Reminiscences of International Congresses of Mathematicians (ICM): Nice-France

Professor Dr. Hashtroudi was requested and he submitted some of his own reminiscences

of international congresses of mathematicians (ICM) that would be in scope of magazine

readers, in order to publish in the magazine.

The organization of the international congresses of mathematicians that holds in various

countries once every four-year and dates back to two centuries ago. In these congresses,

representatives of universities from various countries and mathematicians who are personally

inclined, take part. Typically few number of eminent mathematicians take part according to

the invitation of the host country. During the World Wars, these congresses did not hold, and

before the World War II, the last congress which was held, was ICM-1935 in Moscow. This

year it will be also held in Moscow.

In each congress, a one-hour lecture is considered for prominent mathematicians that give a

lecture about the general progress of mathematics. The other participants could give a quarter-

lecture and present their new theories, however, possibly discussion about some of these

theories takes a number of congress sessions.

I have taken part in all of the congresses after the war and I have been invited in most of them,

just in Stockholm congress, though I was invited, I could not take part in it, since I was in

Moscow on that time.

To speak about the official talks of congresses is wearisome for magazine readers. Some of

memoirs are about circumstance that has happened in the margin of each congress:

In Nice congress, the international congress of Latin mathematicians, Marchoux was the

honorary president, in closing ceremony, a number of participants' relatives have gone to a

night dancing party. There, one of mathematicians' wife and an artist disputed and finally

brother of mentioned lady and the manager of club had quarreled. A journalist of a newspaper

who had sought for such opportunity, had taken several photos of this incident and it was

anticipated that the next day the happening has been reflected with thousand embellishment

and foliage in a newspaper to become a disgrace for congress. Marchaux asked me to interfere

and somehow quiet it; in Nice according to the policy of tourist attraction, they respect

foreigners and in particular journalists abstain to insert and publish something that makes

them resentment. Marchaux and I met the journalist and convinced him with so deceits and

eventually I could take his camera and blacken all photographic films. Journalist who did

not want to be taken a task by manager of newspaper, complained me but just requested the

compensation of a damaged film roll and the incident was finished here.

In this congress, when Arnaud Denjoy who was rather old in this congress and was one of

great professors in Sorbonne University and was also my professor, wanted to lecture, we

all applauded him but just as he wanted to continue his lecture, a number of youth began

again to applaud and wanted to impede his speech. By the way, some of friends and I tried

to conciliate the meeting and he with a high indignant voice that trembled, ended his lecture.

Indeed, Arnodangoux had worked on some subjects in concerning to modern mathematics

in old age and this had not been at all acceptable for youth. They were illiberal youth who

deemed that the way is closed for old, whereas Élie Cartan argued also the theory of isotropic

spaces in the age of eighty years. By the way, in that meeting, I and some others wanted

to soothe him and declared him that they are young, we were also young and sometimes

naughty. He said with the same indignant tone:” you were at all not so , since youth passes,

but maliciousness remains”.

1Arnaud Denjoy(1884-1974)


Translated by Fariba Elliee

A Memory of Moscow Congress, 1935

Reminiscences of International Congresses of Mathematicians



By Dr. Mohsen Hashtroudi

This congress was the last international congress of mathematicians before the World War
II. One night after finishing the session of differential geometry and topology, the late
Cartan (Élie Cartan) and Schouten (who is now the president of Amsterdam mathematics
center) and Hermann Weyl and a group of researchers in tensor calculus and connection
theory negotiated and discussed. Alleys in Moscow in vicinity of Kremlin almost all lead to
Kremlin, indeed they are centralized. The late Weyl propounded this question that: “is there
a geometrical measure that its all geodesics (the shortest distance, here it should be pointed
out that in all measure spaces, geodesics and straight lines don not coincide with each other,
namely, between two points, there exist a straight line and a shortest curve that are distinct)
are centralized?” That night, after separation of this group Schouten overnight found this
connection that at present in his name in Russia it is known as Schouten connection. Strangely
in western countries this connection is called sometimes as Moscow connection.

The author of this lines determined intimate properties of this connection about 15 years ago
and simultaneously André Lichnerowicz, the professor in Collége de France, proved also
that among point spaces (spaces which are introduced just with point not with a point and a
line nor a point and a plane), the only space that are connected to nonholonomic analytical
mechanics, is the same semi-symmetric Schouten connection. This connection is called semi-
symmetric since torsion of space is determined by a vector just by using main tensor (this
space is obviously is nor a usual space, namely, it has curvature and torsion of space is related
to transportation of the origin of coordinates).

