --David Hilbert
• "The knowledge of which geometry aims is the knowledge of the eternal." --Plato
• "The mathematician has reached the highest rung on the ladder of human thought." --Havelock Ellis
• "The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience." --Emmanuel Kant
• "The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life." --Ernest Renan
• "There are three kinds of lies: lies, damned lies, and statistics." --Benajamin Disraeli
• "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." --Nikolai Lobatchevsky
• "You know we all became mathematicians for the same reason: we were lazy." --Max Rosenlicht
• "I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate." --David Mumford

ಗಣಿತಕುರಿತ ಹೇಳಿಕೆಗಳು (ಮುಂದುವರೆದ ಭಾಗ)

“Beauty is the first test: there is no permanent place in the world for ugly mathematics”…..G. H. Hardy

“It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.”….Carl Friedrich Gauss

“If you listen to the great Beatle records, the earliest ones where the lyrics are incredibly simple. Why are they still beautiful? Well, they're beautifully sung, beautifully played, and the mathematics in them is elegant. They retain their elegance.”……….Bruce Springsteen

“When we were making the law, when we were writing the literature and the mathematics the grandfarthers of Blair and little Bush were scratching around in caves.”…Mohammed Saeed al-Sahaf

“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.”

Galileo Galilei

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.”

David Hilbert

”Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.”……….Marcus du Sautoy

“It is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics.”……….Stephen Hawking

“A lot of music is mathematics. It's balance.”……….Mel Brooks

“For the execution of the voyage to the Indies, I did not make use of intelligence, mathematics or maps.”

Christopher Columbus

“There should be no such thing as boring mathematics.”………..Edsger Dijkstra

“My interests started about in science and in mathematics; I always thought I was going to be a mathematician.”……….David Chalmers

“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”

Charles Caleb Colton

“For the things of this world cannot be made known without a knowledge of mathematics.”

Roger Bacon

“Aerodynamics is mathematics for those who haven't learned to do calculus. In my case, too, for one who hasn't learned to add or multiply, at least the first time.”

Richard Bach

Mathematics Quotes

Mathematics Quotes

“Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”…. Shakuntala Devi

“Pure mathematics is, in its way, the poetry of logical ideas”……….Albert Einstein

“One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.”………Danica McKellar

“God used beautiful mathematics in creating the world.” ……………Paul Dirac

“Mathematics is the music of reason.”…………James Joseph Sylvester

“The Universal Zulu Nation stands to acknowledge wisdom, understanding, freedom, justice, and equality, peace, unity, love, and having fun, work, overcoming the negative through the positive, science, mathematics, faith, facts, and the wonders of God, whether we call him Allah, Jehovah, Yahweh, or Jah.”………..Afrika Bambaataa

“The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.” ………..James Newman

“Mathematics is the most beautiful and most powerful creation of the human spirit.”……Stefan Banach

“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.”……..Richard Courant

“All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.” ……………Roger Bacon

“If a man's wit be wandering, let him study the mathematics.”……Francis Bacon

“In mathematics the art of proposing a question must be held of higher value than solving it.”

Georg Cantor

“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”

Albert Einstein

“Worry, Greater, Mine As far as the laws of mathematics refer to reality, they are not certain,

and as far as they are certain, they do not refer to reality.” ……….Albert Einstein

“Mathematics is the art of giving the same name to different things.”……..Henri Poincare