It is by now well known that the
calculus and its infinite series originated in India across a
thousand year period, starting from the 5^{th} c. Aryabhata.
It was needed for agriculture and overseas trade, the two key sources
of Indian wealth.^{1}
Indian monsoon-driven agriculture requires a good calendar, which
requires good astronomy (hence precise trigonometric values) needed
also for navigation.

Europeans then were backward in
navigation and hence European governments offered large prizes for a
solution to the navigational problem from the 16^{th} to the
18^{th} c. In the 16^{th} c., Jesuits had turned
their Cochin college into a centre for mass translation of Indian
texts (on the 12^{th} c. Toledo model of mass translation of
Arabic texts). The content of these Indian texts started appearing in
Europe in the later 16^{th} c. and early 17^{th} c.
and was used to solve the latitude problem (Gregorian reform) and the
problem of loxodromes (Mercator's chart). There is other
circumstantial evidence, as in the works of Tycho Brahe (“Tychonic
model”, identical to Nilakantha's), Christoph Clavius
(trigonometric values, interpolated version of Indian values),
“Julian” day numbers (ahargana), Kepler (Parameswaran's
observations), Cavalieri, Fermat and Pascal (challenge problem,
including probability), and finally Leibniz (“Leibniz”
series) and Newton (sine series).

However, like Indian arithmetic earlier, Europeans did not understand Indian methods of summing infinite series using “non-Archimedean” arithmetic, and a different philosophy, now called zeroism. They tried to fit it into their religious beliefs about mathematics as “perfect” and error-free.

Newton thought, as in his theory of
fluxions, that this could be done by making time metaphysical^{2}
(“mathematical time which flows equably”). The error
about time was the reason why his physics failed.^{3}
This history has contemporary value. Correcting Newton's mistake in
understanding calculus leads to a reformulation of physics, and, in
particular, the theory of gravitation.^{4}
This also corrects various problems of infinity that arise from the
inadequacy of university calculus, or the Schwartz derivative for
quantum field theory,^{5}
general relativity,^{6}
and electrodynamics,^{7}^{,}
^{8}
as also the Lebesgue integral for probability,^{9}
especially in quantum mechanics.

The other contemporary value is
pedagogical. Calculus with add-on metaphysics makes math very
difficult and was globalised during colonialism. Eliminating that
redundant metaphysics in math makes math easy to teach.^{10}^{,}
^{11}

Professor C. K. Raju holds an M.Sc in math and a PhD from the
Indian Statistical Institute, Kolkata. He taught and researched in
formal math (functional analysis) for several years. He was
responsible for porting applications on the first Indian
supercomputer Param, and that experience led him to abandon formal
math. He has authored several books. In *Cultural Foundations of
Mathematics* (Perason Longman, 2007) he proposed a new philosophy
of math, called zeroism, and compiled evidence for the development of
calculus in India and its transmission to Europe. In *Time: Towards
a Consistent Theory *(Kluwer, 1994) he proposed a new physics,
using functional differential equations. In the *Eleven Pictures of
Time* (Sage, 2003) he proposed a new way to relate science and
religion through time. He has developed and taught decolonised
courses on math, and the history and philosophy of science. His
shorter books include *Is Science Western in Origin?*
(Multiversity 2010), *Ending Academic Imperialism* (Citizens
International, 2011) and *Euclid and Jesus* (Multiversity,
2012). He has wide-ranging interests and is also Vice-President of
the Indian Social Science Academy.

1C.
K. Raju, *Cultural Foundations of Mathematics: the nature of
mathematical proof and the transmission of the calculus from India
to Europe in the 16*^{th} *c. CE*, Pearson
Longman, 2007.

2C.
K. Raju, “Time: What is it that it can be measured”,
*Science
& Education*,
**15**(6)
(2006) pp. 537–551. Draft available from
http://ckraju.net/papers/ckr_pendu_1_paper.pdf.

3C.
K. Raju, *Time: Towards a Consistent Theory*, Kluwer Academic,
Dordrecht, 1994.

4C.
K. Raju, “Retarded
gravitation theory” in: Waldyr Rodrigues Jr, Richard Kerner,
Gentil O. Pires, and Carlos Pinheiro (ed.), *Sixth
International School on Field Theory and Gravitation*,
American Institute of Physics, New York, 2012, pp. 260-276.
http://ckraju.net/papers/retarded_gravitation_theory-rio.pdf.

5C.
K. Raju, “On the Square of *x*^{-n}^{ }”
*J. Phys. A: Math. Gen. ***16** (1983) pp. 3739–53.
Also, “Renormalisation, Extended Particles and Non-Locality.”
*Hadronic J. Suppl. ***1** (1985) pp. 352–70.

6C.
K. Raju, “Distributional matter tensors in relativity”.
In: *Proceedings of the Fifth Marcel Grossman meeting on general
relativity*, D. Blair and M. J. Buckingham (ed), R. Ruffini
(series ed.), World Scientific, Singapore, 1989, pp. 421–23.
arxiv: 0804.1998.

7S.
Raju, and C. K. Raju, “Radiative Damping and Functional
Differential Equations”, *Mod. Phys. Lett. A*, **26 **(35)
(2011) pp. 2627-2638. arxiv:0802.3390.

8For
a non-technical account of the above problems with infinities, see
C. K. Raju, “Functional
differential equations. 3: Radiative damping”, *Physics
Education *(India),
**30**(3),
July-Sep 2014, Article 8.
http://www.physedu.in/uploads/publication/15/263/7.-Functional-differential-equations.pdf.

9C.
K. Raju, “Probability in Ancient India”,
chp. 37 in *Handbook of the Philosophy of
Science*, vol 7. *Philosophy
of Statistics*, ed, Dov M. Gabbay, Paul
Thagard and John Woods. Elsevier, 2011, pp. 1175-1196.
http://www.ckraju.net/papers/Probability-in-Ancient-India.pdf.

10“Teaching
mathematics with a different philosophy. Part 1: Formal mathematics
as biased metaphysics.” *Science and Culture* **77**
(7-8) (2011) pp. 274–279.
http://www.scienceandculture-isna.org/July-aug-2011/03%20C%20K%20Raju.pdf,
arxiv:1312.2099.

11“Teaching
mathematics with a different philosophy. Part 2: Calculus without
limits”, *Science
and Culture* **77
**(7-8) (2011)
pp. 280–85.
http://www.scienceandculture-isna.org/July-aug-2011/04%20C%20K%20Raju2.pdf.
arxiv:1312.2100.