Such as this issue has happened in many congresses that a problem has been posed in a
session of a field or even out of that and an overnight it has been solved by one of mighty
mathematician.


Translated by Fariba Elliee

The Foundation of Modern Mathematics

Part 3

Instances of articles, mathematical problems and the other works of Dr. Hashtroudi



1

In each era, mathematics is the mirror of its civilization. Technical, industrial, scientific and

art progress in any century can be realized in worldview of its mathematics.

The history of evolutions in cultures and modernity of thoughts is simultaneous with the

history of progress in mathematics.

In this century that empirical development in natural sciences and biology and evolution in

observational sciences such as astronomy and cosmology with wave knowledge has made far

scientifical research possible, mathematics as an abstract inductiveand discursive knowledge

has led to where abstract mathematics has been introduced without resorting to the study

of classifications in human sciences and on the other hand evolution of mathematical logic

and modern science semantics has made abstract thought search and research regardless of

statement and words quality and has founded the statement of other abstract sciences.

In this brief article, short mention to the quality of mathematical thought evolution will be

accomplished in particular in the 20th century so that readers would get informed more or less

perfectly in this issue.

The basis foundation of abstract mathematics begins with the set theory. This theory that

had been considered more or less in the 18th century, occupied thoughts of mathematicians

at the beginning of the 20th century and made clear coordination and integration of logic and

mathematics. The basic of this theory, later with other generalities that are always required in

mathematics, founded eventually the discursive school in mathematics.

Antinomies that arose in the set theory, was considered by logicians and the coordination

between logic and mathematics (the set theory and categories) led to the building of

semantics.exclude

In order to clarify the issue according to the historical development, we talk about appearance

of the set theory and the existence of antinomies so that we lead eventually to the situation

and establishment of abstract modern mathematics.

***

Category and union of elements in a category is always arbitrarily possible, but the set that is

obtained in this way, is an indeterminate and more or less an ambiguous set. With a particular

definition that includes all members of the set and excludes non members, it can be defined

and determined (Note that here an inclusive and exclusive logical definition is not necessary,

any definition that is containing the result, suffices and such definitions are equivalent).

Clearly, sets can be defined that the own set is apparently also a member of itself. For

instance, if we form the set of all Persian names and we name this set a Persian name, it will

seem so that the set itself is a member of the set. More logical antinomies in the set theory

begins with this point. Resolving such problems that are now so normal, made difficulties at

the beginning for mathematicians that domination them seemed abstained. Later, it became

clear that such antinomies are not confined to the area of mathematics and it occurs in the area

of logic too. For instance, some cases of these antinomies in the area of logic are mentioned

here:

First. The singular sentence antinomy – This antinomy has been known from ancient

and it is quoted from Aristotle. Ghiyath al-Din Jamshid Kashani says that Kashanians are

mendacious. Obviously, this sentence makes a cycle because this quotation has been said by

a Kashanian thus it is included by the sentence itself and that sentence is not true, namely

Kashanians are truthful. And since the narrator is from Kashan (Kashanian), the sentence will

be true and the cycle becomes evident.

Should note that this sentence actually is not a singular sentence and it has been formed

by two sentences: a – Ghiyath al-Din Jamshid Kashani is from Kashan; b – He claims that

Kashanians are mendacious. Hence, the antinomy appears and makes a cycle, since lie

does not form a group, because lie of lie is equivalent to true but not lie, if Ghiyath al-Din

Jamshid Kashani said that Kashanians are truthful, no antinomy arises, because true of true is

equivalent to true and it forms a group.

