Some years ago Julian Huxley proposed to an audience made up of members of the British Association for the Advancement of Science that `` man's supernormal or extra-sensory faculties are ( now ) in the same case as were his mathematical faculties during the ice age ''.

* Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene-M. S. Raghunathan

Some modification of the Feynman rules of calculation may well outlive the elaborate mathematical structure of local canonical quantum field theory ...” So far there are no opposing opinions.

Some of the earliest ideas on how physical and mathematical processes and constraints affect biological growth, and hence natural patterns such as the spirals of phyllotaxis, were written by D ' Arcy Wentworth Thompson and Alan Turing.

Some mathematical games are topics of interest in recreational mathematics.

Some recent work has been done in analysis using concepts from non-standard analysis, particularly in investigating limiting processes of statistics and mathematical physics.

Some encryption schemes can be proven secure on the basis of the presumed difficulty of a mathematical problem, such as factoring the product of two large primes or computing discrete logarithms.

Some of the more well-known topics in recreational mathematics are mathematical chess problems, magic squares and fractals.

Some consider statistics to be a mathematical body of science pertaining to the collection, analysis, interpretation or explanation, and presentation of data, while others consider it a branch of mathematics concerned with collecting and interpreting data.

Some of the notable mathematical concepts named after Banach include Banach spaces, Banach algebras, the Banach – Tarski paradox, the Hahn – Banach theorem, the Banach – Steinhaus theorem, the Banach-Mazur game, the Banach – Alaoglu theorem and the Banach fixed-point theorem.

Some scientists think a more mathematical approach than philosophy is needed for a ToE, for instance Stephen Hawking wrote in A Brief History of Time that even if we had a ToE, it would necessarily be a set of equations.

Some derivation rules and formal languages are intended to capture mathematical reasoning ; the most common examples use first-order logic.

Some mathematicians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.

Some CAD software is capable of dynamic mathematical modeling, in which case it may be marketed as CADD.

Some of the mathematical description work on curves was developed in the early 1940s by Robert Issac Newton from Pawtucket, Rhode Island.

Some approaches are selectively realistic about some mathematical objects but not others.

Some scientists think a more mathematical approach than philosophy is needed for a TOE, for instance Stephen Hawking wrote in A Brief History of Time that even if we had a TOE, it would necessarily be a set of equations.

Some outstanding mathematical and Orientalist works emerged at this time – notably, texts edited by Edward Pococke, the Regius Professor of Hebrew – but no university press on Laud's model was possible before the Restoration of the Monarchy in 1660.

Some texts prefer a more concise mathematical syntax.

Some of these are really coded mathematical problems, expressed using the geometry and pieces of the chessboard.

Some example are: Heidi Gilpin, who translates ideas — linguistic, mathematical or scientific — into an understanding that offers a common ground that facilitates interaction between her and world-famous choreographer Forsythe.

Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.

Some theories tend to focus on mathematical practice, and aim to describe and analyze the actual working of mathematicians as a social group.

Some theorems related to compactness ( see the glossary of topology for the definitions ):

Some of the axioms coincide, while some of the axioms in Moore's system are theorems in Hilbert's and vice-versa.

Some theorems are " trivial ," in the sense that they follow from definitions, axioms, and other theorems in obvious ways and do not contain any surprising insights.

Some modern magicians, such as Aleister Crowley and those who follow the traditions of the Hermetic Order of the Golden Dawn and Ordo Templi Orientis, describe magic in rational terms, using definitions, postulates and theorems.

Some logicians, while accepting that classical mathematics is correct, still believe that the constructive approach gives a better insight into the true meaning of theorems, in much this way.

Some theorems on the coefficients c < sub > n </ sub > include:

Some basic theorems of Riemannian geometry can be generalized to the pseudo-Riemannian case.

Some of the more recent graphing calculators are capable of color output, and also feature animated and interactive drawing of math plots ( 2D and 3D ), other figures such as animated Geometry theorems, preparation of documents which can include these plots and drawings, etc.

* 1951 is Gödel's 1951 Gibbs lecture, " Some basic theorems on the foundations of mathematics and their implications.

Some scholars have debated over what, if anything, Gödel's incompleteness theorems imply about anthropic mechanism.

One of the earliest attempts to use incompleteness to reason about human intelligence was by Gödel himself in his 1951 Gibbs lecture entitled " Some basic theorems on the foundations of mathematics and their philosophical implications ".

He later changed his mind and submitted a thesis in 1926, titled Some theorems about integral solutions to certain algebraic equations and inequalities.

Some major theorems characterise relatively compact subsets, in particular in function spaces.

Some theorems on abelian varieties require the idea of abelian variety up to isogeny for their convenient statement.

Some examples of topics in geometric topology are orientability, handle decompositions, local flatness, and the planar and higher-dimensional Schönflies theorems.

Some theorems from Gauss's theory of circle division

Some theorems from the theory of circle division

Some logical systems are not adequately represented by the set of theorems alone.

Some cognitive linguists have replied to such objections by pointing out that the goal of Cognitive Linguistics is not to construct a formal system in which theorems are proved, but rather to better understand the cognitive basis of language ( cf.