• To understand is to perceive patterns

                                                                      – Isaiah Berlin

• …Still more astonishing is that world  of rigorous fantasy we call mathematics.

                                                                      -Gregory Bateson

• With our thoughts, we make the world.

                                                                       -Gautama Buddha

• Language shapes the way we think , and determines what we can think about.

                                                                         -Benjamin Lee Whorf

•  Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories.

                                                                            -Pierre-Simon Laplace

• So if a man’s wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away ever so little, be must begin again.

                                                                               -Francis Bacon

• He was forty years old before he looked on geometry; which happened accidentally. Being in a gentleman’s library, Euclid’s Elements lay open and ‘twas the forty-seventh proposition in the first book. He read the proposition. ‘by God,’ said he , ‘this is  impossible!’ so he reads the demonstration of it, which referred him back to such a proof; which referred him back to convinced of that truth. This made him in love with geometry.’

                                                                                           -John Aubrey

• Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the  converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
• Halmos , Paul R
• A good proof is a proof that makes us wiser.

                                                                                                       -Yuri I Manin

• Without signs nothing is conceivable.           –David Sless
• The Adventure of the Norwood Builder It isn’t that can’t see the solution. It is that they can’t see the problem.

                                                                                                Chesterton, G. K

• “Algebra is but written geometry; geometry is but drawn algebra”

                                                                                    Sophie Germain

• I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons.

                                                                                    Arthur S. Eddington

• Hold infinity in the palm of your hand and eternity in an hour.

                                                                                    William Blake

• When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached.

                                                                                       Gottfried Leibniz

• The archipelago of modern mathematics is in fact linked together by mysterious and invisible underground passages, brought to light by unexpected convergences of results.

                                                                                   Piergiorgio Odifreddi

• One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

                                                                                       Philip J Davis

•  The combination of these things: beauty exactness, simplicity and crazy  ideas is just the heart of mathematics.

                                                                                      Israel M Gefand

• Revolutions never occur in mathematics.          Michael Crowe

• The mathematical sciences particularly exhibit order, symmetry, and limitation ;and these are the greatest forms of the beautiful .

                                                                                                      Aristotle

• Pure mathematics is , in its way , the poetry of logical ideas.

                                                                                                 Albert Einstein

• The mathematics patterns, like the painter’s or the poet’s must be beautiful ; the ideas , like the colours or the words must  fit tighter in a harmonious way.

                                                                                               Godfrey H . Hardy

• One  truth , many forms.

                                                                               Sanskrit proverb

• The essence of mathematics lies in its freedom.       George Cantor
• “ When I use a word ,Humpty Dumpty said, in a rather scornful tone , “ it means just what I choose it to mean—- neither more nor less.” “ the question is , “ said Alice , “ whether you can make words mean so many different things .” the question is , “ said Humpty Dumpty , “ which is to be master —- that’s all.

                                                                                            Lewis Carroll

• “ [ The universe ] cannot be read until we learnt the language and become familiar with the characters in which it is written [ and it ] is

Written in mathematics language ,  and the letters are triangles , circles and other geometrical figures , without which means it is humanly impossible to comprehend a single word. “

                                                                                Galileo Galilei

• In the final analysis the vitality of mathematics arises from the fact that its concepts and results , for all their abstractness , originate… in the actual world and find widely varied application in the other sciences, in engineering , and in all the practical affairs of daily life ; to realize this is the most important prerequisite for understanding mathematics.

                                                                                 A.D Aleksandrov

• Without the concepts, methods and results found and developed

Previous generations right down to…. Antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years.

                                                                                           Hermann Weyl

• It is a complete misunderstanding of our science to construct differences according to peoples and races… for mathematics, the cultural world is one country.

                                                                                           David Hilbert

• In a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

                                                                                                 Felix klein

• As are the crests on the heads of peacocks, as the jewels on the hoods of cobras, so is mathematics at the top of all sciences.

                                                                                                  The Yajurveda