Second. The Antinomy of Sentences based on Definition – For every number, it can

be mentioned either mathematical definition or another non mathematical definition that

2

determines that number. For instance, the number (a) is defined such that „the smallest

number that its definition requires less than ten words.“. Obviously, the numbers that are

defined by less than ten words, form a set (finite or infinite) that among them, by comparing,

we determine their smallest and the number (a) is specified. For instance, the number π

is defined such that „the ratio of a circle's circumference to its diameter“. This statement

(or sentence) has 9 words, namely, it is a sentence that has less than ten words, thus the

number „Pi“ is such as these numbers. As well, the number 9 (the number of planets in the

solar system), since the sentence „the number of planets in the solar system“ has less than ten

words, it is such as thsese sentences. If it is contented with these two numbers, the number (a)

will be π that is the smallest between two numbers 9 and π. However, if other definitions are

also mentioned for these such numbers, the number (a) can be always determined. Now, we

see that the number (a) itself has been defined by the statement „the smallest number that its

definition requires less than ten words.“ that has eleven words and here antinomy happens,

because the number (a) should be defined by a statement (or a sentence) that has less than

ten words, namely, according to the result of the above definition, the number (a) exists and

according to the sentence form, this number is not contained in the set of numbers which are

determined by this defintion. With a little attention, it can be found that the set of numbers

which definition needs less than ten words, is a sequence of numbers (finite or infinite,

in terms of numbers) and the defintion of the number (a) is indeed such that „the smallest

number of this set“ and in this case, there would be no antinomy, because the last sentence has

less than ten words.

In the set theory, these antinomies had been already seen and their dependence on the logical

area became later clear. The base and the fundamental of the mathematical logic is on the

basis of sentences and theorems and category theory.

If among members of a set (finite or infinite), there are relations such that the result of using

these relations for two members of that set gives another member of the set, that set is called

structu For instance, if we consider the set of integers and the addition operation, since the

sum of two integers is also an integer number, the set of integers with addition opertaion is

called a structure. Without mention to the generalities of structure in mathematics, we content

ourselves with this instance and equivalence of this structure to the structure of integers with

multiplication operation, because the set of integers with multiplication operation forms also

a structure. (In addition operation of the first structure, the number zero is as identity element,

because adding it to every number keeps preserved that number, but in multiplication of the

second structure, the identity element is the number one, because multiplying it by every

number keeps preserved that number). It is possible that two relations are defined between

elements of a set (like the set of integers with multiplication and addition operations), in

this case this such structure is called ring. The equivalence between rings and structures

with two multiplication and addition operations is always obvious. The equivalent structure

to the structure with addition is called module and the equivalent structure to the structure

with multiplication is called group. Thus, ring is indeed a structure both a module and a

group. Field of numbers is a set that the result of the four basic arithmetic operations over

its elements keeps preserved that set (except divisionon zero of module which becomes

exception). For instance, the set of rationals forms a field of numbers, because the result of

the four basic operations on rationals is a rational number. The set of irrationals is also a field

of numbers. If an irrational which integer and decimal parts are integers, is called an integer

irrational number, it is observed that the set of integer irrationals is not a field of numbers, but

rather is just a ring. So, the main classification mathematical structures are:

1- Modules that is also called an additive group and as well group that means multiplicative

group which is called in short group. If in such structure: a . b = b . a, the group is called

abelian group. The equivalence between module and group is obvious, namely, these two

structures are indeed equivalent.

2- Ring is a structure that is either module and also group, namely, the three operations:

addition, subtraction and multiplication are possible in it.

3- Field of numbers that the four basic arithmetic operations are possible in it.

Structures are divided into two fundamental parts: algebraic structures (what are so far

mentioned, are algebraic structures) and logical structures. For every logical structure, there

is a particular algebraic computations that is called correspondence structure. For instance,

Boolean algebra is the fundamental of computations of logical Aristotelian structure (i.e.

binary logic). The importance of this structure is so much in modern mathematics and the

fundamental of electronical machines or automatic systems is based on it.

***

In the history of mathematics, a is well-known, geometry has a distinguished situation. The

evolution of scientific ideas in this area is the oldest and the most acquainted history of

mathematics. Axiomatic geometry that argues about shapes with particular methods, is the

oldest geometrical system that has been ever known (Euclid's elements known as Euclid's

axioms). By applying the principles of algebraic computations in geometry, Descartes has

been known as the founder of analytic geometry (Khayyam's studies and inquiries, without

applying system of algebraic equations is indeed the same analytic geometrical method that

