I'm talking about looking back. For instance, geometry can be said to have started with Euclid (as near as dammit); calculus with Newton.

http://en.wikipedia.org/wiki/CalculusThe history of calculus falls into several distinct periods, most notably the ancient, medieval, and modern periods

The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which an Egyptian worked out the volume of a pyramidal frustrum [1] [2] Eudoxus (c. 408-355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes. Archimedes (c. 287-212 BC) developed this idea further, inventing heuristics which resemble integral calculus.[3] The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere.[2]

In the medieval period, the Indian mathematician Aryabhata used the notion of infinitesimals in 499 AD and expressed an astronomical problem in the form of a basic differential equation.[4] This equation eventually led Bhāskara II in the 12th century to develop an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem".[5] Around 1000 AD, the Iraqi mathematician Ibn al-Haytham (Alhazen) was the first to derive the formula for the sum of the fourth powers, and using mathematical induction, he developed a method for determining the general formula for the sum of any integral powers, which was fundamental to the development of integral calculus.[6] In the 12th century, the Persian mathematician Sharaf al-Din al-Tusi discovered the derivative of cubic polynomials, an important result in differential calculus.[7] In the 14th century, Madhava of Sangamagrama, along with other mathematician-astronomers of the Kerala school of astronomy and mathematics, described special cases of Taylor series,[8] which are treated in the text Yuktibhasa.[9][10][11]

In the modern period, independent discoveries in calculus were being made in early 17th century Japan, by mathematicians such as Seki Kowa, who expanded upon the method of exhaustion. In Europe, the second half of the 17th century was a time of major innovation. Calculus provided a new opportunity in mathematical physics to solve long-standing problems. Several mathematicians contributed to these breakthroughs, notably John Wallis and Isaac Barrow. James Gregory proved a special case of the second fundamental theorem of calculus in 1668.

Leibniz and Newton pulled these ideas together into a coherent whole and they are usually credited with the independent and nearly simultaneous invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today; he often spent days determining appropriate symbols for concepts. The basic insight that both Newton and Leibniz had was the fundamental theorem of calculus.

When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit. Newton derived his results first, but Leibniz published first. Newton claimed Leibniz stole ideas from his unpublished notes, which Newton had shared with a few members of the Royal Society. This controversy divided English-speaking mathematicians from continental mathematicians for many years, to the detriment of English mathematics. A careful examination of the papers of Leibniz and Newton shows that they arrived at their results independently, with Leibniz starting first with integration and Newton with differentiation. Today, both Newton and Leibniz are given credit for developing calculus independently. It is Leibniz, however, who gave the new discipline its name. Newton called his calculus the "the science of fluxions".

Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Cauchy, Riemann, and Weierstrass. It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. Lebesgue further generalized the notion of the integral.

So, yes, Newton

**and Leibniz** were responsible for the modern cohesive structure of calculus, but the ideas they used were not original to them, and it is certainly unfair to suggest that those before them were practising some superstitious dallying. What Newton, and probably even more, Leibniz, created was the modern language of calculus.

Is there a point before which you can say that what was practised was not chemistry as we know it, but more superstitious dallying?

The difference between calculus and chemistry is that calculus is a very narrow field, and not the whole of mathematics; so it is relatively easier to discuss who created the language we use today in discussing a very narrow topic like calculus, then saying the same for the whole of chemistry.

I certainly think it unfair to claim that people preparing gunpowder in ancient China, or experimenting with early metallurgy, were indulging any more in superstitious dallying. Even today, although ever more we begin to use powerful computers to try and model chemical reactions, but certainly in the pre-computer age, much of chemistry (particularly the complex organic chemistry used in pharmaceuticals) was as much educated guesswork and laboratory trial and error. Only now, with the advent of very powerful computers, can we say we can actually start to design drugs for a purpose, rather than simply look through all of the folk knowledge that was accumulated through '

*superstitious dallying*' that provided the basis for drugs such as aspirin and quinine.

I suppose if one wanted to look for point where past knowledge of chemistry was brought together into a single structure in the way that Newton and Liebnitz broght together past ideas of infinitesimals and limits into a single cohesive structure, then maybe one could look at the creation of the periodic table:

http://en.wikipedia.org/wiki/Periodic_tableThe periodic table of the chemical elements is a tabular method of displaying the chemical elements. Although earlier precursors exist, its invention is generally credited to Russian chemist Dmitri Mendeleev in 1869. Mendeleev intended the table to illustrate recurring ("periodic") trends in the properties of the elements. The layout of the table has been refined and extended over time, as new elements have been discovered, and new theoretical models have been developed to explain chemical behavior.

In Ancient Greece, the influential Greek philosopher Aristotle proposed that there were four main elements: air, fire, earth and water. All of these elements could be reacted to create another one; e.g., earth and fire combined to form lava. However, this theory was dismissed when the real chemical elements started being discovered. Scientists needed an easily accessible, well organized database with which information about the elements could be recorded and accessed. This was to be known as the periodic table.

The original table was created before the discovery of subatomic particles or the formulation of current quantum mechanical theories of atomic structure. If one orders the elements by atomic mass, and then plots certain other properties against atomic mass, one sees an undulation or periodicity to these properties as a function of atomic mass. The first to recognize these regularities was the German chemist Johann Wolfgang Döbereiner who, in 1829, noticed a number of triads of similar elements:

In 1829 Döbereiner proposed the Law of Triads: The middle element in the triad had atomic weight that was the average of the other two members. The densities of some triads followed a similar pattern. Soon other scientists found chemical relationships extended beyond triads. Fluorine was added to Cl/Br/I group; sulfur, oxygen, selenium and tellurium were grouped into a family; nitrogen, phosphorus, arsenic, antimony, and bismuth were classified as another group.

This was followed by the English chemist John Newlands, who noticed in 1865 that when placed in order of increasing atomic weight, elements of similar physical and chemical properties recurred at intervals of eight[citation needed], which he likened to the octaves of music, though his law of octaves was ridiculed by his contemporaries. However, while successful for some elements, Newlands' law of octaves failed for two reasons:

- 1. It was not valid for elements that had atomic masses higher than Ca.
- 2. When further elements were discovered, such as the noble gases (He, Ne, Ar), they could not be accommodated in his table.

Finally, in 1869 the Russian chemistry professor Dmitri Ivanovich Mendeleev and four months later the German Julius Lothar Meyer independently developed the first periodic table, arranging the elements by mass. However, Mendeleev plotted a few elements out of strict mass sequence in order to make a better match to the properties of their neighbors in the table, corrected mistakes in the values of several atomic masses, and predicted the existence and properties of a few new elements in the empty cells of his table. Mendeleev was later vindicated by the discovery of the electronic structure of the elements in the late 19th and early 20th century.

Earlier attempts to list the elements to show the relationships between them (for example by Newlands) had usually involved putting them in order of atomic mass. Mendeleev's key insight in devising the periodic table was to lay out the elements to illustrate recurring ("periodic") chemical properties (even if this meant some of them were not in mass order), and to leave gaps for "missing" elements. Mendeleev used his table to predict the properties of these "missing elements", and many of them were indeed discovered and fit the predictions well.

With the development of theories of atomic structure (for instance by Henry Moseley) it became apparent that Mendeleev had listed the elements in order of increasing atomic number (i.e. the net amount of positive charge on the atomic nucleus). This sequence is nearly identical to that resulting from ascending atomic mass.

In order to illustrate recurring properties, Mendeleev began new rows in his table so that elements with similar properties fell into the same vertical columns ("groups").

With the development of modern quantum mechanical theories of electron configuration within atoms, it became apparent that each horizontal row ("period") in the table corresponded to the filling of a quantum shell of electrons. In Mendeleev's original table, each period was the same length. Modern tables have progressively longer periods further down the table, and group the elements into s-, p-, d- and f-blocks to reflect our understanding of their electron configuration.

In the 1940s Glenn T. Seaborg identified the transuranic lanthanides and the actinides, which may be placed within the table, or below (as shown above). Element 106, seaborgium, is the only element that was named after a then living person.