Descartes has laters used). And this method has been finally led to affine and projective

geomtries. Laters, with Poncelet's studies and inquiries, these geometries became

independently and anew the method of analytic geometry was founded much more firmly and

logically than before as axoimatic method. Extensive efforts that have been done in this

method, generalized gradually to other mathematical desiplines and made the basic of other

branches in mathematics to the axiomatic method. And this issue is also researched and

inquired now by mathematicians. By founding the axiomatic method in mathematics and

renewed independence of geometry from algebra, algebraists proceeded anew to establish a

branch called algebraic geometry that is now researched and inquired. Applying the principles

of computations in structures and in particular logical structures in definitions and theorems

in geometry helps suficiently to make clear the basic of geometry. For instance, in 3-

dimensional Euclidean geometry, we denote points (the set of points) with capital Latin letters

such that A, B, C, D, … are the different members of the point set. As well, we denote lines

with small Latin letters like a, b, c and surfaces with Greek letters like α, β, γ, … Now, we

define the classification ring of these factors: the addition operation between two factors of

the universal set S (A, B, C, …, a, b, c, ..., α, β, γ, …) is defined as follows: between two

factors of the members, we define a relation that we show with the sign +, such that the sum

of two factors of members is another factors of members with the least dimension. The set S

contains the subset: S (A, B, C, …), S (a, b, c, …), S (α, β, γ, …) such that every subset has a

dimension which is shown by the index of the subset, namely, the dimension of A, B, …. is

zero, the dimension of a, b, … one and of α, β, γ, … two. The sum of two factors of the

members in S is the other factor of the universal set S such that both given factors lie on it and

this factor has a minimal dimension. For instance, if [P] and [Q] are two indeterminant factors

of S (we denote unknown factors with the capital Latin letters), then [P] + [Q] = [R] is

defined so that R is chosen from the subsets of points, lines or surfaces so that P and Q lie on

it and the index of R (the index of correspondence subset that [R] belongs to it) has a minimal

amount. For example, if we sum a factor like a (line) with a factor like B (point), then we

have: a + B = γ in which the index of a, B and γ equal respectively to one, zero and two,

namely, the sum of a line and a point is a surface which passes through them. Obviously, if

the point B lies on a line a, the sum of them is the same line a, because in this case, the point

lies on the line and all of points of the line a lie also on the line a, so the factor with minimal

dimension which contains both of them, is the same line a. In this case, a + A = a (on the

contrary to usual algebraic addition, the sum of two factors is one of those factors without one

of factors is zero). In order to complete these operations, we need also another definition. We

denote the universal set S (in terms of content) with U (i.e. the whole of geometrical space

which contains all of points, lines and surfaces) and the null set which has no member, with N

(which is like zero in arithmetic); Adding these two concepts generalizes additive and

multiplicative operations (which are later defined). In this case, we observe that the sum of

two lines, a + b, if they are not parallel or intersecting, equals to U, namely, a + b = U. And if

these two lines are parallel or intersecting (i.e. they are in the same surface), the sum of them

is the surface which contains them, namely, a + b = α.

The multiplication of two factors in the universal set S is defined as: the multiplication

of two unknown factors [P] and [Q] as the members of the set S is another factor of S

which is common in both factors [P] and [Q] and has maximum dimension. We denote the

multiplicative operation with the sign × and define as [P] × [Q] = [R]. The index of R is the

greatest index which has the mentioned property in the definition of multiplication in the

subsets. For instance, the multiplication of two intersecting lines is their common point: a × b

= C, and the multiplication of two skew lines is the null set N: a × b = N.

Now, we consider the solution of equation [P] × [X] = N in which P is a point and X is a

factor of shapes (point, line or surface) and N is the null factor or set. Obviously, one of

solution is the same null set N, because the multiplication of each factor in the null factor

will be the null set, the other solution is the same point P, because a geometrical shape

which contains the point P and has the minimum dimension, is the same point P, namely,

the solutions of above equation are: X = [P] and X = N. We consider if the factors of the left

side in the above equation belong to P, then we will see that the point P has no other member

except the point P itself and the null factor, namely in other words, the part and whole of a

point are equal to each other and it is the same Euclidean definition of a point.

The above instance is an example from algebraic geometry which is a subject of mathematical

logic and is necessary for comparison, development and extension of geometrical definitions.

***

The fundamental structures of modern mathematics are logical, algebraic and topological

structures that are requirements in the basic of all mathematical issues. Mathematical analysis

is a particular discipline that applies different methods in real and complex functions (it

means functions of real and complex variable). In the late 19th and at the beginning of the 20th

century, some functions were considered that are not differentiable in any points of interval

continuity and furthermore, there are continous functions that their graph covers completely

inside a square. The concepts of derivation and dimension were needed new inquiries and in

topology, the theory of dimension and measure were defined anewly.

The existence of functions with real variables that all rational points are their disconnected

points and all of these points are also limit (accumulation) points, made to review in basic

of mathematical analysis. In other hand, analysing of harmonic functions and integrals, in

one side, and the convergence theory of Fourier series, in other side, opened a new issue in

mathematics that eventually led to axiomatize potential functions.

***

The applied mathematics, in particular mathematical and theoretical physics, made to appear

especial functions that admit just particular values and thus from theory of Dirac function

to distribution theory, there was just one step to go. To apply the calculation axioms of

probability in applied and theoretical problems led to appear information theory and after that

difficulty or complexity theory that is even now researched and inquired. The appearance of

particular functions in physic such as Dirac function that was mentioned, led mathematicians

in other hand to the problem of eigenvalues or proper values that are necessarily applied in

statistical and Quantum physics and eventually ergodic theory to solve differential equations

brought into existence a general and exact discipline in theoretical physic that classified most

problems under a method.

***

In applied problems and difficulties that arise in emperical sciences, empirical formula and

rules are mostly required and until now mentioned empirical issues were frequently inquired

by convergent extension with appropriate series and validity of formula. To apply method and

principles of dificulties and complexity theory, appropriate functions are before determined

for extension of empirical formulas by analytical criteria and thus applied or empirical

formula is obtained with a high validity.

Applied mathematics and calculus, for instance in numerical solutions of algebraic systems

or differential equations, have developed greatly by electronic computing machines or simple

electrical machines and have evolved much more with respect to saving time. In applied

technical problems and in particular in cosmic problems, determination of ranges of orbital

position and stability and movings have developed considerably by using exact computational

methods known as Lyapunov method. The asymptotic (Poincaré) integration method has

attained maturity and encommpassed much more problems.

Geoemtric interpretation of differential equations (or differential systems) predetermines

solutions of equations in long distances by using global geometry and it made possible to

change movings in distant times and far distances by using topology.

Mathematical analysis has attained considerable development under coordination of different

methods that were mentioned and many unsolved problems have now been in the area of

elementary mathematical knowledge.

The concept of finite and infinite groups and its applications in analysis and geometry has

made coordinated interpretation for various problems in one side and in other side, by transfer

data from a close area to wider, it makes solvable many problems that were not verifiable

in analysis area, in geometry. Hence, the various solutions of Schrödinger equation are

determined by using rotation groups of 3- and 4-dimensional spaces.

***

To apply the concept of connection in infinitesimal geometry and generalize the concept to

existence of general groups and correspond the space of parameters in groups to the space

of geometry of group has solved many problems of differential geometry and mechanics

with a new interpretation so that it was not possible before these concepts. Some particular

differential equations are solved without using quadratic forms in their general solutions.

Combination of eigenvalues with the concepts of finite groups in Quantum and statistical

physics and the problems relating to electrons and the other particles of material to face

with differential equations bases the theory of spinors in Euclidean space that is applied

considerably in relativity theory to solve problems.

***

3

4

The above introductions makes possible to found operator theory in physics and mechanics

and the combination of this concept with the concept of mathematical transformations

introduces the concepts such as homomorphism and isomorphism for general mathematical

and physical problems that can be also applied with a little generalization in problems of

human sciences (such as problems in transportations, sociology, psychology). Gradually,

biology introduces and sets forth its specific problems in mathematics and the abstract

mathematical organizations are applied in this area as well.

***

The history of science has made clear since long that attempt and endeavour for solving some

problems sets forth some other problems that make to introduce some other new sciences,

fields and branches. The 20th century is not also excluded from this general rule. In solving

problems and difficulties of human sciences, though success and evolutions have been

obtained, the other problems have been introduced that no step has been yet taken to solve

them or if a few steps have been gone ahead, it is not yet clear how problem can be solved.

For instance in physics, will gravity like electromagnetics become particle and will quantum

of gravity be discoverd? It is a mystery that

has not been yet expressed any opinion. In spite of all, the 20th century is one of the centuries

that human activities have been efficient and undoubtedly, the continuation of researches that

have been begun in this century, will make generally to change technologies.

As it has been mentioned in introduction that mathematics in an era is the mirror of its

civilization, mathematics in the 20th century is the mirror of development and modernization

of thoughts and ideas. The astonishing result of this development and modernization that are

just now more or less conceivable, is openning gates of unknown skies, whether the sky of

this material universe or whether sky of thought universe.

1The first part of this article, by Dr. Mohsen Hashtroudi, has been firstly published in Yekan magazine, No. 1
(January 19??) and then all of article in Yekan magazine (March 19??).

2Ghiyath al-Din Jamshid Kashani (1380-1429) Persian astronomer and mathematician

3Aleksandr Mikhailovich Lyapunov (1857-1918): Russian mathematician, physicist and mechanician.

4Erwin Schrödinger (1887- 1961) Austrian physicist



Translated by Fariba Elliee

Hashtroudi in words of excellence teacher

Hossein Ghayour

Mr. Hossein Ghayour, associate professor in Teachers Training University, with due attention

to his proficiency and conversancy in geometry, in particular in solving its problems, was

Dr. Mohsen Hashtroudi's full confirmed and cared. The late professor, whether in speech or

lectures and whether in his writings about some of problems, mentioned Hossein Ghayour

as an initiator of the most beautiful solutions of these problems. Hence, Mr. Ghayour was

requested to send memoirs which he had from Prof. Hashtroudi, to publish in this collection.

He wrote his first own memoir.

The first visit with Professor Hashtroudi

In 19?? when I studied in Daneshsara Aali, the National Teacher Training College, in the first

visit with Professor Hashtroudi, the following problem which I myself had propounded and

due to unfamiliarity with advanced mathematics I attempted vainly to solve it, I put up it for

discussion with him.

The problem was this:

Draw a line which creates three chords with equal length in three circles.

The professor, without writing anything on paper, after some minutes walking and thinking,

siad: “the solution of this problem is related to drawing of common tangent to two parabolas

and so it is not solvable by geometrical drawing.”

At the same night of that day, after reading, studying and caring in the problem, I realized

correctness of his words and was surprised his quickness of apprehension and mental acuity.

Laters when I was honoured to become one of his students, I found out frequently that this

answer has been not at all accidental and or precedent.

Most his students who are now professors and teachers, have many memoirs such as this issue

from that great noble man.

For that the statement of above memoir is not attributed to exaggerartion or student's extreme

affection to the late teacher, young students and those who deal with mathematics, think about

this problem and prove how its solution leads to drawing a common tangent to two parabolas.



Translated by Fariba Elliee

Hashtroudi in words of an immemorial friend

In rememberance of a dear friend and an illustrious scientist

By Ahmad Birashk

1

It was 1930. October forreached and a new semester began. A number of youths who had

finished and graduated from high school and were paasionate to become teacher, had joined to

Dar al-Moalemin Aali, the National Teachers' Training College.

Dar al-Moalemin Aali where became later Daneshsara Aali and is now University of

Teachers' Training, began its second academic year in that year. This academic system was a

developed school where had been working to train school teachers since 1918 and Abolhasan

Foroughi undertook to manage it for some years. In 1930, it was set up in one of branching

alley from Amiriyeh Street, in the parish called Sabzikar Takht Zomorod, in a building where

became later the seat of Maarefat high school. There were no trace of gaudiness, glory, luxe,

many employees and servants in it. It had even no head and director. Its headmaster was

undertaken by Hasan Farzani who was from the first alumni of Law College in 1923 and its

registrar was Mohammad Taghi Kerman. A number Iranian teachers such as Gholamhossein

Rahnama, Abbas Eghbal, Dr. Rezazadeh Shafagh, Badia Zaman Forouzanfar and three

French teachers, Dr. Loui Lang, Dr. André and Dr. Arma, taught there.

With all simplicity and perhaps for its simplicity, it was wish Kaaba for those who intended to

become teacher.

***

In that year, 20 people (and apparently exactly 23 people) among who has graduated

with high school diploma in mathematics, had enrolled, among them whom I remember:

Abdolhossein Aghakhani, Ahmad Ahsani, Abolghasem Ahmadvazir, Hosseinali

Akbarnia, Mostafa Bahrami, Mohammad Rokni Qajar, Mohammad Zayandehroud,

Mohammad Taghi Sajadian, Bagher Shahnai, Hossein Gharib, Ali Akbar Gorkani,

Hossein Majzoub, Ali Asghar Mousavi Gharavi, Ahmad Mehran, Taghi Hourfar and

myself.

Among us, Ahmad Mehran was witted, improvisative and he has already been in Europe. He

was sent with despatched students to Europe (to France). I do not know how was happened

that Mehran had returned to Tehran and had been among scholars of mathematics.

***

The semester and courses began.

In the first or second week, I do not remember exactly, a young joined our group, according to

Saadi “spokesman, wise, sweet-spokeman and articulate”.

2

After the graduation from high school, he had studied medicine for some years and then had

joined mathematics and had gone to Europe to study. I do not know why he had also returned

to Iran. He had noble and lovely face, grace words and sweet-spoken, demure and at the

same time magnanimous behavior and above all, predominance which he showed and had in

courses, made him shortly the luminous in circle of friends.

He was Mohsen Hashtroudi.

In that year, three of my friends and I studied and worked with each other and we mostly read,

studied and discussed in our houses and when we got tired, we entertained ourselves with

chess. Someday, I invited Hashtroudi to join us. He said: “how is chess useful? Man must

play with stars in the sky.” It was a sample of his mentality.

***

In 1932, he garduated from Dar al-Moalemin and in order to continue his study, he started

on a journey to Europe. Four or five years later, he returned with PhD degree from Sorbonne

University and imparted in an institute that according to English it was his “almamater” and

as we say, it was his spiritual mother.

I speak nothing about his scientifical works, since others have said.

In 1941 due to my insistence, he and a number of academic teachers, who were Daneshsara

Aali alumni (such as: Dr. Kamal Jenab, Dr. Mohammad Monajemi, Dr. Taghi

Hourfar, ...) accepted my invitation to membership of Daneshsara Aali Alumni Society. On

that time, Daneshsara Aali Alumni Society was adjoint and aid for the Culture Ministry away

from political scuffle and the society was confered in many affairs and contributed in many

projects and was respected by the Culture Ministry.

Again due to my insistence, Dr. Mohsen Hashtroudi who had become the president of the

society, became also the head of high school teaching department. About 1951, he undertook

the chancellorship of Tabriz University. For some time, he became the head of science faculty

in Tehran University. But none of these is discussed by me. I speak about a noble man, about

a person whose vacancy will not soon fill in our society that is unfortunately with this respect

poor. I speak about a person who had always remained demure and submissive despite of his

eminency in science and society (he was university teacher and indeed professor, namely, he

had one of the beloved position in developed countries). He was professor in mathematics,

but he had also profound knowledge in literature, he was philosopher namely he knew well

philosophy, he wrote well and composed also well poems. He was dexterous in other sciences

too, he was a comprehensive man and he supported his friends and indeed he was their

scientific support. If they asked him anything that he could do, he did not stint to do that.

In the last years of his life, the mourning of his older daughter's death made him recluse. A

severe heart rending grief lessened his energy and eventually the light which could remain

still luminous for years and made our needy society light, kept silent.

His rememberance would survive with his friends, his students and in hearts of those who

knew him until they live.

In my opinion, he can be a great pattern for youths who are much more fervent to home. He

did not stop even for an instant to learn. He was one of those who learned until the end of life

and taught. He was active and had dominant over knowledge of his time.

May we learned him.

Peace be to his departed spirit and May he be ever remembered.

1 Ahmad Birashk (1907-2002):Author of a comparative calendar of the Iranian, Muslim lunar, and Christian eras
for three thousand years: 1260 B.H.-2000 A.H./639 B.C.-2621 A.D.

Ahmad Birashk founded Hadaf Educational Group (Goruh Farhangi Hadaf) a pioneering private educational
complex in 1949-50 with a number of well-known high school teachers of mathematics and natural sciences,
including Ahmad Anwari, Taghi Hourfar, Ali Motemadden and Ahmad Reza Gholi-zada. The main objective
of the Group was to offer high quality education from elementary to high school, comparable to that of

American preparatory schools.

2Abu-Mohammad Moslih al-Din bin Abdollah Shirazi, Saadi Shiraz was one of major Persian poets of the
medieval period.



Translated by Fariba Elliee